COMSOL Multiphysics^{®} Version 4.4  Release Highlights
Released November 27, 2013
The most powerful multiphysics software just got more powerful. COMSOL Multiphysics version 4.4 brings an advanced yet intuitive new COMSOL Desktop interface, a completely new tool for setting up multiphysics models, more powerful solvers, textbased search for variables, important fixes, and enhancements in user experience. View this video for a complete summary of the major highlights, or click on one of the below menus to investigate in detail all the enhancements that arrive with COMSOL Multiphysics® version 4.4.
COMSOL Multiphysics 4.4 Video Highlights
Duration: 08:45
Summary of Major News
COMSOL Multiphysics^{®}
 COMSOL Desktop^{®} with ribbon
 COMSOL Desktop^{®} run on Windows® platforms include the new ribbon design to allow for a streamlined workflow. Quickly find the operations you need for setting up a model and running simulations.
 New Multiphysics Node
A completely new Multiphysics node in the model tree for setting up multiphysics models
 Combine physics interfaces to define your own multiphysics
 Choose from builtin multiphysics couplings
 View each physics interface as a separate node in the tree
 OneClick Select
 A new hoverandclick selection method speeds up the modeling process.
 TextBased Search for Variables
 Autocomplete search allows you to quickly find variables to use in results in the Windows version.
 Geometry Subsequences
 Geometry subsequences allows for userdefined geometric primitives
 If/Else Statements
 If/else statements can be used in the model tree for conditional geometry creation.
 TimeUnits in Solvers
 The studies and solvers now handle timeunits.
 NASTRAN® Mesh File Export
 Export a 2D and 3D mesh to the NASTRAN® mesh file format.
Electrical
 AC/DC Module
 A material library with 165 nonlinear magnetic materials has been included in the AC/DC Module.
 RF Module
 Simulate components with ports on interior boundaries.
 Wave Optics Module
 The Wave Optics Module now includes scattering with a Gaussian background field and a new Laser Heating interface.
 Semiconductor Module
 Heterojunction and impact ionization are just two of many updates to the Semiconductor Module.
Mechanical
 Heat Transfer Module
 New tools are available for fast computations of radiation in participating media, the thermoelectric effect, and heating in biological tissue.
 Structural Mechanics Module
 The Structural Mechanics Module gives you easy access to rotordynamic forces, features a new fast penalty method for contact, and has updated solidshell couplings.
 Fatigue Module
 New fatigue evaluation methods for analyzing nonlinear materials including thermal fatigue.
 Multibody Dynamics Module
 Functionality is expanded with three new joint types and friction in joints.
 Acoustics Module
 Run aeroacoustics simulations based on the Linearized Euler equations.
Fluid
 CFD Module
 Model the surface roughness of walls in turbulent flow and get dramatically increased conservation of mass and energy for laminar flow.
 New Product: Mixer Module
 The Mixer Module allows you to simulate stirred mixers and reactors.
Multipurpose
 Optimization Module
 The Optimization Module has an additional gradientfree method (BOBYQA) for dimensional optimization and an additional gradientbased method (MMA) for topology optimization.
 Particle Tracing Module
 Particlefield and fluidparticle interactions are now ably simulated with a new efficient method.
Interfacing
 LiveLink™ for SOLIDWORKS^{®}
 You can now synchronize userdefined selections.
 LiveLink™ for Inventor^{®}
 Synchronize material selections and material names between COMSOL and Inventor^{®}.
 ECAD Import Module
 Import of the ODB++ format enables multiphysics simulations for one of the most popular formats for Printed Circuit Board designs.
All trademarks are the property of their respective owners. See COMSOL Trademarks page.
Previous COMSOL Multiphysics^{®} Versions
New COMSOL Desktop^{®}
Table of Contents:
Modeling with the new COMSOL Desktop
Duration: 06:08
Introducing the COMSOL^{®} Ribbon
Streamlined Workflow
When run on Windows®, the COMSOL Desktop environment has an updated look and feel, and includes a ribbon with tabs that reflect the main operations and workflow for setting up a model and running simulations.
The ribbon Home tab has buttons for the most common operations for making changes to a model and for running simulations: changing model parameters for a parameterized geometry, reviewing material properties and physics, building the mesh, running a study, and visualizing simulation results.
There are also standard tabs for each of the main steps in the modeling process. These are ordered from left to right according to the workflow: Definitions, Geometry, Physics, Mesh, Study, and Results.
The ribbon gives quick access to available commands and complements the Model Tree. The functionality accessed from the ribbon is also accessible from contextual menus by rightclicking nodes in the Model Tree. Certain operations are only available from the ribbon, such as selecting which COMSOL Desktop window to display. On Macintosh® and Linux® platforms, this functionality is available in toolbars which replace the ribbon. There are also several operations that are only available from the Model Tree, such as reordering and disabling nodes.
A new Quick Access Toolbar at the top of the COMSOL Desktop contains a set of commands that are independent of the ribbon tab that is currently displayed. You can customize the Quick Access Toolbar: you can add most commands available in the File menu, commands for undoing and redoing recent actions, for copying, pasting, duplicating, and deleting nodes in the model tree. You can also choose to position the Quick Access Toolbar above or below the ribbon.
New COMSOL Desktop^{®} Highlights
Transparent Control of Your Multiphysics Simulations
COMSOL improves your workflow for modeling multiphysics applications that include thermal stress and electromagnetic heating. A dedicated Multiphysics node is made available in the Model Tree to allow you to control the couplings between the individual physics and heat transfer. When adding a Multiphysics interface such as Joule Heating directly from the Model Wizard, your Model Tree will contain nodes for Electric Currents and Heat Transfer in Solids, and a Multiphysics node with a subnode for the Electromagnetic Heat Source. Alternatively, if you are already using the Electric Currents interface, adding the Heat Transfer in Solids interface will introduce the Multiphysics node to the Model Tree and allow you to select and define the appropriate electromagnetic heating simulation, such as Joule heating, by adding appropriate subnodes.
The following multiphysics phenomena can be modeled using Multiphysics nodes:
 Joule Heating
 Induction Heating (requires the AC/DC Module)
 Microwave Heating (requires the RF Module)
 Laser Heating (requires the Wave Optics Module)
 Thermal Stress (requires the Structural Mechanics or MEMS Module)
 Joule Heating and Thermal Expansion (requires the Structural Mechanics or MEMS Module)
 Thermoelectric Effect (requires the Heat Transfer Module)
Years of working with multiphysics simulations has led COMSOL to develop this style of workflow. Using Multiphysics nodes allows you to deal with your physics either separately, or as coupled phenomena, and you can activate and deactivate these couplings on the fly. This facilitates your workflow through providing:
 Transparent control: View, edit and control all participating physics, as well as the couplings between them, as separate physics interfaces
 Natural workflow: Build multiphysics models of increasing complexity by starting from a single physics model, and then adding further singlephysics interfaces
 Greater extendability: Extend existing multiphysics couplings by including further singlephysics interfaces. This versatility allows you to choose which physics to couple and solve together, so that different simulations can be performed on the same model without having to set up a new one
 The new Multiphysics node in the Model Builder for a Joule Heating simulation. Selecting the Joule Heating interface from the Model navigator sets up the Electric Currents, Heat Transfer in Solids, and Multiphysics nodes. The Electromagnetic Heat Source subnode is where the coupling is controlled. The coupling can be activated and deactivated by selecting and deselecting the Active feature.
OneClick Selections
Selections of geometry objects, domains, boundaries, edges, and points are easierjust hover over a boundary for highlighting it and click, using the left mouse button to select. The previous method of leftclicking to highlight and rightclicking to confirm is still available as an option in Preferences. To select interior boundaries, you can use the mouse scroll wheel or the keyboard up and down arrows.
 When setting boundary conditions, hovering over a surface highlights it in red; already selected surfaces are highlighted in blue.
TextBased Search of Variables with AutoCompletion
A new autocomplete search function allows you to quickly find postprocessing quantities. You can now access postprocessing quantities in three ways: browse the full list of quantities, use textbased search, or type the postprocessing variable name.
Model Components
A Model .mph file is now considered to consist of one or more Model Components. Accordingly, the Model Tree nodes previously named Model 1, Model 2, Model 3, etc. are now called Component 1, Component 2, Component 3, etc. Variable prefixes for new models have changed accordingly: from mod1, mod2, mod3, etc. to comp1, comp2, comp3, etc.
All trademarks are the property of their respective owners. See COMSOL Trademarks page.
COMSOL Multiphysics^{®}
Table of Contents:
Geometry
Work Planes: Vertex Offset, Positioning and Rotation, New Types of Work Planes
For some work plane types you can now control the offset in the normal direction by specifying a vertex. You can precisely control the location of the origin and the directions of the local coordinate axes. By default, the geometry objects of a Work Plane are now united before being embedded into 3D. This is more efficient and less error prone than uniting the objects directly in 3D. To avoid this default action, clear the Unite objects check box.
There are two new work plane types:
 Edge parallel: This work plane type is parallel to a planar curved edge
 Transformed: This work plane type uses an existing work plane as a starting point and then translates and rotates it, resulting in a new work plane.
Accessing Geometry and Mesh Operations from the Ribbon
Geometry and mesh features can now be added by clicking a button or menu item in the Geometry and Mesh tab of the Ribbon. This is available as an alternative to using the context menu by rightclicking in the Model Builder. If you have created a selection of geometry objects or entities before you click a button or choose a menu item, the added feature uses that selection as an input selection (if it is an appropriate selection for that feature).
For geometry operations, the contents of the input selection lists are now always visible. The Build Preceding State button has been replaced with the Active button. If the selection is inactive, clicking this button builds the preceding state and makes it possible to modify the selection by clicking in the Graphics window.
Geometry Subsequences
In the geometry sequence, a geometry subsequence call corresponds to a subroutine call in a programming language. In other words, a geometry subsequence is a geometry sequence with a set of numerical input arguments and a set of geometry objects as output. You can view a geometry subsequence as a userdefined geometry primitive. In the geometry sequence, you can call the subsequence repeatedly, or rather create instances of it, using a unique set of input argument values for each call. Calls can also be nested.
In 3D, there is an easy way to translate and rotate the result of a subsequence call so that it gets the desired position and orientation. You can specify that a work plane in the subsequence should match a work plane defined by some preceding geometry feature. The selections defined in the subsequence are also available in the calling geometry sequence, and also available for use in mesh and physics.
Conditional If/Else Statements
In the Programming submenu of the Geometry node context menu, you can add If, Else If, and Else features for conditional control over geometry object creation. To insert such features without the need to build the feature preceding the desired location, you can use the submenus Add Before and Add After of a geometry feature's context menu. A valid If statement has the structure:
If branch 1 Else If branch 2 ... Else branch n End If
where the Else If and Else features are optional. In the tree, the feature names are automatically indented. The Condition edit field in the If and Else If features can contain parameters from Global Definitions, for example a+b<=3. The condition is considered as true if it evaluates to a nonzero value (logical statements that are true are evaluated to 1). When you build the End If feature or a following feature, only one of the branches will be built, the other branches are treated as if they were disabled. If statements can also be nested.
Cumulative Selections
A cumulative selection is a selection in the geometry sequence that is a union of contributions from several selections. Cumulative selections are especially useful for constructing a selection that has different definitions in different branches of an If statement. There is no node in the tree that corresponds to the cumulative selection.
For a geometry feature that creates a selection, you can let it contribute to an existing cumulative selection by choosing the cumulative selection in the Contribute to list. To let it contribute to a new cumulative selection, click the New button. To remove a contribution to a cumulative selection, select None in the Contribute to list. When a selection contributes to a cumulative selection, the original selection does not appear in lists where you choose among selections  it is replaced with the cumulative selection.
Split Pairs in Connected Components
By default, the Form Assembly feature creates one Pair node for each pair of objects that have touching boundaries. Such a Pair node can have a disconnected set of source boundaries or destination boundaries. Sometimes you want to split such pairs into several Pair nodes, each having connected sets of source/destination boundaries. To this end, there is now a check box Split disconnected pairs.
Mesh
NASTRAN® Mesh File Export
It is now possible to export a 2D or 3D mesh to a NASTRAN® mesh file in the formats: .nas
, .bdf
, .dat
, .nastran
. You can select which elements to export (domain and/or boundary elements), whether property id numbers according to geometric entity information should be exported, and whether second order element information should be exported.
Mesh Import Based on Mesh Type and Mesh Element Number
The Logical Expression feature for partitioning an imported mesh now supports the use of parameters and the variables meshtype
and meshelement
. For example, this means that if you write meshelement
>0
&& meshelement
<=1000
in the Expression field the first 1000 elements of the imported mesh file will form a separate domain.
Updates to the Native Mesh (.mphtxt) Format
The .mphtxt
file format has been made easier to use for the purpose of transferring externally generated mesh data into COMSOL. This was accomplished by eliminating the need for the up/down and parameter fields. A new section in the documentation describes the different aspects of importing external mesh data to COMSOL via the .mphtxt
format. Furthermore, you can now select which elements will be exported into a mesh file (.mphbin
, .mphtxt
, or .nas
) and whether geometric entity information should be exported. The documentation section can be found in the Reference Manual, under Meshing, in the section on Importing and Exporting Meshes.
Swept Mesh Update: New Method for Projecting Source Mesh Points onto Destination Surface
For swept meshes, a new method has been added for transferring the surface mesh from the source to the destination. The new method projects each source point onto the destination and is automatically used when a rigid body transformation method cannot be used and when the sweep has the following properties:
 The source or destination contains several faces (or a virtual composite face)
 The source or destination is nonplanar
 The sweeping distance is short (one element layer)
You can select the method manually in the Swept node settings window by choosing Project source onto destination under Sweep Method > Destination mesh generation.
Studies and Solvers
Updated Parametric Sweep and Parametric Solver Interfaces
Any scalar input to your model can be treated as a parameter that can be solved for over a range of values. COMSOL provides two different algorithms for solving for a range of parameters, the Parametric Sweep algorithm, and the Parametric Solver algorithm. The user interface for these has been updated and additional options have been added to the Parametric Solver.
Parametric Sweep interface: This functionality can be combined with almost any Study Step (Stationary, TimeDependent, Eigenvalue) as well as a Solver Sequence containing multiple Study Steps. The parametric sweep can solve for any Global Parameter in the model, including those which affect the geometry and the mesh. The functionality is used when trying out different dimensions, performing a mesh refinement study, solving for different loadcases, and so on.
Parametric Solver interface: This functionality is available for Stationary analysis steps. The Global Parameters which are being swept with the parametric solver can only affect the loads, boundary conditions, and material properties. Dimensional and mesh changes are not supported, but the parametric solver provides additional functionality for solving nonlinear problems. When solving a nonlinear stationary problem, the choice of initial condition can strongly affect the convergence rate towards the solution, or even the possibility of finding a solution at all. The parametric solver, by default, uses the previous solutions as initial conditions for the next stationary solution step. If the solver is unable to find a solution for a specified value in the range of parameters, the solver will backtrack and take a smaller step in the range of the parameters specified. This algorithm is also known as a continuation method, and the user interface gives you control over how the solver will step through the range of parameters. Either a tangent or constant predictor can now be used. If the solver is unable to find a solution for a requested parameter step, the solver will now either terminate, or continue to the next requested parameter value.
The Parametric Sweep and the Parametric Solver interfaces can be combined within a single study. There is a computational advantage to using the parametric solver, and the software will automatically call the parametric solver algorithm when possible, even if you are using the Parametric Sweep interface. The Parametric Sweep interface can also be used on a cluster system, when using a Floating Network License, to distribute the computational load.
Time Units in Studies and Results
You can now change the unit for the time (t) variable in a Study. These settings will propagate to Results and be used as the new default. The Time unit setting is placed first in a Time Dependent study.
This setting determines the unit for input in the study and solver. For example, the Times: edit field is interpreted in hours (h) for the example above. Internally to the solver, the unit for the time variable is seconds (s).
The default unit in the Time setting for Plots is the same as the unit set for the study.
Modeling Tools
Mass Properties
An option for Mass Properties is now available under Component Definitions. The feature takes a selection and a density expression as input, and automatically defines variables for volume, mass, center of mass, and moment of inertia. Typing material.rho
in the Density expression edit field causes the density values to be taken from the Materials node.
Summation Operator
A new summation operator makes it easy to compute the sum of an indexed expression. The syntax is: sum(expr,k,a,b)
which computes the sum of expr
as the integer valued index k
runs from a
to b
.
 The new summation operator used to construct a sawtooth wave from a Fourier series with 10000 terms.
New Faster Client/Server Architecture
Version 4.4 features a completely new client/server architecture that minimizes communication overhead between a COMSOL Client and a COMSOL Server. This leads to significantly better performance, particularly when the COMSOL Client (typically the COMSOL Desktop) and the COMSOL Server is running on different computers, but also for connections with LiveLink for MATLAB and LiveLink for Excel.
All trademarks are the property of their respective owners. See COMSOL Trademarks page.
Fluid
Table of Contents:
General Fluid Flow Highlights
Permeability Tensor for the Brinkman Equations
For porous media flow, the Brinkman equations extend the wellknown Darcy’s law. New in version 4.4 is support for an anisotropic permeability tensor. Different domains can have different anisotropic materials and the tensor components can even vary spatially. This capability is available in the following products:
 Batteries and Fuel Cells Module
 CFD Module
 Chemical Reaction Engineering Module
 Corrosion Module
 Electrochemistry Module
 Electrodeposition Module
 Microfluidics Module
 Subsurface Flow Module
Point and Line Mass Sources for Fluid Flow and Mass Transport
A point source can be used to simulate a source distributed over a very small volume. While it can be applied to points in 3D or on the symmetry axis in axisymmetric models, its actual effect is distributed throughout the close vicinity of the point. The size of the distribution depends on the mesh and strength of the source  a finer mesh spreads the source over a smaller region but results in a more extreme pressure value. A line source in 3D and 2D axisymmetric models represents a source emanating from a tube with a very small crosssectional area. Line sources can be added to lines in 3D and the symmetry axis in 2D axisymmetric models, or to points in 2D, for which they represent the cross section of the tube of very small area.
Point and line mass sources for fluid flow are included as contributions to the continuity equation. This functionality has been added to the following physics interfaces for fluid flow:
 SinglePhase Flow
 Brinkman Equations
 Free and Porous Media Flow
 Reacting Flow in Porous Media, Diluted Species (requires the Batteries & Fuel Cells Module, CFD Module, or Chemical Reaction Engineering Module)
 TwoPhase Flow (requires the CFD Module or the Microfluidics Module)
 Rotating Machinery, Fluid Flow (requires the CFD Module or the Mixer Module)
 FluidStructure Interaction (requires the Structural Mechanics Module or the MEMS Module)
 TwoPhase Flow, Moving Mesh (requires the Microfluidics Module)
Point and line mass sources for mass transport are included as contributions to the mass transport equations in the form of concentration values. This functionality has been added to the following physics interfaces for mass transport:
 Transport of Diluted Species
 NernstPlanck Equations (requires the Chemical Reaction Engineering Module)
 Solute Transport (requires the Subsurface Flow Module)
 Species Transport in Porous Media
 Reacting Flow in Porous Media, Diluted Species
 Tertiary Current Distribution, NernstPlanck (requires one of: the Batteries & Fuel Cells, Electrochemistry, Electrodeposition, or Corrosion Modules)
 Corrosion, Tertiary NernstPlanck (requires one of: the Batteries & Fuel Cells, Electrochemistry, Electrodeposition, or Corrosion Modules)
 Electrodeposition, Tertiary NernstPlanck (requires one of: the Batteries & Fuel Cells, Electrochemistry, Electrodeposition, or Corrosion Modules)
These new features are available not only in the CFD Module, but also in several other modules:
 Batteries and Fuel Cells Module
 Mixer Module
 Chemical Reaction Engineering Module
 Corrosion Module
 Electrochemistry Module
 Electrodeposition Module
 Microfluidics Module
 Pipe Flow Module
 Subsurface Flow Module
Drag Model for NonSpherical Particles
In addition to the previously available drag models, SchillerNaumann, HadamardRybczynski, and Gidaspow, there is now a new HaiderLevenspiel drag model for nonspherical particles. This new drag model is available for the following physics interfaces:
 Mixture Model (requires the CFD Module)
 EulerEuler Model (requires the CFD Module)
 Particle Tracing for Fluid Flow (requires the Particle Tracing Module)
The settings are somewhat different for each physics interface. The picture below shows the settings window in the EulerEuler Model. The model requires the sphericity, , which is a measure of how spherical a particle is. For a spherical particle , while nonspherical particles have . Nonspherical particles typically result in higher drag than spherical particles.
 View screenshot »
 Fluid flow around the tubes in a shellandtube heat exchanger.
New Outlet Boundary Condition
The Outlet boundary condition for fluid flow has been revised for improved mass conservation as well as faster and more robust convergence. The new Outlet feature has only one Pressure option, which corresponds to the Normal Stress option of earlier versions. The settings window for the new Pressure option is shown below. In addition to an edit field for the pressure, p0, there are two new checkboxes: Normal flow and Suppress backflow.
 Normal flow prescribes a zero tangential velocity at the outlet. This can be expected if the outlet represents a straight pipe or channel. However, it is not selected by default since the flow can be disturbed upstream of the outlet, potentially altering the solution significantly.
 Suppress backflow reduces the tendency for fluid to enter the domain from the outside. It does not completely prevent backflow, and in the case that backflow occurs, this option locally decreases the specified pressure. Controlling backflow is important when combining fluid flow with other transport equations, such as mass and heat transport. If the flow reverses, the outlet boundary condition for the transport equations is no longer valid; this can lead to convergence problems or nonphysical solutions. The Suppress backflow option is therefore selected by default.
The Outlet feature has been revised for the new version in the following physics interfaces:
 SinglePhase Flow
 Brinkman Equations
 Free and Porous Media Flow
 TwoPhase Flow
 LevelSet
 PhaseField
 NonIsothermal Flow and Conjugate Heat Transfer
 Reacting Flow
 Reacting Flow in Porous Media
 Diluted Species
 Concentrated Species
 Rotating Machinery
 SinglePhase Flow
 NonIsothermal Flow (requires the Mixer Module)
 Reacting Flow (requires the Mixer Module)
 TwoPhase Flow, Moving Mesh (requires the Microfluidics Module)
 Slip Flow (requires the Microfluidics Module)
 FluidStructure Interaction (requires the Structural Mechanics Module or the MEMS Module)
The change applies to laminar flow, Stokes flow, and turbulent flow when applicable. The Outlet boundary condition from previous versions still exists, but has been excluded from the physics context menu. Models created in previous versions retain the old Outlet feature, but adding a new Outlet feature gives them the new functionality.
CFD Module
Wall Roughness for Turbulent Flow
For modeling surface roughness of walls in turbulent flow, there are now two roughness models available: Sand Roughness and Generic Roughness. The Wall roughness feature modifies the turbulence wall functions and is available for the kepsilon and komega turbulence models in the CFD Module. The Sand Roughness model is commonly used in engineering applications and introduces a single parameter for the Equivalent Sand Roughness Height. The Generic Roughness model is more general and has, in addition to the Roughness Height, a Roughness Parameter which can be used to model other types of roughness. The default value for the Roughness Parameter corresponds to that for Sand Roughness.
Wall functions for rough walls have been implemented for the following physics interfaces:
 SinglePhase Flow,
 Turbulent Flow, kepsilon
 Turbulent Flow, komega
 SinglePhase Flow, Rotating Machinery
 Turbulent Flow, kepsilon
 Turbulent Flow, komega
 Bubbly Flow, Turbulent Bubbly Flow
 Mixture Model, Turbulent Flow
 Turbulent TwoPhase Flow, Level Set
 Turbulent TwoPhase Flow, Phase Field
 FluidStructure Interaction interface with turbulence model selected
Mixer Module
Model Rotating Machinery with Fluid Flow
COMSOL introduces the Mixer Module, which is an addon to the CFD Module, and allows you to analyze stirred mixers and reactors. With this product comes two Mixer Applications specific for the modeling of standard flatbottom and dishbottom mixers with a variety of impeller types. The Mixer Module is ideal for simulating mixer and impeller designs as well as the concentration, velocity, and temperature profiles in mixers from a variety of industrial processes such as the manufacturing of pharmaceuticals, food, and consumer products. It also provides results on a number of quantities specific to mixing, such as mixing efficiency, power draw, and the impeller pumping number.
 The new Mixer Module allows you to model mixers and stirredvessels for laminar, turbulent, nonisothermal, and nonNewtonian flow with and without considering free surfaces.
The Frozen Rotor Feature
The Mixer Module comes with a Frozen Rotor feature that saves you computational time and resources. It simulates rotating flow by modeling the system's topology as being frozen through adding centrifugal and Coriolis forces to the rotating domains, and solving for the stationary NavierStokes equations. Using this feature provides reasonably accurate solutions for mixers without baffles, pipes, or other geometric entities whose positions need to be modeled relative to the rotating machinery. It can also be used to reduce the computational resources required to solve a fully timedependent rotating system. The solution reached with the frozen rotor approach can also be used as the initial guess for the timedependent solution, where the full rotation of the rotor is simulated, to reach a pseudo steadystate much faster than if you had started with a stationary fluid.
Physics Interfaces for the Mixer Module
Simulations performed with the Mixer Module can use sliding mesh technology between a domain that encompasses the impeller, and a surrounding domain for the area of the mixer reaching out to the wall. Physics interfaces are then available in the Mixer Module to simulate laminar and turbulent flow, incompressible and weakly compressible flow, and nonNewtonian flow. The Rotating Machinery, Turbulent Flow interfaces support the kepsilon model, the komega model, and the Low Reynolds number kepsilon model. You can use the kepsilon model for standard turbulent flow within mixers as it provides a good tradeoff between accuracy and computational resources. The Low Reynolds number kepsilon model is more accurate, but more computationallyintensive; likewise, the komega model delivers more accurate results but is less robust than the kepsilon model.
The Mixer Module also contains multiphysics interfaces for a number of coupled phenomena. Among these is nonisothermal flow, where temperature gradients contribute to the momentum equations, for both laminar flow and turbulent flow. The Mixer Module also contains a physics interface for reacting flow where variations in composition and density, due to chemical reactions, also affect the flow field in vessels containing rotating machinery.
 Nonisothermal flow in a mixer is also influenced by the heating arising from the pipes in this mixer, as well as the cooling effects of losing heat through the walls.
Considering Free Surfaces in Mixers
Moving mesh technology is used by the Mixer Module to simulate free surfaces. A specialized domain is introduced where the fluidfluidsolid interface is free to translate up and down the walls and rotor surfaces. You can specify contact angles between the walls and the fluids as well as surface tension forces in a specialized boundary condition. A library of surface tension coefficients between a variety of liquids helps specify the fluidfluid interface between the fluid being mixed and the atmosphere above it. This includes surface tension coefficients between water and a number of fluids, such as benzene, hexane, and olive oil, as well surface tension coefficients between air and some fluids like water, acetone, and ethanol.
Microfluidics Module
New Model: Microchannel Dispersion Optimization
A new Model Library example has been added which optimizes the shape of a curved microchannel to improve the performance of a chemical species detector downstream of the curve. The shape of the channel is defined as a set of Bezier curves which depend on five optimization parameters. The model then computes the values of these parameters to minimize the difference in time required for fluid to reach the detector by moving along the inner and outer walls of the curved channel. The model uses the new gradient free optimization solver: Bound Optimization by Quadratic approximation (BOBYQA), a trust region gradient free optimization solver, written by Professor M.J.D Powell (Cambridge).
 A neutral species band approaches a curve in a microchannel, driven by electroosmotic flow (top). If the shape of the channel is not optimized, the band disperses as it moves through the curved section (middle). Using the Optimization Module, the model obtains an optimized geometry, allowing the band to remain intact (bottom).
Molecular Flow Module
New Model: Monte Carlo Reconstruction of Number Density
It is now possible to model molecular flows using a particlebased approach with the Particle Tracing Module. A new example model has been added that compares the computed number density in an Sbend geometry using a particlebased approach and the Free Molecular Flow interface. While the results are in good agreement, the particlebased approach introduces statistical noise and takes more than 100 times longer to solve. This shows the advantage that using the angular coefficient method in the Molecular Flow Module has over a Monte Carlo based approach.
All trademarks are the property of their respective owners. See COMSOL Trademarks page.
Mechanical
Table of Contents:
Heat Transfer Module
New Methods for Radiation in Participating Media
Two new fast and memory efficient methods are available for Radiation in Participating Media:
 Rosseland approximation
 P1 approximation
These are approximate methods and are basically not as accurate or as general as the discrete ordinate method, available since earlier versions of the software. Yet they solve applications simulating radiation in participating media much faster. The Rosseland approximation is only available with the full Heat Transfer in Solids or Fluids interfaces and is not available in the radiationonly interface for participating media. Both methods are also available for 2D axisymmetric geometries. For comparison, the verification model Radiative Heat Transfer in Finite Cylindrical Media solves in a couple of seconds, with the P1 approximation method, as opposed to more than two hours, with the discrete ordinate method.
The Thermoelectric Effect Multiphysics Node
Materials that display the thermoelectric effect are able to convert temperature differences to electric voltages as the heat flux contains charge carriers. Alternatively, applying a voltage to these materials results in a temperature gradient across the material. Devices made from these materials are often used as thermoelectric coolers for electronic cooling or portable refrigerators, while thermoelectric energy harvesting devices are also starting to become popular.
While Joule heating (resistive heating) is an irreversible phenomena, the thermoelectric effect is in principle reversible. Historically, the thermoelectric effect is known under three different names, reflecting its discovery in experiments by Seebeck, Peltier, and Thomson. The Seebeck effect is the conversion of temperature differences into electricity, the Peltier effect is the conversion of electricity to temperature differences, while the Thomson effect is heat produced by the product of current density and temperature gradients. These three effects are thermodynamically related.
The new Thermoelectric Effect multiphysics interface is available in the Heat Transfer Module and is a multiphysics combination of the Electric Currents and Heat Transfer in Solids interfaces. Choosing the interface from the Model Wizard will subsequently add a dedicated Multiphysics node in the Model Builder to allow you to control the couplings between the individual physics. Alternatively, you can start with the singlephysics, such as the Electric Currents interface, and then add the Heat Transfer in Solids interface later on, which will automatically also add the Multiphysics node. As with all other interfaces within COMSOL, the Thermoelectric Effect multiphysics interface can be coupled to any other physics interface, such as the Solid Mechanics interface for example. Two thermoelectric materials have been added to the Material Library: Bismuth Telluride and Lead Telluride.
Thermoelectric Leg Model
This model of a thermoelectric leg shows Peltier cooling. It is a verification model and demonstrates how to use the new Thermoelectric Effect multiphysics interface and reproduces results available in literature.
New Methods and Variables for Heat and Energy Balances
The mathematical formulations for heat transport computations have been enhanced. This has resulted in revised variables for heat and energy balances. In addition, heat fluxes on boundaries can now be computed with increased accuracy.
Variables for Boundary Fluxes
For boundary fluxes, the following variables now provide the accurate value of fluxes when they are available:
 ndflux: Normal convective heat flux
 nteflux: Normal total energy flux
 ntflux: Normal total heat flux
These boundary flux variables are available in all physics interfaces for Heat Transfer and all multiphysics interfaces that include Heat Transfer. The new method is active by default, but can be switched off by clearing the Compute boundary fluxes checkbox in the Discretization section of the physics interfaces for heat transfer. To view the Discretization section, enable it from the Show menu of the Model Builder toolbar. If this checkbox is not selected, then the computations of fluxes on boundaries are performed by extrapolating values from within neighboring finite elements, which was the method used in COMSOL 4.3b and prior versions.
Variables for Global Heat and Energy Balances
Energy balance is now easier and faster to check through the introduction of new global variables. Evaluating these scalar quantities replaces the need for integrating all the contributions to the energy balance over domains, boundaries, edges, and points.
The following global variables have been added to Heat Transfer in Solids, Heat Transfer in Fluids, Heat Transfer in Porous Media, Heat Transfer with Phase Change, and Heat Transfer in Biological Tissue interfaces:
 dEiInt: Total accumulated heat power
 dEi0Int: Total accumulated energy power
 ntfluxInt: Total net heat power
 ntefluxInt: Total net energy power
 QInt: Total heat source
 WInt: Total work source
 WnsInt: Total fluid losses
The following global variables have been added to many of the heat transfer boundary conditions:
 Tave: Weighted average temperature
 ntfluxInt: Total net heat power
 ntefluxInt: Total net energy power
 ntfluxInt_u: Total net heat power, upside
 ntefluxInt_u: Total net energy power, upside
 ntfluxInt_d: Total net heat power, downside
 ntefluxInt_d: Total net energy power, downside
Cooling and Solidification of Metal Model
This example shows a continuous casting process with the Heat Transfer with Phase Change and SurfacetoAmbient radiation interfaces. Liquid metal is poured into a mold of uniform cross section. The outside of the mold is cooled and the metal solidifies as it flows through it. When the metal leaves the mold, it is completely solidified on the outside, but is still liquid inside. The metal will continue to cool and eventually solidify completely, at which point it can be cut into sections. This model does not include computing the flow field of the liquid metal; it is assumed that the velocity of the metal is constant throughout. The phase transition from molten to solid state is modeled via a temperature dependent specific heat. Techniques for reaching convergence and selecting a proper mesh are addressed for this highly nonlinear model.
Heat Transfer in Biological Tissue with Damage Integral Analysis
Tissue necrosis (permanent damage or death of living tissue) occurs when one of two things happen, either too much thermal energy has been absorbed or a critical temperature has been exceeded (typically boiling). This analysis is utilized in medical treatment and surgical methods based on tissue heating. Thermal energy absorption is often modeled by so called damage integrals. The Biological Tissue interface in the Heat Transfer Module includes two forms of Damage integral: Temperature threshold and Energy absorption.
 A tumor ablation simulation showing the fraction of necrotic tissue as a Slice plot and at three different locations vs. elapsed time.
The Temperature threshold form is a simple integrated inequality of how long tissue has been above a certain temperature. Userdefined parameters include Damage temperature, Damage time, and Necrosis temperature. In this case, tissue necrosis is assumed to occur due to the following two mechanisms:
 When the tissue temperature exceeds a given damage temperature for more than a certain time period
 Instantly after the tissue temperature exceeds the necrosis temperature
The Energy absorption form uses an Arrhenius type expression to directly estimate absorbed energy. Userdefined parameters include Frequency factor and Activation energy for the integrated Arrhenius equation.
The material properties of the damaged tissue is modified to take into account the influence of tissue damage. The conductivity and the effective heat capacity (density multiplied by heat capacity) are modified with respect to the volume fraction of necrotic tissue. Six new generic biomaterials are available in the material library shipped with the Heat Transfer Module: Bone, Fat, Liver, Muscle, Prostate, and Skin.
The new physics interface for heat transfer in biological tissue with damage integrals is available for Heat Transfer in Solids as well as for any multiphysics combination where this physics interface participates, including the following:
 Joule Heating
 Induction Heating
 Microwave Heating
 Laser Heating
 Thermal Stress
 Joule Heating and Thermal Expansion
 Thermoelectric Effect
Two models, Microwave Cancer Therapy and Tumor Ablation, that are available in the Model Library of the Heat Transfer Module have been updated with the new damage integral analysis.
Line and Point Heat Sources on Axis of Symmetry
For 2D axisymmetric models, you can now define line and point heat sources on the axis of symmetry. The previous point heat source has been replaced by a line heat source applicable at points and now provides a Total Line Power option. The Line Heat Source on Axis is applicable on the symmetry axis only. The Line Heat Source feature is applicable at points and represents a line revolved about the axis of symmetry. This feature is not applicable on the symmetry axis. The Point Heat Source on Axis feature is a point source that is applicable only at points on the symmetry axis. In 2D, the Point Heat Source has been replaced by a Line Heat Source applicable at points and now provides a Total Line Power option through the thickness and multiple points – representing lines – selection.
Heat Transfer in Porous Media
Coordinate Systems for Anisotropic Porous Media
For Heat Transfer in Porous Media, it is now possible to choose any coordinate system from the Definitions node. This is useful when defining heat transfer in anisotropic materials where the thermal conductivity varies with the direction.
You can now easily define multiple porous materials using material selections, and then link the fluid material property to another material from the domain material list. This avoids multiple heat transfer in porous media feature definitions.
Fan, Interior Fan, Grille, Screen, and Vacuum Pump Boundary Conditions
The boundary conditions Fan, Interior Fan, Grille, Screen, and Vacuum Pump are now available in both the CFD Module and the Heat Transfer Module.
New Models for Thermal Performance of Windows, following Norm ISO 100772:2012
These benchmarks reproduce the ten test cases from the ISO 100772:2012 standard related to thermal performance of windows. Thermal performance is evaluated through thermal conductance and transmittance of the shutter and results are validated against published data.
 The temperature plot of a thermal performance benchmark model with results validated against published data.
DiskStack Heat Sink Model
This model of a diskstack heat sink shows the cooling effects of a diskstack heat sink on an electronic component. The heat sink consists of several thin aluminum disks stacked around a central hollow column. Such a configuration allows for cooling of large surfaces of aluminum fins by air at ambient temperature.
Thermal Effects of the Sun as an External Heat Radiation Source
This model, representing a beach umbrella and two boxes, illustrates how thermal effects of the sun can be modeled as an external heat radiation source. The simulation is run from 10am to 4pm. During this part of the day, the umbrella protects the boxes from the sun irradiation. This model uses the external radiative heat source feature with solar position option. The sun's position and shadow effects are automatically updated during the simulation.
Structural Mechanics Module
Fast Contact with the Penalty Method
A new approximate penalty contact method is available that is more robust and converges faster than the standard Augmented Lagrangian formulation. It avoids solving for the degrees of freedom associated with the contact pressure, and negates the need for a special segregated solver. While expediting the solving process, the penalty formulation does not converge towards a zero gap distance between contact surfaces, and the formulation that estimates contact pressure is not as precise as the heavyduty Augmented Lagrangian formulation. The contact pressure and friction force formulations are independent of each other. The desired contact method can be selected in the new Contact Pressure Method and Tangential Force Method sections of the Contact settings window.
The penalty factor needs to be set by the user. For the normal pressure it is also possible to define an offset. This means that the gap overclosure can be reduced if a good estimate for the contact pressure can be given. For the Friction feature, it is possible to inherit the penalty factor from the parent in the case where the normal contact pressure is also using the penalty method.
 Analysis of a tube connection with prestressed bolts and mechanical contact. The tube is subjected to an external bending moment. The stress in the bolts as a function of the applied external load is calculated.
New Loads and Forces: Gravity, Centrifugal, SpinSoftening, Coriolis, and Euler
Mass forces and loads such as gravity, centrifugal forces, Coriolis forces, and Euler forces can now be added with the aid of two new options, for Gravity and Rotating Frames. This makes it easy to define loads that act on all objects having mass, i.e. domains with mass density, point masses, added mass, rigid connectors with mass, etc. The forces and loads are added from the domain level, even though they may be automatically applied to features at boundaries, edges, and points. Load cases are supported.
The Rotating Frame feature includes all types of fictitious forces occurring in a rotating system. By default, Centrifugal force and Spinsoftening are included.
The rotordynamics tutorial called Rotating Blade, available in the Model Library, has been updated and now uses the builtin Rotating Frame loads rather than the expressions for Body Load.
Since Added Mass is sometimes used to describe load effects which are not true structural masses, sometimes the contribution from Added Mass is not wanted. The option to include or exclude the contribution is controlled from a check box in a new section called Frame Acceleration Forces.
New Multiphysics Node for Thermal Stress
COMSOL has introduced Multiphysics nodes to facilitate the modeling of multiphysics applications, such as thermal stresses. These nodes provide better control over modeling and allow you to increase your workflow complexity by adding further singlephysics interfaces. Adding the Thermal Stress interface from the Model Builder will add the Solid Mechanics and Heat Transfer in Solids interfaces along with the Multiphysics node, which is tailormade for simulating the physics couplings involved in modeling thermal stress. Alternatively, if you have already set up the Solid Mechanics interface and performed some modeling, you can then add the Heat Transfer in Solids interface and the Multiphysics node will automatically be added to the Model Builder.
The Joule Heating and Thermal Expansion interface also comes with a new Multiphysics node. Adding this interface directly from the Model Wizard will add the Electric Currents, Heat Transfer in Solids, and Solid Mechanics interfaces to the Model Builder, together with the Multiphysics node. You can also add the contributing singlephysics interfaces, sequentially, to increase the model's complexity. Once the second physics interface has been added, the Multiphysics node will show up in the Model Builder. Its possibilities for defining multiphysics couplings will increase once the third physics interface is added. Various simulations can then be run on the model, including variations in the multiphysics couplings, as you can activate and deactivate these couplings on the fly through the Multiphysics node.
Viscoelasticity Updates
A new Viscoelasticity subnode is available for the Linear Elastic Materials subnodes. This allows for the seamless extension of linear elastic models with viscoelastic properties. The combination of the Linear Elastic Material and Viscoelasticity interfaces replaces the Linear Viscoelastic Material feature available in earlier versions. With the new formulation, there is no longer a need for using the viscoelastic initialization step in the Solver node.
Two new viscoelastic material models are available: the Standard Linear Solid model and the KelvinVoigt model. This is in addition to the Generalized Maxwell Model, which was available in previous versions.
The Static Stiffness property allows you to choose between Longterm or Instantaneous stiffness in Stationary analyses.
The Thermal Effects section now includes two new formulations to prescribe the timeshift for thermorheologically simple solids: Arrhenius and User defined shifts. This is in addition to the alreadyavailable WilliamsLandelFerry (WLF) shift function.
SolidShellBeam Connections
A suite of solidshellbeam connections makes it much easier to set up models that mix solids, shells, and beams. The connections are available as several different options:
3D
 Connect a shell edge to a solid boundary
 Connect a shell boundary to a solid boundary (also known as "cladding")
2D
 Connect a beam point to a solid boundary
 Connect a beam edge to a solid boundary
Overview of the Connections
In all cases, the connection is created by adding two features, one in each physics interface.
Connecting Solid with Shell
In the Shell Connection settings in the Solid Mechanics interface, the following settings are available:
The connected entity has two selectors:
 Shell edge or Shell boundary
 The Solid Connection feature in the Shell interface which supplies the other half of the connection
The connected area is used for an edgetoboundary connection, and determines how much of the solid boundary the shell is connected to. The default case is Shell Thickness, in which case half the shell thickness up and down from the shell midsurface is connected. If Selected boundaries is chosen, then the entire selection in the Shell connection feature is connected. In the last case (Distance from shellmidsurface), the user has full control over how far the connection acts from the shell edge.
When Shell boundary is selected, Boundary type is used for a boundarytoboundary connection, and defines the type of connection. For Shared, the shell boundary is a face of the solid, for Parallel it is not.
When Boundary type is Parallel, there are three different options for how the distance between the shell and the solid should be computed: based on shell properties, based on geometrical distance between the boundaries, and based on a user defined expression.
Connecting Shell with Solid
In the Solid Connection settings in the Shell interface there is only one setting: Connection type. This setting is only available for the edgetoboundary option. The default Softened connection is very accurate, but has a few drawbacks: it adds degrees of freedom on the shell edge, and may become singular if the mesh on the solid is very coarse. The Simplified connection is similar to a local rigid connector. It constrains the solid to the shell, and will introduce local stress disturbances. The 2D case is analogous, but with beams instead of shells.
New Rigid Domain Feature
A new feature called Rigid Domain has been added to the Solid Mechanics interface, replacing the Rigid Domain subnode under Rigid Connector. The Rigid Domain is available for the Solid Mechanics and Multibody Dynamics interfaces.This feature has several advantages when compared to the previouslyavailable Rigid Domain subnode including:
 It is a proper material model and overrides other material models such as Linear Elastic
 It has its own degrees of freedom and it is possible to initialize them with Initial Values
 It has its own specialized constraints and loads boundary conditions in the form of subnodes
 It is very easy to define a location using the centroid of selected surfaces, edges, or points to initialize, prescribe, or apply a load
 It supports structural load boundary conditions such as gravity, rotating frame, body load, and spring foundation
 It automatically eliminates nonapplicable structural constraint boundary conditions
 It creates automatic continuity with the neighboring material models
 It has its own global postprocessing variables as well as domain postprocessing variables, similar to other material models
 It is possible to plot results inside of Rigid Domains
Timoshenko Beams
The formulation of the beam element has been changed completely, so that incorporation of shear flexibility (socalled Timoshenko theory) may be taken into account. This is in addition to the previouslyavailable EulerBernoulli beams. Timoshenko beams are used when the crosssectional dimensions are large relative to the beam length, but still thin enough for a beam approximation to be used. In the case of Timoshenko theory, shear correction factors must be given in addition to the other cross section data..
A note regarding backwards compatibility: If an old model is opened, the EulerBernoulli formulation is used. The Beam Formulation selection is still shown but cannot be changed from EulerBernoulli. If Advanced Physics Options are shown, then the new section Backward Compatibility is shown. If the check box Use pre 4.4 formulation is cleared, then the new formulation is used. Doing so enables the use of Timoshenko beams, but you must manually handle solver settings like segregation and scaling. This legacy option does not support beams mixed with solids or shells if the same degree of freedom names were used in both physics interfaces.
 View screenshot »
 The Shear correction factor settings for Timoshenko beams.
Nonlinear Structural Materials Module and Geomechanics Module
Plasticity Hardening Data from Material
There is now a From material selection option for the Hardening function in the Plasticity node. This makes it easier to build your own material libraries with elastoplastic material properties.
Dissipated Plastic Energy Density
Dissipated plastic energy can now be computed for Creep, Plasticity, and Viscoelasticity, which are all available as subfeatures for a Linear Elastic Material. However, doing this adds one extra degree of freedom to the solving process, which requires extra computational resources. You can control whether you want this computed or not, through enabling and disabling it in the Energy Dissipation section in the Linear Elastic Material and Hyperelastic Material setting windows. This is only displayed if the Show Advanced Physics Options is enabled.
Fatigue Module
New Fatigue Models and Thermal Fatigue
The Fatigue Module has added functionality for thermal fatigue through two families of fatigue models. One predicts fatigue based on the inelastic strains, and the other based on the dissipated energy. Both models are also suitable for lowcycle fatigue prediction in ductile materials.
EnergyBased Fatigue Models
The Energybased fatigue option provides fatigue models that are based on energy dissipation. Two models are available:
 Morrow
 Darveaux
The Morrow model uses pointwise fatigue life evaluation, while the Darveaux model computes fatigue life based on volumeaveraged energy dissipation. The Darveaux model is only available at the domain level, while the Morrow model is available on all dimensional levels. The volume average of the Darveaux model can be evaluated in two ways: for the Individual domains option, each individual geometric domain is evaluated separately; while for the Entire selection option, the volume average is evaluated over all geometric domains simultaneously. Since the Darveaux model separates the total life into crack initiation and crack propagation, it is possible to evaluate the number of cycles necessary for each event.
 Life prediction in solder material based on the dissipated energy volume average according to the Darveaux model.
In both fatigue models, different types of energy change can be evaluated. The predefined ones are:
 Creep dissipation density
 Plastic dissipation density
 Total dissipation density
 User defined
All of the first three options require that the evaluated material be modeled with nonlinear materials, and that calculation of energy dissipation be enabled using the Advanced Physics Options. The User defined option allows you to specify a custom energy density variable and use it in one of the above models. This can be done either by combining existing energy variables, or by defining new energy variables, based on equations using one of the Mathematics interfaces for PDEs and ODEs.
CoffinManson Type StrainBased Fatigue Models
The family of strainbased models has been extended with a model based on the CoffinManson relation. This model is frequently used for lowcycle fatigue evaluation.
The model has been modified so that different types of inelastic strains can be used in the CoffinManson relation. The following strain types are available:
 Effective creep strain
 Effective plastic strain
 User defined
The User defined option allows you to evaluate all the other strains defined in any of the structural interfaces or to evaluate a customized strain expression based on equations using one of the Mathematics interfaces for PDEs and ODEs. This allows you to evaluate different shear and normal strain components and even different creep contributions, such as secondary creep, when simulating fatigue. The original CoffinManson relation is obtained by selecting Effective plastic strain as the Inelastic strain option.
New Tutorial Model: Thermal Fatigue in a Solder Joint of a Surface Mount Resistor
A new tutorial shows a surface mount resistor subjected to accelerated thermal cycling. A cycled temperature change of 50°C takes place over a 2minute period and is followed by a dwell of 3 minutes. Thermal stresses are introduced by the differences in thermal expansion in different parts of the assembly. The solder joint that connects the resistor to the printed circuit board is the weakest link in the assembly. It responds nonlinearly to changes in both temperature and time, and is modeled using the Garofalo creep material model. In order to assure structural integrity of the component, a fatigue analysis is made based on creep strain and dissipated energy. Several cycles of heating and cooling are simulated followed by a fatigue study.
 View screenshot »
 Life prediction in solder material based on the dissipated energy volume average according to the Darveaux model.
Multibody Dynamics Module
Three New Joint types: Fixed Joint, Distance Joint, and Universal Joint
Three additional joint types have been added to the Multibody Dynamics interface: Fixed Joint, Distance Joint, and Universal Joint. They can be found under More Joints in the Joints menu. These new joint types differ from the ones already available in that they are more abstract and they do not have any subfeatures. A Fixed Joint welds two parts together. A Distance Joint is similar to a rigid link with ball joints at the ends, but the distance may change since it is possible to set a variable the Extension edit field. A Universal Joint is also known as a Cardan Joint.
Friction on Joints
It is now possible to add friction to the Prismatic, Hinge, Cylindrical, Screw, Planar, and Ball joint types. Including friction in your multibody dynamics models can only be done in timedependent studies.
Acoustics Module
Aeroacoustics with the Linearized Euler Equations
Ideally, aeroacoustic simulations would involve solving the fully compressible NavierStokes equations in the time domain. The acoustic pressure waves would then form a subset of the fluid solution. This approach is often impractical for realworld applications due to the required computational time and memory resources. Instead, for solving many practical engineering problems, a decoupled twostep approach is used: first solve for the fluid flow, then the acoustic perturbations of the flow.
The new Linearized Euler physics interfaces compute the acoustic variations to pressure, velocity, and density for a given background meanflow. They solve for the linearized Euler equations, including the energy equation, with the assumptions that the background flow is an ideal gas (or is wellapproximated by an ideal gas) and that there are no thermal or viscous losses. The Linearized Euler physics interfaces are available for time domain, frequency domain, and eigenfrequency studies.
Application examples include analyzing the propagation of noise from jet engines, modeling the attenuation properties of mufflers in the presence of nonisothermal flow, and the study of gas flow meters. These are all situations where a gas background flow influences the propagation of acoustic waves in the fluid.
Below is an example of a validation model taken from a journal paper (A. Agarwal, P. J. Morris, and R. Mani, AIAA 42, pp. 80, 2009), which is also a benchmark problem from the fourth computational aeroacoustics (CAA) workshop (Proceedings of the 4th CAA Workshop on Benchmark Problems, NASA CP, 2004212954, 2004). A Gaussian point source is located in a highspeed jet with large gradients. The jet greatly influences the propagation of the sound waves in the fluid. In this example model, available in the Model Library, an analytical result exists and agrees well with the model results.
 A Gaussian point source is located in a highspeed jet flow with large gradients. The Mach 0.75 flow comes in from the left, along the negative xaxis. Due to symmetry, only the top portion (y>0) of the fluid domain is computed. The flow highly influences the propagation of the sound waves in the fluid; the acoustic pressure waves are clearly distorted by the velocity field. To simulate an unbounded modeling domain and absorb the outgoing pressure waves, perfectly matched layers (PMLs) are used for the frequency domain model.
Boundary conditions for the Linearized Euler physics interfaces include:
 Rigid wall (default)
 Prescribed fields
 Symmetry
 Impedance (frequency domain only)
 Moving wall
 Interior wall
 Analyzing the eigenmodes of a living room with this COMSOL model; any sound field in the room is a combination of these modes. The model shows the mode at about 93 Hz. The response of the speaker system can be modeled with a frequency domain analysis by adding the speaker diaphragm movement and sweeping over frequencies.
New Structure for Pressure Acoustics Fluid Models
The fluid models for pressure acoustics are now organized into Pressure Acoustics, Poroacoustics, and Narrow Region Acoustics. The Dipole and Monopole domain sources can now be found under the More menu.
Poroacoustics
For poroacoustics, the fluid models are now given names conforming with industry standards: DelanyBazleyMiki and JohnsonChampouxAllard. In addition, the defaults and organization of parameters have been streamlined.
Narrow Region Acoustics
For Narrow Region Acoustics, two options are available: Wide duct approximation and Very narrow circular duct. In addition, the defaults and organization of parameters have been streamlined.
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Chemical
Table of Contents:
Chemical Reaction Engineering Module
Global Quantities for Flow at Boundaries
The mathematical formulations for mass transport computations have been enhanced. This has resulted in revised variables for mass balances. In addition, mass fluxes on boundaries can now be computed with increased accuracy.
Based on these improvements, a variety of averaged global quantities for inflow and outflow boundaries have been introduced. These are:
 The Total mass flow and Average pressure within
 Darcy's Law calculations of fluid flow
 The Total mass flow at the outlet when modeling laminar flow
 The Cupmixing temperature when modeling nonisothermal flow
 The Averaged mass fraction when modeling the transport of both dilute and concentrated species
Syngas Combustion in a RoundJet Burner Model
This model simulates the turbulent combustion of syngas in a roundjet burner. Syngas is fed from a pipe into an open region with a slow coflow of air where, upon exiting the pipe, the syngas mixes and combusts with the surrounding air. The model is solved by combining the Reacting Flow and the Heat Transfer in Fluids interfaces. The turbulent flow in the jet is modeled using the kε turbulence model, and the turbulent reactions are modeled using the eddy dissipation model.
Wizard Support for Multicomponent Flash Calculations
The Chemical Reaction Engineering Module now includes the ability to perform flash calculations as part of its Thermodynamics interface. A flash calculation determines the equilibrium state between phases in a system of one or several chemical species and phases, when the system has been subjected to a large decrease in pressure, usually caused by passing through a throttling device. Using inputs provided by CAPEOPEN compliant external thermodynamic property function libraries, COMSOL is able to perform flash calculations of multicomponent mixtures and couple these calculations to other physics involved in your chemical process simulations.
The Chemical Reaction Engineering Module is able to easily perform flash calculations for vapor/liquidequilibrium through combining the thermodynamic equations with the contributing species' mass and energy balances. By doing this, you can receive results that will give you:
 The bubble point at given T
 The bubble point at given p
 The dew point at given T
 The dew point at given p
 The flash at given p and T
 The flash at given p and H
 The flash at given p and S
 The flash at given U and V
Electrodeposition Module
Model Electrodeposition Processes through New Primary Current Distribution Interface
You can model primary current distribution directly by selecting the Electrodeposition, Primary interface in the Model Wizard.
Electrodeposition Interfaces can now Postprocess Accurate Boundary Fluxes
Two postprocessing variables, nIs and nIl, are available for calculating the normal current density in the electrode and the electrolyte phase.
Electrocoating on a Car Door Model
A primary current distribution model of the electrocoating of a car door. The thickness distribution of the deposited paint becomes more uniform due to the high resistivity of the paint. A varying film resistance together with a constant electrolyte conductivity is used to describe the charge transport in the electrolyte.
Corrosion Module
Primary Current Density Distribution Interfaces for Corrosion Processes
You can specify that you want to model primary current distribution in the physics interfaces for corrosion by choosing the Corrosion, Primary interface. Previously, you had to specify this from the Corrosion, Secondary interface.
Accurate Boundary Fluxes in Corrosion Interfaces
Two new postprocessing variables, nIs and nIl, have now been implemented for calculating the normal current density in the electrode and electrolyte phases, respectively.
Electrochemistry Module
Calculation of Boundary Fluxes in Electrochemistry Interfaces
Two variables for postprocessing have been implemented in order to provide accurate data on the normal current density in the electrolyte and electrode phases.
Electrochemical Glucose Sensor Model
Electrochemical glucose sensors use amperometric methods to measure the concentration of glucose in a sample. This example models the diffusion of glucose and ferri/ferrocyanide redox mediators in a unit cell of electrolyte above an interdigitated electrode. The sensor gives a linear response over a suitable range of concentrations. The Electroanalysis interface is used to couple the chemical species transport to the electrolysis at the working and counter electrodes, and the glucose is oxidized by the glucose oxidase enzyme in solution according to MichaelisMenten kinetics.
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Electrical
Table of Contents:
AC/DC Module
Nonlinear Magnetic Materials Database
A database of 165 ferromagnetic and ferrimagnetic materials has been included in the AC/DC Module. The database contains BHcurves and HBcurves enabling the material properties to be used in the magnetic fields formulations. The curve data is densely sampled, and has been processed to eliminate hysteresis effects. Outside of the range of experimental data, linear extrapolation is used for maximal numerical stability.
 View screenshot »

Sample BHcurve data
Sample BHcurve data
New Powerful User Interfaces for Induction Heating
The workflow for setting up simulations with induction heating has been significantly improved with the introduction of a dedicated Multiphysics node in the Model Builder. The new user interfaces are appropriate when each of the constitutive physics can be modeled separately. Since the electrical time scales of a typical inductive process are on the order of thousands of cycles per second, whereas the temperature fields vary on the order of seconds, it is appropriate to model the electrical problem in the frequency domain, and the thermal problem in the time domain, or stationary domain.
The new Inductive Heating interface brings up interfaces for computing the induced currents and losses via the Magnetic Fields interface, the temperature rise via the Heat Transfer interface, as well as a Multiphysics node, which keeps track of the couplings between the physics. The magnetic fields and the heat transfer problems can also be solved separately.
RF Module
Transition Boundary Condition for High Conductivity
The Transition boundary condition formulation has been improved to handle the case of an interior boundary that has very high material conductivity. This can be used to model a layer of metal that is much thinner than any of the other model dimensions.
Interior Port Boundary Conditions
When modeling electromagnetic wave sources in the RF Module, port boundary conditions are usually set at the exterior boundaries of a model to represent a source that is located outside the modeling space. However, sometimes it is more convenient to place the source inside the modeling domain. The new Slit Port introduces the capability to place a source at an interior boundary. This source can be Domainbacked or PECbacked. The PECbacked slit port will introduce two boundary conditions at an interior boundary. On one side of the boundary, the PEC condition will be applied, on the other side any of the regular port boundary conditions can be used to excite a field propagating away from the boundary. The direction in which the field propagates away from the boundary is specified by the Port Orientation. The domainbacked slit port, on the other hand, is a transparent boundary. It can excite a wave propagating away from the boundary, and any wave incident upon the domainbacked port will pass through unimpeded.
 The walls of this 2D horn antenna are modeled with the new Transition boundary condition. The antenna is excited with a PECbacked Slit Port excitation.
The domainbacked slit port is also useful for modeling periodic problems. When modeling structures that have many higherorder diffraction orders, such as gratings, one must account for each diffracted order with a separate port boundary condition. For 3D structures, there can even be diffraction into multiple planes. However, sometimes we are not interested in considering each diffracted order separately, and only want to know the bulk transmittance and reflectance of a periodic structure. In this case, a domainbacked slit port can be used. The slit port can insert an incident plane wave, coming in at any angle, and any wave reflected back towards the port will pass through, and into a PML placed behind it. The PML will absorb all of the higher order modes simultaneously.
Additional Antenna Postprocessing Variables
In the RF Module, it is now possible to extract the antenna gain (in linear and dB scale), the axial ratio (in linear and dB scale), as well as the farfield variables in terms of theta and phi, elevation, and azimuthal angles.
 Frequency selective surface with complementary split ring resonators. This model will be available after the version 4.4 release via a Model Library Update.
Deposited Port Power
In many microwave heating applications, it is desirable to control the amount of power that is deposited into the model. By specifying the deposited power, a feedback condition is added to the model and the applied power is adjusted so that the desired power is deposited within the model. This has applications in biomedical RF heating, plasma modeling, and other areas.
Numeric Port Boundary Mode Analysis with Impedance Boundary Conditions
The Numeric Port boundary condition is used to compute the fields at a boundary to a waveguide where the field distributions cannot be computed analytically (such as rectangular, coaxial, or circular ports.) These numeric port calculations can now consider the impedance boundary condition. The impedance boundary condition considers the effect of lossy walls, instead of assuming that the walls are perfect electric conductors. The periodic boundary condition can also be considered.
 The numerically computed waveguide mode shapes at either end consider the finite conductivity of the waveguide walls.
Gaussian Beam Background Field
The scattered field formulation is used to compute the scattering of electromagnetic fields off of an object. Typically, a uniform plane wave is specified as the background field, but the new Gaussian beam background field allows you to specify a Gaussian beam, propagating along one of the axis directions, of a specified beam waist and focal point. The polarization of the beam can also be specified.
 View screenshot »
 The scattered field formulation background Gaussian beam.
New Powerful User Interfaces for Microwave Heating
A new functionality introduced to COMSOL has allowed for the setting up simulations involving microwave and RF heating to be easier to manage. A dedicated Multiphysics node is introduced to the Model Builder when the Microwave Heating multiphysics interface is chosen from the Model Wizard, together with the appropriate Electromagnetic Waves interface, and the Heat Transfer in Solids interface.
This allows you to model the constitutive physics separately, in order to understand your model's reactions to the contributing physics, before considering both their effects in a coupled problem. This is also appropriate in managing the Study sequence when solving first for the electromagnetic waves in the frequency domain, and then the heat transfer in the time or stationary domains. The Multiphysics node allows you to keep track of the microwave heat sources on domains and boundaries, as well as the temperature nonlinearities in all of the material properties.
Wave Optics Module
UserDefined Phase Functions for the Beam Envelopes Formulation
The Beam Envelopes formulation can solve for the electromagnetic field envelope under the assumption that the propagation vector of the fields is approximately known everywhere in the modeling domain. It is especially memory efficient for problems where the field envelope varies slowly relative to the wavelength, and the direction of propagation is known. It is now possible to explicitly enter a phase function in different domains, which is useful if the beam is changing directions.
Other New Functionality
The new slit port functionality, as described for the RF Module, is also available for Wave Optics.
The new functionality for numeric ports, as described for the RF Module, is also available for the Wave Optics Module.
Laser Heating
A new Laser Heating multiphysics interface has been introduced, which combines the Electromagnetic Waves, Beam Envelopes, and the Heat Transfer in Solids interfaces. The Laser Heating multiphysics interface utilizes a new dedicated Multiphysics node in the Model Builder in a similar way to Joule Heating (COMSOL Multiphysics), Induction Heating (AC/DC Module), and Microwave Heating (RF Module). The beam envelope method formulation is appropriate for beams of light that have a slowly varying envelope, such as along an optical fiber. The Laser Heating multiphysics interface couples the electromagnetic losses with the heat transfer in solids. The temperature variation can be computed in time, or under steady state conditions. Material dependency on temperature can be considered such that thermal and optical material properties can depend directly on temperature.
The Multiphysics node also allows for much better control over modeling your multiphysics applications. This is epitomized by the Activation and Deactivation features of within the Multiphysics node, that allow the singlephysics applications to be modelled separately. Alternatively, combinations of two of the three contributing physics interfaces can also be simulated using this feature.
New Model: StepIndex Fiber Bend
In this new tutorial, a step index fiber bent into a 3 mm radius is analyzed with respect to propagating modes and radiation loss. It is shown how to find the poweraveraged mode radius and how to use this to compute the effective mode index. For a bent fiber, the mode is no longer completely guided by the refractive index structure. This can be qualitatively explained by considering that for a straight waveguide, the wavefronts (planes with a constant phase) are orthogonal to the fiber axis. For a circularly bent fiber, the wavefronts rotate around the center point of the circle with a constant angular velocity. As a result, the propagation constant varies with the distance from the circle center point. At some distance from the center point, the propagation constant is larger that the local wave number, defined by the vacuum wavelength and the refractive index of the cladding material. Beyond this radius, the wave cannot have a constant angular velocity and the wavefronts must bend, implying that the wave starts to radiate energy out from the fiber.
Matched Boundary Condition
The new Matched boundary condition in the Beam Envelopes formulation is perfectly transparent to a wave of known direction. Since the wavevector is typically known at the boundaries when using the Beam Envelopes interface, this boundary condition will introduce less artificial reflections as compared to the Scattering boundary condition and requires less memory than the Perfectly Matched Layer domain truncation.
 A Gaussian beam incident upon a dielectric interface. Since the wavevector is known in all domains, a very coarse mesh can be used. The incident and reflected waves are solved using the Bidirectional Beam Envelopes formulation, and the Matched Boundary Conditions absorb all of the light incident on the boundaries. Electric field intensity and the Poynting vector are plotted.
Gaussian Beam Background Field
The scattered field formulation is used to compute the scattering of electromagnetic fields off of an object. Typically, a uniform plane wave is specified as the background field, but the new Gaussian beam background field allows you to specify a Gaussian beam, propagating along one of the axis directions, of a specified beam waist and focal point. The polarization of the beam can also be specified.
New Multiphysics Model: A MachZehnder Modulator
A MachZehnder modulator is used for controlling the amplitude of an optical wave. In this model, the input waveguide is split up into two waveguide interferometer arms. If a voltage is applied across one of the arms, a phase shift is induced for the wave passing through that arm. When the two arms are recombined, the phase difference between the two waves is converted to an amplitude modulation. This is a multiphysics model, showing how to combine the Electromagnetic Waves, Beam Envelopes user interface with the Electrostatics user interface to describe a realistic waveguide device.
MEMS Module
Improved Workflow for Thermal Stress and Joule Heating Interfaces
The new Multiphysics nodes improve modeling workflow, enabling users to progressively increase the complexity of the system being modeled. Taking the example of a thermal stress simulation, it is now possible to begin by solving a simple thermal problem and then add structural effects and the thermal stress coupling subsequently. It is still possible to add the thermal and structural effects simultaneously using the Thermal Stress physics option in the Model Wizard, and this option automatically adds the Heat Transfer in Solids and Solid Mechanics interfaces together with the appropriate Multiphysics coupling nodes.
This same functionality has also been included in the Joule Heating and Thermal Expansion interface. Once again, the contributing physics interfaces can be added one at a time, and their couplings managed from the Multiphysics node that shows up in the Model Builder. Furthermore, selecting the Joule Heating and Thermal Expansion interface in the Model Wizard will setup the Heat Transfer in Solids, Solid Mechanics, and Electric Currents interfaces together with the Multiphysics node in the Model Builder. This approach makes is possible to straightforwardly activate or deactivate the contributing interfaces. Consequently you can choose to solve the same model for each physics individually, for a combination of multiphysics couplings, or for all three at the same time.
New Model: RF MEMS Switch
This model analyzes an RF MEMS switch consisting of a thin micromechanical bridge suspended over a dielectric layer. A DC voltage greater than the pullin voltage is applied across the switch, causing the bridge to collapse onto the dielectric layer with a resulting increase in the capacitance of the device. A penalty based contact force is implemented to model the contact forces as the bridge comes into contact with the dielectric. The dielectric itself is represented by using a spatially varying function for the dielectric constant between the two terminals.
New Loads and Forces: Gravity, Centrifugal, SpinSoftening, Coriolis, and Euler
Mass forces and loads such as gravity, centrifugal forces, Coriolis forces, and Euler forces can now be added with the aid of two new options, for Gravity and Rotating Frames. This makes it easy to define loads that act on all objects having mass, i.e. domains with mass density, point masses, added mass, rigid connectors with mass, etc. The forces and loads are added from the domain level, even though they may be automatically applied to features at boundaries, edges, and points.
The Rotating Frame feature includes all types of fictitious forces occurring in a rotating system. By default, Centrifugal force and Spinsoftening are included.
Since Added Mass is sometimes used to describe load effects which are not true structural masses, sometimes the contribution from Added Mass is not wanted. The option to include or exclude the contribution is controlled from a check box in a new section called Frame Acceleration Forces.
Plasma Module
Thermal Diffusion of Electrons
Thermal diffusion of electrons will contribute to the electron current density and this phenomenon can now be included in plasma simulations. Thermal diffusion is available as a property in the physics interfaces for: Capacitively Coupled Plasma, DC Discharge, Drift Diffusion, Inductively Coupled Plasma, and Microwave Plasma.
The additional contribution to the current density only makes a difference when the electron diffusivity is nonconstant, i.e. a function of the electron temperature. Note that this option is only available for the finite element formulation.
Semiconductor Module
Heterojunction Boundary Condition
A heterojunction boundary condition is made available by default for interior boundaries. It determines the conditions for continuity of the normal component of the electric field and currents for homojunctions and heterojunctions. Two heterojunction models are defined with the new interface:
 The continuous quasiFermi model (default)
 The thermionic emission model.
The continuous quasiFermi model ensures current continuity by forcing both sides of the junction to have equal quasiFermi energies. The thermionic emission model defines the thermionic currents generated by the potential barrier created by the junction of the dissimilar materials.
Support for Small Signal Analysis
The Semiconductor interface now supports the small signal analysis, frequency domain study type. This enables the calculation of AC device response so that quantities such as the output conductance and the transconductance can be computed.
Impact Ionization
In regions where the electric field perpendicular to the direction of current flow is high, electrons and holes are generated by impact ionization, which is now supported by the Semiconductor Module. This allows for modeling of avalanche effects in photodiodes and avalanche breakdown in MOSFETs. Initially, the currentvoltage relation is linear (this is the ohmic region). As the drainsource voltage increases, the extracted current begins to saturate (this is the saturation region). As the drainsource voltage is further increased, the breakdown region is entered, where the current increases exponentially for a small increase in the applied voltage. This is due to impact ionization.
 View screenshot »
 Logarithmic and nonlogarithmic plots of the impact ionization generation source at a high drainsource voltage of a MOSFET. The generation rate is very high, over 1036[1/(m3s)]. This creates new electronhole pairs, which in turn cause an increase in the current flowing from the source to the drain.
Terminals for Gates
The Thin Insulator Gate boundary condition is now defined using terminals. Three terminal options are available:
 Voltage
 Charge
 Circuit
Improved Initial Values Specification
With COMSOL version 4.4 there are now several ways to specify the initial conditions for the potential and concentration of electrons and holes. This added flexibility makes it easier to obtain a converged solution. The Initial Values options are:
 Default: Automatically chooses a proper Initial Value depending on the discretization method. For the finite volume method it is equivalent to the Equilibrium conditions, while for the finite element method it is equivalent to the Intrinsic concentrations.
 Equilibrium conditions: The field variables for electron concentration (N), hole concentration (P), and potential (V) are set to their calculated equilibrium values.
 Equilibrium carriers only: Same as for Equilibrium conditions, but the user can specify the initial value of the potential field (V).
 Intrinsic concentrations: The field variables for electron concentration (N) and hole concentration (P) will have their initial values set to the intrinsic concentration. You will be able to specify the potential field (V).
 Userdefined: Three user inputs will be displayed for each field variable: electron concentration (N), hole concentration (P), and potential (V).
These options will maximize flexibility when solving an assortment of different models requiring different initial values.
Improved Variables for Calculating Currents and Current Components
New current variables for holes and electrons are available for display in the plot menu:
 Drift current density
 Diffusion current density
 Thermal diffusion current density
The norm and the log of the norm of these quantities are also available.
Improved Circuit Coupling
The Circuit Terminal option for the Metal Contact and Thin Insulator Gate boundary conditions is now functioning in the same way as the Circuit Terminal option of the AC/DC Module.
FieldDependent Mobility Models
The fielddependent mobility models are now available. These allow the mobility of the holes and electrons to decrease according to an empirical model. There are two field dependent mobility models available: CaugheyThomas and Lombardi surface. The CaugheyThomas model is generally applicable for all types of semiconductor devices. The mobility of the electrons and holes is reduced with the increase of the component of the electric field parallel to the current flow. This inhibits current flow compared to the constant mobility case. The Lombardi surface model is applicable for modeling the variation in mobility in the vicinity of surfaces, for example under the gate of a MOSFET.
 Electron drift velocity using the CaugheyThomas mobility. For Silicon, the drift velocity begins to saturate at around 105[V/m].
Incomplete Ionization
The Dopant Ionization settings now include a new option for Incomplete ionization. At low temperatures in silicon and at room temperature for wide bandgap semiconductors, not all of the donors and acceptors are ionized. In these cases, the ionization of the donors and acceptors must be computed as a function of temperature. The dopant ionization is a function of the donor and acceptor energies and their corresponding degeneracy factors. A userdefined option is available to allow the user to specify the ionization ratio directly as any function.
Finite Element Based Logarithmic Formulation
Because of the high degree of nonlinearity inherent to the driftdiffusion equations, the electron and hole number densities can span 10 orders of magnitude over a very small distance. This can create numerical instabilities when using the finite element method, such as for negative concentrations for example. One way of handling this from a numerical point of view is to solve for the logarithm of the electron and hole number density. This has been added to the Semiconductor interface as an additional discretization option.
Metal Contact Boundary Condition
The Metal Contact boundary condition includes the previous Schottky contact and Ohmic contact boundary conditions. This more general feature is a parent feature for both the Ohmic Contact (highly doped semiconductor with negligible barrier thickness) and the Schottky Contact (thermionic emission for large barrier thickness) that are ideal cases of metal contacts. The names of the Schottky Contact and Ohmic Contact boundary conditions have been changed to Ideal Schottky Contact and Ideal Ohmic Contact.
PhysicsBased Meshing for Semiconductor Simulations
Physicsbased meshing can now be used in the Semiconductor interface. A very fine mesh is automatically generated for Ohmic contact, Thin insulator gate, and Schottky boundaries. This removes the need to manually create mesh sequences based on the settings in your model. The defaults have been carefully tuned for balancing accuracy and speed. Physicsbased meshing is the new default and is recommended for all Semiconductor models.
Continuity Settings for Doping and for Nonlinear Features
The new Continuity Settings enable ramping parameters that can be used to gradually introduce quantities into the equation system. For example the doping concentration or the thermionic current can be slowly turned on, which makes it easier to solve strongly nonlinear models. In order to use this setting, one has to use the study extensions setting and ramp the continuation parameter as part of the intended study steps. The Continuation settings for introducing, for example, a thermionic current to the system provide three options:
 No continuation
 Use interface continuation parameter
 Userdefined
The Use interface continuation parameter option links the continuation settings of the feature to an interface level continuation parameter (Cp) defined in the semiconductor interface node. This enables multiple equation terms to be ramped up together simultaneously. The userdefined option allows you to define a specific parameter for the doping continuation.
New Materials for the Material Library
The material library shipped with the Semiconductor Module now includes the following new materials:
 Al(x)Ga(1x)As
 GaN (Wurtzite)
 GaN (Zinc Blende)
 GaP
 GaSb
 InAs
 InP
 InSb
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Multipurpose
Table of Contents:
Optimization Module
Additional Optimization Solvers
Two new optimization solvers expand the scope of the Optimization Module. One of the solvers (BOBYQA) is a gradientfree method and can be applied to a great variety of optimization problems, including those that vary one or more geometry dimensions of a CAD model created directly in COMSOL Multiphysics or via the LiveLink™ products. The other solver (MMA) requires the derivatives to be computed and is more limited in its scope but, when applicable, is much faster to converge.
New GradientFree Optimization Solver: Bound Optimization by Quadratic Approximation (BOBYQA)
The new Bound Optimization by Quadratic Approximation (BOBYQA) method is a socalled trust region gradientfree optimization solver. The method uses an iteratively constructed quadratic approximation of the objective function that is valid in a region around the current iteratethe trust region. This solver is very efficient in that it requires fewer objective function evaluations than early generation gradientfree optimization solvers. The method supports socalled simple bounds but not general constraints, and is expected to outperform the NelderMead and Coordinate Search methods as the number of control variables grow. In summary, the following gradientfree methods are available in COMSOL version 4.4:
 Coordinate search
 Monte Carlo
 NelderMead
 BOBYQA
You can access these optimization methods from the Optimization study type. Control parameters are not limited to geometric dimensions but can represent nearly any quantity in a model, including parameters controlling the mesh.
New GradientBased Optimization Solver: Method of Moving Asymptotes (MMA)
The Method of Moving Asymptotes (MMA) is a gradientbased optimization solver written by Professor K. Svanberg at the Royal Institute of Technology in Stockholm, Sweden. It is designed with topology optimization in mind. The method is called GCMMA in the literature and is available in the Optimization Module under the name MMA.
In summary, the following gradientbased methods are available in COMSOL version 4.4:
 SNOPT
 MMA
 LevenbergMarquardt
Particle Tracing Module
Efficient Calculation of ParticleField and FluidParticle Interactions
A new approach to modeling particlefield and fluidparticle interactions is now available. In this approach, the particle trajectories are computed using a timedependent study step, and the fields in the surrounding medium are computed using a stationary study step. These two steps are repeated until a selfconsistent solution for the particle trajectories and the surrounding fields is reached. This procedure greatly reduces the number of model particles needed to model systems operating under steadystate conditions, like charged particle beams. The new approach makes it easy to quantify the amount of beam spreading occurring due to its self potential.
 A beam of electrons diverges due to its own space charge. The shape of the beam envelope depends on the charge and mass of the particles, the inlet current, and the initial particle velocity. Here the particle trajectory color represents the radial displacement of each particle from its initial position, the slice color represents the self potential of the beam, and the yellow arrows indicate the electric force acting on the beam due to its self potential.
In the settings for the Charged Particle Tracing interface, changing the Release Type to Static causes all release features to provide a specified charged particle current. Similarly, in the Particle Tracing for Fluid Flow interface, changing the Release Type to Static causes all release features to provide a specified mass flow rate. The Particle Field Interaction or Fluid Particle Interaction features then compute the space charge or force density exerted by the particles.
Solver Setup
New solver nodes are available to compute the selfconsistent interaction between particles and fields. The addition of the For and End For nodes to a Solver sequence allows a part of the sequence to run in a continuous loop. This approach allows the particle trajectories to be computed with a timedependent solver and the fields with a stationary solver.
 This is an extension of the magnetic lens model, where the electron beam creates its own self potential which inhibits the ability to focus the beam. The slice shows the electric potential created by the electron beam.
Releasing Particles in a Cone
It is now possible to specify the initial velocities of released particles in a cone with a userspecified angle between 0 and 180 degrees.
 When using the Release from Grid or Release features, a new option, Constant speed, cone is available in the Initial velocity settings.
 You can specify the initial speed of the particles, the direction of the cone axis, and the cone angle.
 By releasing particles in a cone, it is now much easier to create models involving jets or sprays of incoming particles.
 The Constant speed, cone setting can be thought of as a generalization of the Constant speed, hemispherical and Constant speed, spherical settings, the latter two corresponding to the special cases of a 90degree cone and a 180degree cone.
 Particles are injected from a system of injection nozzles into a CVD chamber with a cone angle of 15 degrees. Initially they have enough inertia to follow their original trajectory, but ultimately the drag force takes over and the particles begin to follow the background gas out of the exhaust port.
Statistics for each Release Feature
The total number of particles released by a given release feature is now available as a variable to use in equations and to evaluate during results processing. This provides a convenient means of keeping track of the number of particles released from each feature, even when using a Mesh based initial position.
Elastic Collision Counters
It is now possible to count the number of elastic collisions between a model particle and background gas particles simply by selecting a check box.
 In the settings for the Elastic Collision Force feature, when the Collision Model is set to Monte Carlo, a new section, Collision Statistics, becomes available.
 In the Collision Statistics section, clicking the Count Collisions check box will introduce a new degree of freedom for each particle, which is incremented by one every time an elastic collision occurs.
 The variable introduced by the Count Collisions check box applies only to a specific Elastic Collision Force feature. This means that it is possible to separately count the collisions of a model particle with several different background species.
 Plot of the trajectories of argon ions in a drift tube. Each time they undergo an elastic collision with the background gas, their velocity vector is altered. The color represents the number of times the ion has collided with the background gas.
New Drag Model  HaiderLevenspiel
A new option is available to compute the drag force for nonspherical particles. The mathematical model employed is similar to the SchillerNaumann option, except the sphericity of the particles is taken into account. Nonspherical particles typically result in higher drag than spherical particles.
Reinitialization of Auxiliary Dependent Variables
The Velocity Reinitialization and Elastic Collision Force features can now reinitialize auxiliary dependent variables whenever a velocity reinitialization takes place.
 In the settings for the Velocity Reinitialization feature, a new section, New Value of Auxiliary Dependent Variables, is available.
 Reinitialization can be activated or deactivated separately for each variable.
 The New Value of Auxiliary Dependent Variables section is also available in the settings for the Elastic Collision Force feature when the Collision Model is set to Monte Carlo.
 Use this section to reinitialize auxiliary variables every time a collision occurs.
 In 2D and 2D axisymmetric models, the outofplane velocity component can be reinitialized as well.
 As a consequence, when the Collision Model is set to Monte Carlo in 2D and 2D axisymmetric geometries, the results are now just as accurate as full 3D models.
 View screenshot »
 Plot of ions in a particle accelerator. Auxiliary dependent variables can be used to monitor the residence time and distance traveled by the ions. Here the color expression represents the residence time, which is reset to zero when the particles reach a certain position.
Minimum, Maximum, and Average Operators
Minimum, maximum, and average operators are now available for the particles. These operators allow you to use the following in equations, as stop conditions, or during results processing:
 Minimum value of a variable, evaluated over all particles
 Maximum value of a variable, evaluated over all particles
 Average value of a variable, evaluated over all particles
These variables typically evolve over time and can be used in, for example, stop conditions to terminate the simulation when the average kinetic energy of the particles reaches some threshold. They have been added for the Newtonian and Lagrangian formulations.
New Model  Electron Beam Divergence
When modeling the propagation of charged particle beams at high currents, the space charge force generated by the beam significantly affects the trajectories of the charged particles. Perturbations to these trajectories, in turn, affect the space charge distribution. The Charged Particle Tracing interface includes an iterative procedure to efficiently compute the strongly coupled particle trajectories and electric field for systems operating under steadystate conditions. Such a procedure reduces the required number of model particles by several orders of magnitude, compared to methods based on explicit modeling of Coulomb interactions between the beam particles. A mesh refinement study confirms that the solution agrees with the analytical expression for the shape of a nonrelativistic, paraxial beam envelope.
This model requires the Particle Tracing and AC/DC Modules.
 A beam of electrons diverges due to its own space charge. The shape of the beam envelope depends on the charge and mass of the particles, the inlet current, and the initial particle velocity. Here the particle trajectory color represents the radial displacement of each particle from its initial position, the slice color represents the self potential of the beam and the yellow arrows indicate the electric force acting on the beam due to its self potential.
New Model  Ion Drift Velocity Benchmark
The drift velocity of Ar+ is calculated using a Monte Carlo simulation in which the elastic collisions of argon ions with ambient neutrals are explicitly modeled. The model uses data from energydependent collision crosssection experiments. The average ion velocity values are consistent with the experimental data over a wide range of reduced electric field magnitudes. This agreement suggests that Monte Carlo simulations of elastic collisions between particles may be applied to a wide variety of devices.
 An ensemble of particles in a uniform electric field moving through a drift tube. The color represents the magnitude of the particle velocity. Despite the ions having substantially different velocities, the average particle velocity matches the experimental data.
New Model  Ion Funnel
This model investigates the focusing effect of an electrodynamic ion funnel. Because of their ability to operate at high background gas pressures, ion funnels are often used to couple devices such as ion mobility spectrometers and mass spectrometers, improving the sensitivity of these devices. The model uses a Monte Carlo collision setting to model the interaction of ions with the neutral background gas.
This model requires the Particle Tracing and AC/DC Modules.
 A slice through the ion funnel where the colored surface represents the sum of the AC and DC potential at a phase angle of zero degrees. The imprint of the particle trajectories is also shown. As they move through the system, they are focused by the electrodes. The time evolution of the particles through the funnel is indicated by the different colors for the particles. Initially the particles are represented in grey. The red particles show the position 0.1msec later. The black particles show the location 0.2msec after the initial release, and so on. Eventually, after 0.6msec, the particles are focused into a very small region shown in yellow.
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Interfacing
Table of Contents:
CAD Import Module and LiveLink™ Products for CAD
CAD Import Module Geometry Kernel Upgrade
The CAD Import Module and the LiveLink™ products for CAD utilizes the Parasolid^{®} geometry kernel from Siemens PLM for solid modeling operations, geometry repair, and defeaturing (without these products, a COMSOL^{®}native geometry modeling kernel is used). The CAD Import Module released with COMSOL^{®} version 4.4 features an upgraded version of the Parasolid^{®} kernel and as a result a number of stability issues have been fixed which makes import of CAD models and solid operations more robust.
LiveLink™ for SOLIDWORKS^{®}
Expanding on the functionality that synchronizes selections based on material assignments to the CAD design in SOLIDWORKS^{®}, the LiveLink™ interface now adds support for userdefined selections. Working in the newly added COMSOL^{®} Selections interface in SolidWorks you can define selections that are synchronized to the COMSOL^{®} model. You can choose to synchronize selections for bodies, faces, edges, or points, which become selections in the model when the design is synchronized with COMSOL Desktop^{®}. Setting up a model becomes more efficient as you can also create selections from features of the Model Builder, or from components of an assembly.
LiveLink™ for Inventor^{®}
Synchronizing the geometry between Inventor^{®} and COMSOL now also encompasses the synchronization of material selections. Selections that contain synchronized geometry objects (bodies) are created in COMSOL based on the material definitions from the CAD design. The selections get their names from the material name in Inventor^{®}. Use these selections as input for geometry features requiring object selections, or for any model definitions, physics, or material settings requiring domain selections. The LiveLink™ node contains a table with a list of the synchronized selections.
ECAD Import Module
ODB++™ Import
By implementing import of the ODB++™ format, the functionality of the ECAD Import Module is expanded to include support for one of the most popular formats for transferring printed circuit board (PCB) data. Using this new import capability you can now extract geometrical data from an ODB++™ file, and use it to create a geometry of the PCB for simulation in COMSOL Multiphysics. Geometry import in the ECAD Import Module now supports the additional file extensions .zip, .tar, .tgz, .gz, and .Z for the ODB++™ file format.
Support for implementation of the ODB++™ Format was provided by Mentor Graphics Corporation pursuant to the ODB++ Solutions Development Partnership General Terms and Conditions (http://www.odbsa.com/). ODB++ is a trademark of Mentor Graphics Corporation.
LiveLink™ for Excel^{®}
Connecting to a COMSOL^{®} Server
With a Floating Network License, LiveLink™ for Excel^{®} now allows computations to take place on a different computer running a COMSOL^{®} Server. In addition, instead of displaying the graphics from the COMSOL^{®} server you can optionally configure LiveLink™ for Excel^{®} to work with the COMSOL Desktop, by having both Excel^{®} and COMSOL Desktop^{®} connect to the same COMSOL^{®} server. Any change you make in a model from COMSOL Desktop^{®} can be applied to the model that has been opened from the LiveLink™ and vice versa.
Export of Field Dependent Material Properties
The export of material properties stored in an Excel^{®} file to a COMSOL^{®} material library now includes the export of field dependent properties. This includes, for example, temperature dependent properties, and material properties such as the BH curve.
Parametric Sweeps
You can now extract the list of parameter values for a sweep to a range of cells in a worksheet. You can also edit the parameter values and update the model with the new values.
LiveLink™ for MATLAB^{®}
New Client/Server Functionality
Version 4.4 features a completely new client/server architecture that minimizes communication overhead between a COMSOL^{®} client and a COMSOL^{®} server. This leads to significantly better performance, particularly when the COMSOL^{®} client and the COMSOL^{®} server is running on different computers, but also for connections with LiveLink™ for MATLAB^{®}. Running a COMSOL^{®} server on a different computer requires a Floating Network License. The new architecture also enables multiple connections to a server. Having simultaneous access to a model from COMSOL Desktop^{®} and MATLAB^{®} will allow you to access any setting in a model from either environment. This streamlines the workflow and you can now use MATLAB^{®} as a macro language for making updates or extracting results from the model and at the same time have the comfort of being able to view the model settings and results in COMSOL Desktop^{®}.
Export Plot Data for Delayed Plotting
Exporting plot data using the command mphplot to a data structure is now supported for all plot types. This enables delayed plotting of the data, and the possibility to plot additional data together with the exported data structure.
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