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COMSOL Multiphysics® Installation Guide
Before you Begin
Installation Media Options
System Requirements
Previous Installations
Software License Agreement
License Types
License Management Tools
COMSOL Access
Installing on Windows
Downloading and Installing the COMSOL Software
Installation from a USB Flash Drive
Running the COMSOL Installer
Removing (Uninstalling) the COMSOL Installation
Installing Software Updates
Automated Installation
Product Updates and Library Updates
LiveLink™ for Excel® Installations
LiveLink™ for SOLIDWORKS®: Add-In for SOLIDWORKS
LiveLink™ for Inventor®: Add-in for Autodesk Inventor
LiveLink™ for AutoCAD® Installations
LiveLink™ for PTC® Pro/ENGINEER®: Changing the Installation Path
LiveLink™ for PTC® Creo® Parametric™: Add-in for PTC Creo Parametric
LiveLink™ for Revit®: Add-in for Revit
LiveLink™ for Solid Edge®: Add-in for Solid Edge
Cluster Installation
License Manager Installation on Windows
What is the FlexNet® License Manager?
System Requirements for the FlexNet® License Manager
FlexNet® License Manager Software Components
FlexNet® License Manager Documentation
The License File
Installing the License Manager
Starting the License Manager
Verifying that the License Manager is Running
Starting COMSOL
Changing the License
Troubleshooting License Errors
Running COMSOL on Windows
The COMSOL Folder on The Windows Start Menu
Running COMSOL on Windows® 10
Starting COMSOL for a Classkit License
Creating Desktop Shortcuts Manually
Running COMSOL in Client-Server Mode
Running COMSOL in Batch Mode
Multicore Settings
Running COMSOL on Clusters
Running COMSOL on the Cloud
Running COMSOL with MATLAB
Installing on OS X
Downloading and Installing the COMSOL Software
Installation from USB Flash Drive
Running The COMSOL Installer
Automated Installation
Removing (Uninstalling) the COMSOL Installation
Product Updates and Application Library Update
Changing the Path to the MATLAB® Installation
License Manager Installation on OS X
FlexNet License Manager Software Components
FlexNet License Manager Documentation
The License File
Installing the License Manager
Starting the License Manager
Verifying that the License Manager is Running
Starting COMSOL
Changing the License
Troubleshooting License Errors
Running COMSOL on OS X
Running COMSOL from a Terminal Window
Running a Classkit License
Running COMSOL in Client-Server Mode
Running COMSOL in Batch Mode
Multicore Settings
Running COMSOL on Clusters
Running COMSOL on the Cloud
Installing on Linux
Downloading and Installing the COMSOL Software
Installing from a DVD
Installation from USB Flash Drive
Running The COMSOL Installer
Web Browser for Viewing the Documentation
Automated Installation
Removing (Uninstalling) the COMSOL Installation
Product Updates and Application Library Update
Changing the Path to the MATLAB® Installation
Cluster Installation
License Manager Installation on Linux
FlexNet License Manager Software Components
FlexNet License Manager Documentation
The License File
Installing the License Manager
Starting the License Manager
Verifying that the License Manager is Running
Starting COMSOL
Changing the License
Troubleshooting License Errors
Running COMSOL on Linux
Running COMSOL
Multicore Settings
Running COMSOL in Batch Mode
Running COMSOL in Client-Server Mode
Running a Classkit License
Running COMSOL on Clusters
Running COMSOL on the Cloud
Running COMSOL with MATLAB
Troubleshooting License Errors
License Agreement
COMSOL Software License Agreement
Academic Addendum
Licensee Application Addendum
COMSOL Multiphysics Release Notes
Release Notes
COMSOL Multiphysics
New Functionality in the Application Builder
New Functionality in COMSOL Server
New and Improved General Functionality in COMSOL Multiphysics
New Geometry and Mesh Functionality
New and Updated Operators, Functions, and Definitions
New Functionality in Studies and Solvers
New and Improved Results and Visualization Functionality
General Backward Compatibility Considerations
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.1
Backward Compatibility with Version 5.0
Backward Compatibility with Version 4.4
Backward Compatibility with Version 4.3b
Backward Compatibility with Version 4.3a
Backward Compatibility with Version 4.3
AC/DC Module
New Application in Version 5.2a
Backward Compatibility with Version 5.2 and older
Backward Compatibility with Version 5.0 and older
Acoustics Module
New Functionality in Version 5.2a
New Models in the Application Library in Version 5.2a
New Models and Apps in the Application Gallery in Version 5.2a
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.1
Backward Compatibility with Version 4.3a and Older
Backward Compatibility with Version 4.3
Batteries & Fuel Cells Module
New and Updated Models and Applications in Version 5.2a
Backward Compatibility with Previous Versions
CAD Import Module, Design Module, and LiveLink™ Products for CAD
New Functionality in LiveLink™ for AutoCAD® in Version 5.2a
New Functionality in LiveLink™ for Inventor® in Version 5.2a
New Functionality in LiveLink™ for PTC® Creo® Parametric™ in Version 5.2a
New Functionality in LiveLink™ for PTC® Pro/ENGINEER® in Version 5.2a
New Functionality in LiveLink™ for Revit® in Version 5.2a
LiveLink™ for Solid Edge®
LiveLink™ for SOLIDWORKS®
Backward Compatibility with Previous Versions
CFD Module
Backward Compatibility with Version 5.0
Backward Compatibility with Version 4.4
Backward Compatibility with Version 4.3b
Backward Compatibility with Version 4.3a
Backward Compatibility with Version 4.3
Chemical Reaction Engineering Module
Backward Compatibility with Version 5.0 and Earlier
Corrosion Module
New and Updated Models in Version 5.2a
Backward Compatibility with Earlier Versions
ECAD Import Module
Electrochemistry Module
Updated Models in Version 5.2a
Backward Compatibility with Previous Versions
Electrodeposition Module
Updated Model in Version 5.2a
Backward Compatibility with Previous Versions
Fatigue Module
New and Updated Models in Version 5.2a
Geomechanics Module
Heat Transfer Module
New Applications in Version 5.2a
Updated Application in Version 5.2a
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.1
Backward Compatibility with Version 5.0
Backward Compatibility with Version 4.4
Backward Compatibility with Version 4.3b
Backward Compatibility with Version 4.3a
Backward Compatibility with Version 4.3
Obsolete Features and Variables
MEMS Module
Backward Compatibility with Version 5.2
Backward Compatibility with Version 4.3b
Microfluidics Module
Backward Compatibility with Version 4.3a
Backward Compatibility with Version 4.3
Mixer Module
Updated Application in Version 5.2a
Molecular Flow Module
Multibody Dynamics Module
New Applications in Version 5.2a
Nonlinear Structural Materials Module
Optimization Module
Backward Compatibility with Version 4.3a
Particle Tracing Module
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.1
Backward Compatibility with Version 5.0 and Earlier
Pipe Flow Module
Backward Compatibility with Version 5.1 and older
Plasma Module
Backward Compatibility with Version 5.2 and Earlier
Backward Compatibility with Version 5.1
Backward Compatibility with Version 4.4
Ray Optics Module
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.0
RF Module
New and Updated Models and Applications in Version 5.2a
Backward Compatibility with Version 4.3a
Semiconductor Module
New Application in Version 5.2a
Structural Mechanics Module
Backward Compatibility with Version 5.2
Backward Compatibility with Version 4.3b
Backward Compatibility with Version 4.3a
Subsurface Flow Module
Backward Compatibility with Version 5.2
New Applications in Version 5.2a
Wave Optics Module
New Models and Applications in Version 5.2a
Backward Compatibility with Version 5.2 and Earlier
Material Library
LiveLink™ for MATLAB®
Backward Compatibility with Version 5.2
Backward Compatibility with Version 5.0
LiveLink™ for Excel®
New Functionality in Version 5.2a
The COMSOL API for Use with Java®
COMSOL 5.1 API Changes
COMSOL 5.0 API Changes
COMSOL 4.4 API Changes
COMSOL 4.3b API Changes
COMSOL 4.3a API Changes
COMSOL 4.3 API Changes
COMSOL 4.2a API Changes
COMSOL 4.1 API Changes
COMSOL 4.0a Java API Changes
COMSOL Multiphysics Reference Manual
Introduction
About COMSOL Multiphysics
The COMSOL Modules and Interfacing Options
COMSOL Documentation and Help
The Help Window and Topic-Based Help
The Documentation Window
Searching Help and Documentation Content
The About COMSOL Multiphysics Box
Checking for Product Software Updates
Typographical Conventions
Overview of the Reference Manual
The COMSOL Modeling Environment
The COMSOL Desktop
Basic Navigation
Adjusting Window Location and Size on the Desktop
The COMSOL Desktop Windows
The COMSOL Desktop Menus and Toolbars
Windows Toolbars and Menus
Cross Platform (Mac and Linux) Toolbars and Menus
Features Available on Toolbars and From Menus
The Messages Window
About the COMSOL Model File Formats
Saving COMSOL Files
Saving and Opening Recovery Files
The Root Settings and Properties Windows
Unit Systems
Searching and Finding Text
The Application Libraries Window
The Applications Folder
Running or Opening a Model or Application and Its Documentation
Downloading MPH-Files With Solutions
Searching the Application Libraries
The Application Library Update Window
The Part Library Update Window
The Physics Interfaces
Introduction to the Physics Interfaces
Physics Groups and Subgroups
The Add Physics Window
Physics Interface Guide
Common Physics Interface and Feature Settings and Nodes
Creating a New Model
Open a New Window to Begin Modeling
The Model Wizard
Toolbars and Keyboard Shortcuts
Home Toolbar
Definitions Toolbar
Geometry Toolbar
Work Plane Modal Toolbar
Materials Toolbar
Physics Toolbar
0D Component Toolbar
Mesh Toolbar
Study Toolbar
Results Toolbar
Plot Group Contextual Toolbar
Report Group Contextual Toolbar
View Toolbar
Keyboard Shortcuts
Building a COMSOL Multiphysics Model
Building Models in the Model Builder
The Model Builder
About the Sequence of Operations
The Global Definitions Node
The Component Node
Adding Extra Dimensions to a Model
Branches and Subbranches in the Tree Structure
Settings and Properties Windows for Features Nodes
Displaying Node Names, Tags, and Types in the Model Builder
Opening Context Menus and Adding Nodes
The Physics Nodes
Physics Interface Default Nodes
Physics Interface Node Context Menu Layout
Physics Exclusive and Contributing Node Types
Physics Node Status
Dynamic Nodes in the Model Builder
Structural Mechanics Physics Feature Symbols
Errors and Warnings
Working with Nodes in the Model Builder
Copying, Pasting, and Duplicating Nodes
Undoing and Redoing Operations
Going to the Source Node
Clearing Sequences and Deleting Sequences or Nodes
Disabling or Enabling Nodes
Modeling Guidelines
Selecting Physics Interfaces
Using Symmetries
Effective Memory Management
Selecting an Element Type
Analyzing Model Convergence and Accuracy
Achieving Convergence When Solving Nonlinear Equations
Avoiding Strong Transients
Physics-Related Checks and Guidelines
Results With Unphysical Values
Multiphysics Modeling Approaches
Creating a Multiphysics Coupling
Advantages of Using the Multiphysics Coupling Features
The Add Multiphysics Window
The Multiphysics Node
Uncoupling a Multiphysics Coupling
Model Inputs and Multiphysics Couplings
Specifying Model Equation Settings
Specifying Equation Coefficients and Material Properties
Modeling Anisotropic Materials
Specifying Initial Values
Equation View
Physics Nodes — Equation Section
Boundary Conditions
Boundary Condition Types
Physics Interface Boundary Types
Continuity on Interior Boundaries
Physics Interface Axial Symmetry Node
Constraint Reaction Terms
Weak Constraints
Periodic Boundary Conditions
Computing Accurate Fluxes
Flux Calculation Example — Heat Transfer Model
Using Load Cases
Defining Load Groups and Constraint Groups
Load Group
Constraint Group
Defining and Evaluating Load Cases
Numerical Stabilization
Consistent Stabilization and Inconsistent Stabilization Sections on Settings Windows
An Example of Stabilization
Stabilization Techniques
References for Stabilization Techniques
Using Units
Using Standard Unit Prefixes and Syntax
SI Base, Derived, and Other Units
Special British Engineering Units
Special CGSA Units
Special EMU Units
Special ESU Units
Special FPS Units
Special IPS Units
Special MPa Units
Special Gravitational IPS Units
Switching Unit System
About Temperature Units
About Editing Geometry Length and Angular Units
Units and Space Dimensions
Customizing the COMSOL Desktop
Customizing a Model
Customizing the Desktop Layout
Changing Fonts and the Desktop Language
Editing Node Properties, Names, and Labels
Grouping Nodes by Space Dimension and Type
Setting the Unit System for Models
Checking and Controlling Products and Licenses Used
Preferences Settings
Advanced Physics, Study, and Results Sections
Global and Local Definitions
Global Definitions, Geometry, Mesh, and Materials
Global Definitions
Global Geometry Parts
Global Mesh Parts
Global Materials
Definitions
About Parameters, Variables, and Expressions
Parameters
Variables
Common Settings for the Definitions Nodes
Operators, Functions, and Constants
Unary, Binary, and List Operators and Their Precedence Rules
Mathematical and Numerical Constants
Mathematical Functions
Physical Constants
Built-In Operators
Predefined and Built-In Variables
Predefined Physics Variables
Variable Naming Convention and Namespace
Variable Classification and Geometric Scope
Built-In Global Variables
Geometric Variables and Mesh Variables
Material Group Indicator Variables
Shape Function Variables
Solver Variables
Entering Ranges and Vector-Valued Expressions
Summary of Built-In Variables With Reserved Names
Mass Properties
Mass Properties
Mass Contributions
Functions
Switch for Functions
About User-Defined Functions
Common Settings for the Function Nodes
Analytic
Elevation (DEM)
External
Gaussian Pulse
Image
Interpolation
MATLAB
Piecewise
Ramp
Random
Rectangle
Step
Thermodynamics Package
Triangle
Waveform
Specifying Discontinuous Functions
Component Couplings and Coupling Operators
General Extrusion
Linear Extrusion
Boundary Similarity
One-Point Map
Two-Point Map
Edge Map
Identity Mapping
General Projection
Linear Projection
Integration
Average
Maximum and Minimum
Common Settings for Component Couplings
Coordinate Systems
Base Vector System
Boundary System
Cylindrical System
Mapped System
Rotated System
Spherical System
Scaling System
Identity and Contact Pairs
About Identity and Contact Pairs
Identity Pair
Contact Pair
Probes
Common Settings for Probes
Domain Probe, Boundary Probe, and Edge Probe
Domain Point Probe
Boundary Point Probe
Point Probe Expression
Global Variable Probe
Infinite Elements, Perfectly Matched Layers, and Absorbing Layers
Standard Geometry Configurations
Manual Settings for Nonstandard Geometries
Note on Availability
PML Implementation
PMLs in Multiphysics
Perfectly Matched Layer
Known Issues When Modeling Using PMLs
Infinite Element Implementation
Infinite Element Domain
Known Issues When Modeling Using Infinite Elements
Absorbing Layer
References for PMLs and Infinite Element Domains
Visualization and Selection Tools
Working with Geometric Entities
About Geometric Entities
The Graphics Window
Basic Selection Concepts
About Highlighted Geometric Entities in the Graphics Window
About Selecting Geometric Entities
The Selection List Window
Selecting and Clearing Selection of Geometric Entities
The Graphics Window Toolbar Buttons
Named Selections
Creating Named Selections
Copying and Pasting Selection Lists
Adjacent
Ball
Box
Cylinder
Explicit
Union, Intersection, Difference, and Complement
Creating Named Selections in the Geometry Sequence
Adjacent Selection (Geometry Sequences)
Ball Selection (Geometry Sequences)
Box Selection (Geometry Sequences)
Cylinder Selection (Geometry Sequences)
Explicit Selection (Geometry Sequences)
Union Selection, Intersection Selection, Difference Selection, and Complement Selection (Geometry Sequences)
Cumulative Selections
User-Defined Views
View (1D and 2D)
Axis (2D and 2D Axisymmetric)
Axis (1D and 1D Axisymmetric)
View (3D)
Camera
About the 3D View Light Sources and Attributes
Directional Light
Point Light
Spotlight
Headlight
Hide for Geometry
Hide for Physics
Hide for Mesh Import
Geometry Modeling and CAD Tools
Creating a Geometry for Analysis
Techniques for Creating Geometries
Associative Geometry and Selections of Geometry Objects
Choosing the Right Space Dimension
Removing Interior Boundaries
Working with Geometry Sequences
The Geometry Toolbar
The Geometry Node
Plane Geometry
Creating a Geometry Sequence
Editing and Building Geometry Nodes
Exporting a Geometry
Measuring Geometry Objects
The Form Union/Assembly Node — Uniting the Geometry
Using Geometry Parts
Geometry Part Settings
Loaded Part Settings
Local Parameters
Part Libraries
Using Part Libraries
Creating a Part
Geometric Primitives
Bézier Polygon
Block
Circle
Cone
Cylinder
Eccentric Cone
Ellipse
Ellipsoid
Helix
Hexahedron
Interpolation Curve
Interval
Parametric Curve
Parametric Surface
Point
Polygon
Pyramid
Rectangle
Sphere
Square
Tetrahedron
Torus
Composite Object (Backward Compatibility)
Geometry Operations
Array
Chamfer
Compose
Convert to Curve
Convert to Point
Convert to Solid
Convert to Surface
Copy
Cross Section
Deformed Configuration
Delete Entities
Difference
Edit Object
Extrude
Fillet
If, Else If, Else, End If
Import
Intersection
Mirror
Move
Parameter Check
Part Instance
Partition Objects
Partition Domains
Partition Edges
Partition Faces
Revolve
Rotate
Scale
Split
Sweep
Tangent
Union
Work Plane
Using Work Planes
Virtual Geometry and Mesh Control Operations
Collapse Edges
Collapse Faces
Form Composite Domains
Form Composite Edges
Form Composite Faces
Ignore Edges
Ignore Faces
Ignore Vertices
Merge Edges
Merge Vertices
Mesh Control Domains
Mesh Control Edges
Mesh Control Faces
Mesh Control Vertices
Geometry Modeling Examples
Creating a 3D Geometry Model
Forming Composite Edges and Faces by Ignoring Vertices and Edges
Merging Vertices by Collapsing Edges
Meshing
Creating a Mesh for Analysis
Meshing Concepts
Mesh Elements for 1D, 2D, and 3D Geometries
Free (Unstructured) Meshing
Structured Meshes
About Swept Meshes
Mesh Control Entities
The Mesh Toolbar
Adding, Editing, and Building Meshing Sequences
Using Mesh Parts
Mesh Part Settings
The Mesh Statistics Window
Meshing Techniques
Choosing a Meshing Sequence Type
Mesh Element Quality and Size
Avoiding Inverted Mesh Elements
Troubleshooting Boundary Layer Mesh Generation
Troubleshooting Free Tetrahedral Mesh Generation
Meshing Operations and Attributes
Boundary Layers
Boundary Layer Properties
Convert
Corner Refinement
Copy Domain
Copy Edge
Copy Face
Copy
Distribution
Edge
Edge Groups
Edge Map
Free Quad
Free Tetrahedral
Free Triangular
Mapped
One-Point Map
Reference
Refine
Scale
Size
Swept
Two-Point Map
Importing and Exporting Meshes
Exporting Meshes
Importing Meshes
Creating Geometry from Mesh
Operations on Imported Meshes
Using Operations on an Imported Mesh
Ball
Box
Create Vertex
Cylinder
Delete Entities
Detect Faces
Finalize
Import
Join Entities
Logical Expression
Mesh Object
Meshing Examples
Using Mesh Control Entities to Control Element Size
Using Structured and Unstructured Mesh with Boundary Layers
Materials
Materials Overview
About the Material Databases
About Using Materials in COMSOL Multiphysics
Working with Materials
The Add Material Window
Materials
The Settings Window for Material
Property Groups
Material Link
Switch for Materials
Material Properties Reference
About Model Inputs
About the Output Material Properties
Acoustics Material Properties
Electrochemistry Material Properties
Electromagnetic Models
Equilibrium Discharge
Gas Models
Piezoelectric Models
Piezoresistive Models
Semiconductors Material Properties
Solid Mechanics Material Properties
Solid Mechanics Material Properties: Nonlinear Structural Materials Module
Solid Mechanics Material Properties: Fatigue Module
Solid Mechanics Material Properties: Geomechanics Material Model
User-Defined Materials and Libraries
Importing a Material Library
Creating a New Material Library and Adding Materials
Restoring a Deleted User-Defined Library
Using Functions in Materials
Adding a Function to the Material
Defining an Analytic Function
Working with External Materials
Using External Materials in Physics Interfaces
Built-in Material Function Interface Types
How to Compile and Link an External Material Model
Known Issues for External Materials
External Material
Module-Specific Material Databases
AC/DC Material Database
Batteries and Fuel Cells Materials Database
Bioheat Material Database
Equilibrium Discharge Material Database
Liquids and Gases Material Database
MEMS Material Database
Nonlinear Magnetic Material Database
Piezoelectric Materials Database
Piezoresistivity Materials Database
Optical Materials Database
Semiconductor Materials Database
Thermoelectric Materials Database
References for the Material Databases
The AC/DC Interfaces
The Electromagnetics Interfaces
Fundamentals of Electromagnetics
Constitutive Relations
Potentials
Material Properties
About the Boundary and Physics Interface Conditions
Electromagnetic Forces
References for Electromagnetic Theory
Theory of Electrostatics
Charge Relaxation Theory
Electrostatics Equations
The Electrostatics Interface in Time Dependent or Frequency Domain Studies
Theory of Electric Currents
Electric Currents Equations in Steady State
Theory of Magnetic Fields
Magnetostatics Equation
Frequency Domain Equation
Transient Equation
Maxwell’s Equations
Magnetic and Electric Potentials
Gauge Transformations
Selecting a Particular Gauge
The Gauge and Equation of Continuity for Dynamic Fields
Time-Harmonic Magnetic Fields
The Electrostatics Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the Electrostatics Interface
Charge Conservation
Initial Values
Space Charge Density
Zero Charge
Ground
Electric Potential
Surface Charge Density
External Surface Charge Accumulation
Electric Displacement Field
Periodic Condition
Thin Low Permittivity Gap
Line Charge
Line Charge (on Axis)
Line Charge (Out-of-Plane)
Point Charge
Point Charge (on Axis)
Change Cross Section
Change Thickness (Out-of-Plane)
Charge Conservation, Piezoelectric
The Electric Currents Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the Electric Currents Interface
Current Conservation
Initial Values
External Current Density
Current Source
Electric Insulation
Boundary Current Source
Normal Current Density
Distributed Impedance
Contact Impedance
Sector Symmetry
Line Current Source
Line Current Source (on Axis)
Point Current Source
Point Current Source (on Axis)
Piezoresistive Material
The Magnetic Fields Interface
Domain, Boundary, Point, and Pair Nodes for the Magnetic Fields Interface
Ampère’s Law
Ampère’s Law, Magnetostrictive
Initial Values
External Current Density
Velocity (Lorentz Term)
Magnetic Insulation
Magnetic Field
Surface Current
Magnetic Potential
Perfect Magnetic Conductor
Line Current (Out-of-Plane)
The Pressure Acoustics Interface
Fundamentals of Acoustics
Acoustics Explained
Examples of Standard Acoustics Problems
Different Acoustic Interfaces
Mathematical Models for Acoustic Analysis
The Pressure Acoustics, Frequency Domain Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the Pressure Acoustics, Frequency Domain Interface
Pressure Acoustics
Sound Hard Boundary (Wall)
Initial Values
Monopole Source
Dipole Source
Normal Acceleration
Sound Soft Boundary
Pressure
Impedance
Symmetry
Plane Wave Radiation
Spherical Wave Radiation
Cylindrical Wave Radiation
Incident Pressure Field
Interior Sound Hard Boundary (Wall)
Periodic Condition
Axial Symmetry
Continuity
Theory for Pressure Acoustics, Frequency Domain
Frequency Domain Study
Eigenfrequency Study
References for the Pressure Acoustics, Frequency Domain Interface
The Chemical Species Transport Interfaces
Theory for Transport of Diluted Species
Convective Term Formulation
Crosswind Diffusion
Mass Balance Equation
Solving a Diffusion Equation Only
References
The Transport of Diluted Species Interface
Domain, Boundary, and Pair Nodes for the Transport of Diluted Species Interface
Transport Properties
Initial Values
Mass-Based Concentrations
Reactions
No Flux
Inflow
Outflow
Concentration
Flux
Symmetry
Flux Discontinuity
Periodic Condition
Thin Diffusion Barrier
Thin Impermeable Barrier
Hygroscopic Swelling
The Fluid Flow Interface
Theory of Laminar Flow
General Single-Phase Flow Theory
Compressible Flow
Weakly Compressible Flow
The Mach Number Limit
Incompressible Flow
The Reynolds Number
The Boussinesq Approximation
Theory for the Wall Boundary Condition
Prescribing Inlet and Outlet Conditions
Normal Stress Boundary Condition
Pressure Boundary Condition
Numerical Stability — Stabilization Techniques for Fluid Flow
Solvers for Laminar Flow
Pseudo Time Stepping for Laminar Flow Models
Discontinuous Galerkin Formulation
Particle Tracing in Fluid Flow
References for the Single-Phase Flow, Laminar Flow Interfaces
The Single-Phase Flow, Laminar Flow Interface
The Laminar Flow Interface
Domain, Boundary, Pair, and Point Nodes for Single-Phase Flow
Fluid Properties
Volume Force
Initial Values
Wall
Inlet
Outlet
Symmetry
Open Boundary
Boundary Stress
Periodic Flow Condition
Pipe Connection
Flow Continuity
Pressure Point Constraint
Point Mass Source
Line Mass Source
Gravity
The Heat Transfer Interfaces
Theory for Heat Transfer
Theory for Heat Transfer in Fluids
About the Heat Transfer Interfaces
Space Dimensions
Study Types
Versions of the Heat Transfer Physics Interface
Settings for the Heat Transfer Interface
References for the Heat Transfer Interfaces
The Heat Transfer in Solids Interface
Feature Nodes for the Heat Transfer in Solids Interface
The Heat Transfer in Fluids Interface
Feature Nodes for the Heat Transfer in Fluids Interface
The Joule Heating Interface
Electromagnetic Heat Source
Boundary Electromagnetic Heat Source
Temperature Coupling
Domain Features
Change Thickness
Heat Source
Heat Transfer in Fluids
Heat Transfer in Solids
Initial Values
Translational Motion
Boundary Features
Continuity
Diffuse Surface
Heat Flux
Line Heat Source on Axis
Outflow
Periodic Condition
Symmetry
Temperature
Thermal Insulation
Thin Layer
Edge and Point Features
Point Heat Source
Point Heat Source on Axis
Heat Transfer Variables
Predefined Variables
Global Variables
Domain Heat Fluxes
Boundary Heat Fluxes
Internal Boundary Heat Fluxes
Domain Heat Sources
Boundary Heat Sources
Line and Point Heat Sources
Using the Boundary Conditions for the Heat Transfer Interfaces
Temperature and Heat Flux Boundary Conditions
Overriding Mechanism for Heat Transfer Boundary Conditions
Heat Transfer Consistent and Inconsistent Stabilization Methods
Consistent Stabilization
Inconsistent Stabilization
Handling Frames in Heat Transfer
Physics Feature Nodes and Definition Frame
Definition Frame of Domain Nodes
Definition Frame of Boundary Nodes
Definition Frame of Edge and Point Nodes
Solver Settings
Linear Solver
Nonlinear Solver
Solid Mechanics
The Solid Mechanics Interface
Domain, Boundary, Edge, Point, and Pair Nodes for Solid Mechanics
Initial Values
Change Thickness
Linear Elastic Material
Damping
Free
Prescribed Displacement
Fixed Constraint
Roller
Body Load
Boundary Load
Edge Load
Point Load
Point Load (on Axis)
Periodic Condition
Ring Load
Equation-Based Modeling
The Mathematics Interfaces
Modeling with PDEs
About Equation Forms
Notational Conventions
PDE Interface Variables
The General Form PDE
The Coefficient Form PDE
Multiple Dependent Variables — Equation Systems
Solving Time-Dependent Problems
Solving Eigenvalue Problems
About Weak Form Modeling
Introduction to the Weak Form
The Weak Form PDE
Specifying and Interpreting Boundary Conditions
Symmetric and Nonsymmetric Constraints
The PDE Interfaces
Adding a PDE Interface to a Component
Settings for the Discretization Sections
The Coefficient Form PDE Interfaces
The General Form PDE Interfaces
The Weak Form PDE Interfaces
The Classical PDE Interfaces
Domain, Boundary, Pair, Edge, and Point Conditions for PDEs
Initial Values
Coefficient Form PDE
General Form PDE
Weak Form PDE
Source, Edge Source, and Point Source
Classical PDE Domain Nodes
Dirichlet Boundary Condition
Constraint
Excluded Points, Excluded Edges, Excluded Surfaces
Flux/Source
Zero Flux
Periodic Condition
Destination Selection
Theory for the Wave Form PDE
Derivation of the Weak Form of the Wave Form PDE
Time Explicit Integrator
Local Time Stepping
Reference for the Wave Form PDE Interface
The Wave Form PDE Interface
Domain and Boundary Physics for the Wave Form PDE Interface
Wave Form PDE
Initial Values
Zero Flux
Flux/Source
Interior Source
Interior Flux
About Auxiliary Equation-Based Nodes
Weak Contribution (PDEs and Physics)
Weak Contribution on Mesh Boundaries
Auxiliary Dependent Variable
About Explicit Constraint Reaction Terms
Pointwise Constraint
Weak Constraint
Discretization (Node)
Modeling with ODEs and DAEs
Adding ODEs, DAEs, and Other Global Equations
Solving ODEs: An Example
Solving Algebraic and Transcendental Equations: An Example
Distributed ODEs and DAEs
The ODE and DAE Interfaces
About ODEs, Initial-Value Problems, and Boundary-Value Problems
Global Equations
Global Constraint
Weak Contribution (ODEs and DAEs)
The Distributed ODEs and DAEs Interfaces
Distributed ODE
Algebraic Equation
The Events Interface
Discrete States
Indicator States
Explicit Event
Implicit Event
Reinitialization on Domains, Boundaries, Edges, or Points
The Wall Distance Interface
Domain and Boundary Nodes for the Wall Distance Interface
Distance Equation
Initial Values
Wall
Wall Distance Continuity
Periodic Condition
Theory for Wall Distance
Modified Eikonal Equation
Reference for the Wall Distance Interface
Curvilinear Coordinates
The Curvilinear Coordinates Interface
Diffusion Method
Adaptive Method
Elasticity Method
Flow Method
User Defined
Inlet
Jump
Outlet
Wall
Interior Wall
Coordinate System Settings
Using Extra Dimensions
Attached Dimensions
Points to Attach
Integration Over the Extra Dimension
Example: Solving Poisson’s Equation in a Cylinder by Means of Extra Dimensions
Sensitivity Analysis
Theory for the Sensitivity Interface
Sensitivity Problem Formulation
Theory for Stationary Sensitivity Analysis
Specification of the Objective Function
Choosing a Sensitivity Method
Postprocessing Sensitivities
Issues to Consider Regarding the Control Variables
Issues to Consider Regarding the Objective Function
Issues to Consider Regarding Constraints
The Sensitivity Interface
Integral Objective
Probe Objective
Control Variable Field
Global Objective
Global Control Variables
Deformed Geometry and Moving Mesh
Deformed Mesh Fundamentals
Deformed Geometry vs. Moving Mesh
Arbitrary Lagrangian-Eulerian Formulation (ALE)
About Frames
Mathematical Description of the Mesh Movement
Derivatives of Dependent Variables
Smoothing Methods
Limitations of the ALE Method
Tips for Modeling Using Deformed Meshes
Remeshing a Deformed Mesh
Moving Mesh Interface
Domain and Boundary Nodes in the Moving Mesh Interface
Fixed Mesh
Prescribed Mesh Displacement
Free Deformation
Prescribed Deformation
Prescribed Mesh Velocity
Prescribed Normal Mesh Velocity
Zero Normal Mesh Velocity
Zero Normal Mesh Displacement
Deformed Geometry Interface
Domain and Boundary Nodes for Deformed Geometry
Fixed Mesh
Prescribed Mesh Displacement
Free Deformation
Prescribed Deformation
Prescribed Mesh Velocity
Prescribed Normal Mesh Velocity
Zero Normal Mesh Velocity
Zero Normal Mesh Displacement
Studies and Solvers
Introduction to Solvers and Studies
The Add Study Window
Study
Solver Configurations
The Relationship Between Study Steps and Solver Configurations
Study Reference
Study and Study Step Types
Common Study Step Settings
Using a Solution From Previous Study Steps
Physics and Variables Selection
Goal-Oriented Error Estimation
Stationary
Time Dependent
Time Discrete
Time-Dependent Modal
Frequency to Time FFT
Eigenfrequency
Eigenvalue
Frequency Domain
Frequency-Domain Modal
Time to Frequency FFT
Batch
Batch Sweep
Bidirectionally Coupled Particle Tracing
Bidirectionally Coupled Ray Tracing
Cluster Computing
Cluster Sweep
Function Sweep
Material Sweep
Modal Reduced Order Model
Multigrid Level
Parametric Sweep
Sensitivity
Boundary Mode Analysis
Coil Geometry Analysis
Electrochemistry Studies and Study Steps
Fatigue
Frequency-Domain Perturbation
Frequency-Stationary
Frequency-Transient
Frozen Rotor
Frozen Rotor with Initialization
Stationary Free Surface
Linear Buckling
Mean Energies
Mode Analysis
Optimization
Parameter Estimation
Particle Trajectories
Prestressed Frequency Analyses Studies
Ray Tracing
Reduced Electric Fields
Semiconductor Initialization
Small-Signal Analysis, Frequency Domain
Stationary and Time Dependent One-Way Coupled Studies for Fluid-Structure Interaction
Stationary Plug Flow
Stationary with Initialization and Transient with Initialization
Transient with Phase Initialization
Wavelength Domain
Computing a Solution
Getting Results While Solving
Computing the Initial Values
The Progress Window
Convergence Plots
The Log Window
The External Process Window
Solution Operation Nodes and Solvers
Selecting a Stationary, Time-Dependent, or Eigenvalue Solver
Remarks on Solver-Related Model Characteristics
Scaling of Variables and Equations
About the Stationary Solver
About the Parametric Solver
About the Time-Dependent Solver
About the Time Discrete Solver
The Eigenvalue Solver Algorithm
The Modal Solver Algorithm
The Time Explicit Solver Algorithms
The AWE Solver Algorithm
AWE Solver
Dependent Variables
Eigenvalue Solver
FFT Solver
Modal Solver
Optimization Solver
Plug Flow Solver
Stationary Solver
Time-Dependent Solver
Time Discrete Solver
Time Explicit Solver
References for the Solution Operation Nodes and Solvers
Solution Attribute Nodes
About the Advanced Attribute Settings
Choosing the Right Linear System Solver
About Incomplete LU
The Adaptive Mesh Refinement Solver
The Domain Decomposition Solver
The Fully Coupled Attribute and the Double Dogleg Method
The Iterative Solvers
The Multigrid Solvers
The Parametric Solver Algorithm
The SCGS Solver
The Segregated Solver
The Sensitivity Analysis Algorithm
About the SOR, SOR Gauge, SOR Line, and SOR Vector Iterative Solver Algorithms
The Sparse Approximate Inverse (SAI) Preconditioner
The Vanka Algorithm
Adaptive Mesh Refinement
Advanced
Auxiliary Space Maxwell (AMS)
Automatic Remeshing
Coarse Solver
Control Field
Control State
Direct
Direct Preconditioner
Domain Decomposition
Domain Solver
Error Estimation
Field
Fully Coupled
Incomplete LU
Iterative
Jacobi
Krylov Preconditioner
Lower Limit
Lumped Step
Multigrid
Parametric
Postsmoother
Presmoother
Previous Solution
Sparse Approximate Inverse (SAI)
SCGS
Segregated
Segregated Step
Sensitivity
SOR
SOR Gauge
SOR Line
SOR Vector
State
Stationary Acceleration
Stop Condition
Time Parametric
Vanka
References for the Linear System Solvers and the Preconditions
Solution Utility Nodes
Adaptive Mesh Refinement (Utility Node)
Assemble
Compile Equations
Copy Solution
For and End For
The Statistics Page
Input Matrix
Solution Store
State Space
Job Configurations
Parametric Sweep (Job Configurations)
Batch (Job Configurations)
Cluster Computing (Job Configurations)
Function Sweep (Job Configurations)
Material Sweep (Job Configurations)
Optimization (Job Configurations)
Sequence
Using a Job Configuration to Store Parametric Results on File
Batch Data
Derived Value
Evaluate Derived Value
Export to File
External Class
External Process
Geometry Sequence
Job
Meshing Sequence
Plot Group
Save Model to File
Solution
Harmonic Perturbation, Prestressed Analysis, and Small-Signal Analysis
Frequency-Domain Perturbation Study Step
Harmonic Perturbation — Exclusive and Contributing Nodes
Results Analysis and Plots
Results Overview
Common Results Node Settings
Selecting a Data Set for Plots
Inputs for Parametric Solver and Parametric Sweep Studies
Entering Axis Data for a Data Set
Expressions and Predefined Quantities
Defining Plane Data for a Data Set
Plot Titles for Plot Groups and Plot Types
Using Special Formats and Symbols in Titles
Arrow Positioning
Principal Components and Positioning
Defining the Number of Levels
Selecting Color Tables
Defining the Color and Data Ranges
Defining the Coloring and Style
Defining Element Filters
Defining Shrinking of Elements
Entering Quality Settings for Plot Settings Windows
Inheriting Style Options
Integration Settings for a Derived Value
Data Series Operation Settings for a Derived Value
Small-Signal Analysis, Prestressed Analysis, and Harmonic Perturbation Plot Settings
Node Properties for Reports
Data Sets
Data Set Types
Array 2D and Array 3D
Average and Integral
Contour
Cut Line 2D and Cut Line 3D
Cut Plane
Cut Point 1D, Cut Point 2D, and Cut Point 3D
Edge 2D and Edge 3D
Grid1D, Grid 2D, and Grid 3D
Intersection Point 2D and Intersection Point 3D
Isosurface
Join
Maximum and Minimum
Mesh (Data Set)
Mirror 2D and Mirror 3D
Parameterized Curve 2D and Parameterized Curve 3D
Parameterized Surface
Parametric Extrusion 1D and Parametric Extrusion 2D
Particle (Data Set)
Ray (Data Set)
Revolution 1D and Revolution 2D
Sector 2D and Sector 3D
Solution
Surface
Time Average and Time Integral
Derived Values and Tables
The Table Window and Tables Node
Derived Value Types
Volume Average, Surface Average, and Line Average
Volume Integration, Surface Integration, and Line Integration
Volume Maximum, Volume Minimum, Surface Maximum, Surface Minimum, Line Maximum, and Line Minimum
Point Evaluation
Global Evaluation
Global Matrix Evaluation
Particle Evaluation
Point Matrix Evaluation
Ray Evaluation
Aberration Evaluation
System Matrix
Table
Plot Groups and Plots
Plot Types
The Plot Windows
Creating Cross-Section Plots and Combining Plots
Plotting and Cross-Section Interactive Toolbar
1D, 2D, and 3D Cross-Section Point Plots
2D Cross-Section Line Plots
3D Cross-Section Line Plots
3D Cross-Section Surface Plot
1D Plot Group and Polar Plot Group
Smith Plot Group
2D Plot Group and 3D Plot Group
Admittance Graph
Annotation
Arrow Line
Arrow Surface
Arrow Volume
Contour
Coordinate System Volume, Coordinate System Surface, and Coordinate System Line
Directivity
Far Field
Global
Histogram
Impedance Graph
Interference Pattern
Isosurface
Line Graph
Line
Matrix Histogram
Max/Min Volume, Max/Min Surface, and Max/Min Line
Mesh (Plot)
Multislice
Nyquist
Octave Band
Optical Aberration
Particle (Plot)
Particle Tracing
Particle Tracing with Mass
Particle Trajectories
Filter for Particle Trajectories
Phase Portrait
Poincaré Map
Point Graph
Point Trajectories
Filter for Point Trajectories
Principal Stress Volume
Principal Stress Surface
Ray (Plot)
Ray Trajectories
Filter for Ray and Ray Trajectories
Reflection Graph
Scatter Surface and Scatter Volume
Slice
Streamline
Surface
Table Graph
Table Surface
Volume
Color Expression
Deformation
Filter
Height Expression
Exporting Data and Images
About the Sectionwise Data Format for Data Export
Animation
Data
Mesh (Export)
Table
1D Image, 2D Image, or 3D Image
Plot
Reports
Generating a Model Report
Report Types
The Report Node
The Title Page
The Table of Contents
Sections in the Report
Custom Report Components
Declaration Components
Arrays and Scalars
Mathematical Symbols and Special Characters
Model Contents — Report Components
Root Report Node
Component Report Node
Definitions Report Nodes
Geometry Report Node
Material Report Node
Physics Interface Report Node
Multiphysics Coupling Report Node
Mesh Report Node
Study Report Node
Solver Report Node
Results Report Nodes
Declaration Contents
Printing and Capturing Screenshots
Capturing and Copying Screenshots
Setting the Thumbnail Image
Running COMSOL Multiphysics
Running COMSOL Multiphysics
Windows and the Cross-Platform Desktop
COMSOL Multiphysics Client-Server Architecture
Parallel COMSOL
LiveLink for MATLAB
LiveLink for Excel
COMSOL Batch
COMSOL API
Security Settings
COMSOL Multiphysics Client-Server Architecture
Running COMSOL Multiphysics as a Client-Server Application
Running COMSOL with MATLAB or Excel
Running COMSOL Multiphysics in Client-Server Mode
Advantages of Using COMSOL Multiphysics in Client-Server Mode
Running COMSOL Multiphysics in Client-Server Mode
Connecting and Disconnecting from the Desktop
Shared Libraries
Running COMSOL in Parallel
Shared-Memory Parallel COMSOL
COMSOL and BLAS
Distributed-Memory Parallel COMSOL
Benefits of Running COMSOL in a Distributed Mode
Running COMSOL in Parallel on Clusters
Grid Computing and Remote Computing in COMSOL Multiphysics
The COMSOL Commands
COMSOL Commands on Windows
COMSOL Commands on Linux
COMSOL Commands on Macintosh
The COMSOL Convertpre35a Command
Glossary
Glossary of Terms
Physics Builder Manual
Introduction
About the Physics Builder
What Can You Do With the Physics Builder?
Where Do I Access the Documentation and Application Libraries?
Overview of the Manual
Physics Builder Design
Overview of the Physics Builder
Creating a New Physics Builder File
The Physics Builder Window
The Physics Builder Manager
Saving and Opening Custom Physics Interfaces
Designing the GUI Layout
User Inputs and GUI Components
User Input Group GUI Options
Entering Names and Expressions
Entering Names
Using Customized Names and Descriptions
Entering Names of Operators and Functions
Adding a Delimiter to a String
Tensor Parser
Using Coordinate Systems
The Base Vector System
The Input Base Vector System
Transformation Between Coordinate Systems
Specifying Selections
Selection Terminology
The Physics Builder Manager
Testing Custom Physics Interfaces
The Development Files
Compiling an Archive
Working with Builder Archives
Searching in Archives
Physics Builder Tools
Building Blocks
Components
Properties
Features
Multiphysics Couplings
Code Editor
About Links
Dependencies
External Resources
Import
Definitions Library
Components
Creating Components
Component
Physics Interface Component
Usage Condition
Equation Display
Component Link
Extra Dimension Link
Properties
Property
Property Link
Tensor-Valued Function
Physics and Multiphysics Interfaces
Creating a Physics Interface or a Multiphysics Interface
Physics Interface
Multiphysics Interface
Contained Interface
Physics Interface Component Link
Auxiliary Settings (Physics Interface)
Disable Allowed Study Types
Menu
Menu Item
Physics Interface — Preview
Multiphysics Interface — Preview
Features
Generic Feature
Domain Condition
Boundary Condition
Global Feature
Domain Feature
Boundary Feature
Edge Feature
Point Feature
Pair Feature
Contact Pair Feature
Device Model Feature
Periodic Feature
Feature Link
Multiphysics Feature
Multiphysics Coupling
Generic Multiphysics Coupling
Global Multiphysics Coupling
Domain Multiphysics Coupling
Boundary Multiphysics Coupling
Edge Multiphysics Coupling
Point Multiphysics Coupling
Coupling Type Contribution
Contained Feature
Auxiliary Settings (Feature Nodes)
Auxiliary Settings (Multiphysics Couplings)
Geometric Nonlinearity
Physics Symbol
User Inputs
Creating User Inputs
User Input
Selectable Input
Boolean Input
User Input Group
Section
Constraint Settings Section
Material Property
External Material List
Socket Input
Socket Output
Material List
Feature Input
Activation Condition
Additional Requirement
Allowed Values
Activating Allowed Values
Integer Values Check
Regular Expression Check
Named Group Members
Variables
Creating Variables
Variables for Degrees of Freedoms
Variable Declaration
Variable Definition
Dependent Variable Definition
Dependent Variable Declaration
Initial Values
Hide in GUI
Disable in Solvers
Degree of Freedom Initialization
Component Settings
Frame Shape
ODE States Selection
Equations
Weak Form Equation
General Form Equation
Coefficient Form Equation
Shared Quantity Definition
Constraints
Constraint
Weak Constraint
Excluding Selection
Device Systems
Creating Device Systems
Device Model
Port Model
Device Constants
Device Inputs
Device
Input Modifier
Device Variables
Device Equations
Port
Port Connections
Device Feature
Operators and Functions
Functions
Average
Integration
Maximum
Minimum
Integration Over Extra Dimension
Physics Areas
Physics Area
Predefined Multiphysics
Contained Multiphysics Coupling
Contained Interface (Predefined Multiphysics)
Selections
Selection
Selection Filter Sequence
Override Rule Filter
Selection Component Filter
Multiphysics Coupling Selection Filter
Extra Dimension Selection
Extra Dimensions
1D Interval
Multiple 1D Intervals
2D Rectangle
Auxiliary Definitions
Material Property Group
Material Property (Auxiliary Definitions)
Physical Quantity
Override Rule
Plot Menu Definition
Equation Display (Auxiliary Definitions)
Mesh Defaults
Mesh Size
Study and Solver Defaults
Field
Absolute Tolerance
Segregated Step
Outer Job Parameters
Eigenvalue Transform
Study Sequence
Stationary
Time Dependent
Result Defaults
Plot Defaults
Migration
About Backward Compatibility
Version
Physics Interface (Migration)
Feature (Migration)
Property (Migration)
Change Type
Rename Inputs
Migration Links
Documentation
Introduction to Comments and Documentation
Physics Interface Documentation
User Documentation
Comments
The Documentation Node
Documentation Text Components
The Preview Window
Elements
Element
GeomDim
Src
Array
Record
String
Elinv
Elpric
Event
DG Wave Element, General Form
Degree of Freedom Re-Initialization
Shape Interpolation Element
Examples of Custom Physics
The Thermoelectric Effect
Introduction to the Thermoelectric Effect
Equations in the Physics Builder
Thermoelectric Effect Implementation
Overview
Thermoelectric Effect Interface — Creating It Step by Step
Testing the Thermoelectric Effect Interface
Example Model — Thermoelectric Leg
Introduction to the Thermoelectric Leg Model
Results
Reference
Modeling Instructions
The Schrödinger Equation
Introduction to the Schrödinger Equation
Schrödinger Equation Implementation
Overview
Schrodinger Equation Interface — Creating It Step by Step
Testing the Schrodinger Equation Interface
Example Model — Hydrogen Atom
Introduction to the Hydrogen Atom Model
Results
Modeling Instructions
COMSOL Multiphysics Programming Reference Manual
Introduction
About the COMSOL API
Where Do I Find More Information?
Getting Started
The Model Object
Compiling a Model File for Java®
The Model File for Java
Running a Compiled Model File for Java from the Desktop
Running a Compiled Model File as a Batch Job from the Desktop
Running a Compiled Model File with the COMSOL Batch Command
Getting the COMSOL Installation Path from the Windows Registry
Setting up Eclipse for Compiling and Running a Java® File
General Commands
About General Commands
get* and Selection Access Methods
set()
setEntry()
setIndex()
Methods Associated to Set, SetIndex, and the Various Get Methods
Selections
The loadFile and saveFile Methods
ModelUtil
model
model.attr()
model.attr(<tag>)
model.batch()
model.bem()
model.capeopen()
model.coeff()
model.constr()
model.coordSystem()
model.cpl()
model.elem()
model.elementSet()
model.extraDim
model.field()
model.frame()
model.func()
model.geom()
model.group()
model.init()
model.intRule()
model.massProp()
model.material()
model.mesh()
model.modelNode()
model.multiphysics()
model.ode()
model.opt()
Least-Squares Objective Functions
model.pair()
model.param() and model.result().param()
model.physics()
model.probe()
model.result()
model.savePoint()
model.selection()
model.shape()
model.sol()
model.solverEvent()
model.study()
model.unitSystem()
model.variable()
model.view()
model.weak()
Errors and Warnings
Retrieving Problem Information
Geometry
About Geometry Commands
Features for Creating Geometric Primitives
Features for Geometric Operations
Selection Features
Features for Virtual Operations
Features for Mesh Control
Geometry Object Information Methods
Working with a Geometry Sequence
Adding a Model Component (Geometry)
Adding a Geometry Feature
Editing a Geometry Feature
Building Geometry Features
Feature Status
Accessing Geometry Object Names
Deleting and Disabling Geometry Features
Deleting Geometry Objects
Moving and Scaling Geometry Objects
Geometry Settings
Length Unit
Angular Unit
Scale Values When Changing Unit
Geometry Representation in 3D
Default Repair Tolerances
Automatic Rebuild
Work Planes
Selections of Geometric Entities
Using Selection Features
Cumulative Selections
Virtual Operations
Mesh Control Entities
Geometry Object Information
General Information
Geometric Entity Counters
Adjacency
Evaluation on an Edge
Evaluation on a Face
Geometry Representation Arrays
Measurements
Measuring Geometric Entities in Objects
Measuring Objects
Inserting Geometry Sequences from File
Example of Importing Geometry Sequences
Exporting Geometry to File
Exporting to an ACIS File
Exporting to a Parasolid File
Exporting to an STL File
Compatibility for mphbin/mphtxt in 2D and 3D
Using Geometry Parts
Geometry Commands
AdjacentSelection
Array
BallSelection, BoxSelection, CylinderSelection
BezierPolygon
Block
Chamfer
Circle
CollapseEdges
CollapseFaces
Compose, Union, Intersection, Difference
CompositeDomains
CompositeEdges
CompositeFaces
Cone
ConvertToSolid, ConvertToSurface, ConvertToCurve, ConvertToPoint
CrossSection
Cylinder
Delete
ECone
EditObject
Ellipse
Ellipsoid
ExplicitSelection
Extrude
Fillet
Finalize
FromMesh
Helix
Hexahedron
If, ElseIf, Else, EndIf
IgnoreEdges
IgnoreFaces
IgnoreVertices
Import DXF
Import Geometry Sequence
Import Mesh Part or Meshing Sequence
Import mphbin/mphtxt
Interpolation Curve
Interval
MergeEdges
MergeVertices
MeshControlDomains
MeshControlEdges
MeshControlFaces
MeshControlVertices
Mirror
Move, Copy
ParameterCheck
ParametricCurve
ParametricSurface
PartInstance
Partition
PartitionDomains
PartitionEdges
PartitionFaces
Point
Polygon
Pyramid
Rectangle
Revolve
Rotate
Scale
Sphere
Split
Square
Sweep
Tangent
Tetrahedron
Torus
UnionSelection, IntersectionSelection, DifferenceSelection, ComplementSelection
WorkPlane
Mesh
About Mesh Commands
Operation Features
Attribute Features
Features for Imported Meshes
Working with a Meshing Sequence
Adding a Meshing Sequence
Adding a Mesh Feature
Editing a Mesh Feature
Building Mesh Features
Using Mesh Parts
Feature Status
Deleting Mesh Features
Disabling Mesh Features
Clearing Meshes
Units
Selections
Physics-Controlled Meshing
Information and Statistics
Statistics
Number and Types of Elements
Quality of Elements
Volume of Elements and Mesh
Growth Rate in Mesh
Mesh Status
Getting and Setting Mesh Data
Accessing Mesh Data
Setting or Modifying Mesh Data
Block Versions
Element Numbering Conventions
Errors and Warnings
Continuing Operations
Stopping Operations
The MeshError Feature
The MeshWarning Feature
Exporting Meshes to Files
Exporting Mesh to a COMSOL Multiphysics File
Exporting Mesh to a NASTRAN ® File
Mesh Commands
Ball
BndLayer
BndLayerProp
Box
Convert
CopyEdge
CopyFace
CopyDomain
Copy
CornerRefinement
CreateVertex
Cylinder
Delete
DeleteEntities
DetectFaces
Distribution
Edge
EdgeGroup
EdgeMap
FreeQuad
FreeTet
FreeTri
Import
JoinEntities
LogicalExpression
Map
OnePointMap
Point
Reference
Refine
Scale
Size
Sweep
TwoPointMap
Elements and Shape Functions
Shape Functions and Element Types
Finite Elements
Shape Function Types (Elements)
Solvers and Study Steps
About Solver Commands
Features Producing and Manipulating Solutions
Features with Solver Settings
Solution Object Information Methods
Solution Feature Information Methods
Solution Object Data
General Information
Solution Data
SolutionInfo Object and Its Methods
Solution Creation
General Matrix Information
Matrix Data
Matrix Creation
Adaption
Advanced
Assemble
AutoRemesh
AWE
CopySolution
Eigenvalue
FFT
For, EndFor
FullyCoupled
InputMatrix
Linear
Lower Limit
Lumped Step
Modal
Optimization
Parametric
PlugFlow
Previous Solution
Segregated
SegregatedStep
Sensitivity
StatAcceleration
StateSpace
Stationary
StopCondition
StoreSolution
StudyStep
Time
TimeDiscrete
TimeExplicit
TimeParametric
Variables
XmeshInfo
Study Steps
Batch
Batch Sweep
Cluster Computing
Cluster Sweep
Eigenfrequency
Eigenvalue
Frequency Domain and Frequency Domain Perturbation
Frequency to Time FFT
Function Sweep
Material Sweep
Multigrid Level
Parametric Sweep
Sensitivity
Stationary
Time Dependent
Time Discrete
Time to Frequency FFT
Results
About Results Commands
Commands Grouped by Function
Use of Data Sets
Extracting Data
Retrieving Plot Data
Retrieving Numerical Results
Solution Selection
About Selecting Solutions
Selecting Solutions by Solution Number
Selecting Solutions by Solution Level
Choosing Solution Selection Method
Animation
Annotation
Array2D, Array3D
ArrowVolume, ArrowSurface, ArrowLine
AvVolume, AvSurface, AvLine
Average, Integral, Maximum, Minimum
Color
Contour
Contour (data set)
CoordSysLine, CoordSysSurface, CoordSysVolume
CutLine2D, CutLine3D
CutPlane
CutPoint1D, CutPoint2D, CutPoint3D
Data
Deform
Directivity
Edge2D, Edge3D
Eval
EvalGlobal
EvalGlobalMatrix
EvalPoint
EvalPointMatrix
FarField
Filter
Filter (Particle Tracing, Point Trajectories, Ray Tracing,)
Global (numerical)
Global (plot)
Grid1D, Grid2D, Grid3D
Height, HistogramHeight, TableHeight
Histogram
Image1D, Image2D, Image3D
InterferencePattern
Interp
IntersectionPoint2D, IntersectionPoint3D
IntVolume, IntSurface, IntLine
Isosurface
Isosurface (data set)
Join
Line
LineGraph
MatrixHistogram
MaxMinVolume, MaxMinSurface, MaxMinLine
MaxVolume, MaxSurface, MaxLine, MinVolume, MinSurface, MinLine
Mesh
Mesh (data set)
Mesh (export)
Mirror2D, Mirror3D
Multislice
Nyquist
OctaveBand
Parametric1D, Parametric2D
ParCurve2D, ParCurve3D
ParSurface
Particle
Particle (1D Plot)
Particle (data set)
Particle (Evaluation)
ParticleMass
ParticleTrajectories
PhasePortrait
Plot
PlotGroup1D, PlotGroup2D, PlotGroup3D
PoincareMap
PointGraph
PointTrajectories
PolarGroup
PrincipalSurface, PrincipalVolume
Ray (1D Plot)
Ray (Data Set)
Ray (Evaluation)
Ray Trajectories
ReflectionGraph, ImpedanceGraph, AdmittanceGraph
Revolve1D, Revolve2D
ScatterVolume, ScatterSurface
Sector2D, Sector3D
Slice
SmithGroup
Solution
Streamline
Surface
Surface (data set)
SystemMatrix
Table
Table (export)
Table (plot)
TableSurface
TimeAverage, TimeIntegral
Volume
Graphical User Interfaces
Getting Started
Example Graphical User Interface
Introduction
Downloading Extra Material
Creating the Code for the Model
Construction of the Initial GUI with Graphics
Handling of Progress Information
Setting Up Inputs From the GUI to the Model
Displaying Results in the GUI
Other Details
GUI Classes
ProgressContext
ProgressWorker
SWTGraphicsPanel
SwingGraphicsPanel
The COMSOL File Formats
File Formats
Data Formats
Spreadsheet Data Format
Grid Data Format
Sectionwise Data Format
Supported Microsoft Excel File Types
Color Tables
Continuous Color Tables
Discrete Color Tables
Binary Data Files and Text Data Files
File Structure
Records
Terminology
Text File Format
Binary File Format
Serializable Types
Attribute
BezierCurve
BezierMfd
BezierSurf
BezierTri
BSplineCurve
BSplineMfd
BSplineSurf
Ellipse
Geom0
Geom1
Geom2
Geom3
Manifold
Mesh
MeshCurve
MeshSurf
Plane
PolChain
Serializable
Solution
Straight
Transform
VectorDouble
VectorInt
VectorString
Examples of the Serialization Format
A Mesh with Mixed Element Types
A Planar Face
Application Builder Manual
Introduction
About the Application Builder
What Can You Do with the Application Builder?
Where Do I Access the Documentation?
Overview of the Manual
Application Builder Tools
Introduction
Starting the Application Builder
Opening the Application Builder from the COMSOL Desktop
Application Examples in the Application Libraries
The Application Builder and the Application Tree
The Home Toolbar
Copying Application Components Between Applications
The Main Window Branch
The Main Window Node
The Menu Bar Node
The Toolbar Node
The Menu Node
The File Menu Node
The Ribbon Node
The Ribbon Tab Node
The Ribbon Section Node
The Item Node
The Toggle Item Node
The Separator Node
The Forms Branch
The Forms Node
The Form Node
The Events Branch
The Events Node
The Event Node
The Declarations Branch
Array Syntax
The String Node
The Boolean Node
The Integer Node
The Double Node
The Array 1D String Node
The Array 1D Boolean Node
The Array 1D Integer Node
The Array 1D Double Node
The Array 2D String Node
The Array 2D Boolean Node
The Array 2D Integer Node
The Array 2D Double Node
The Choice List Node
Activation Condition
The File Node
The Unit Set Node
Adding Shortcuts
Editing Initial Values and Arguments in Declarations and Command Sequences
The Methods Branch
The Method Node
The Libraries Branch
Images
Sounds
Files
Planning and Preparing an Application
Preparing an Application
Creating Applications from Models
Copy as Code to Clipboard
Testing the Application
Keyboard Shortcuts
Working With Forms
Introduction
Working with a Form and Using the New Form Wizard
Model Data Access
The Form Toolbar
The Form Window Layout Modes
The Sketch Mode
The Grid Mode
Previewing and Testing the Form
Running Methods in Form Objects
The Form Objects
Input Field
Button
Toggle Button
Check Box
Combo Box
Text Label
Unit
Equation
Line
Data Display
Graphics
Web Page
Image
Video
Progress Bar
Log
Message Log
Results Table
Form
Form Collection
Card Stack
Card
File Import
Information Card Stack
Array Input
Radio Button
Selection Input
Text
List Box
Table
The Edit Custom Toolbar Button Dialog Box
Slider
Hyperlink
Toolbar
Spacer
Working with Methods
Overview
Opening a Method Editor Window
Coding and Methods Overview
The Application Builder Window
The Method Windows
The Method Toolbar
The Method Nodes and Method Editor Windows
The Utility Class Node
The External Java Library Node
The External C Library Node
Using External C Libraries
File Schemes and File Handling
Getting Files To and From the Client File System
Creating Methods
Syntax Highlighting
Code Completion
Code Folding
Adding Language Elements
Adding Model Expressions
Adding Model Code and Form Objects
Going to Node the Source Code is Mapped To
Recording Code
Extracting Variables
Calling Other Methods Directly
Using Properties Defined in Declarations as Variables
Searching and Finding Text
Indentation and Whitespace Formatting
Brace Matching
Debugging Methods for Applications
Debugging Tools
The Errors and Warnings Window
Handling Run-Time Errors in Methods
Stopping a Running Method