Uppsala, November 24, 2011
Jacob Yström, doc. Numerical Analysis
Team leader Numerical Methods
jacob@comsol.se
Introduction to COMSOL Multiphysics
• COMSOL - the company and the products
• Modelling steps in COMSOL Multiphysics
– Live demo
• Basic numerical techniques
• Extensions
– Examples: moving meshes, time-dependent h-adaption, particle
dynamics
• Core algorithms
– Two larger examples (CFD and RF)
World leader in multiphysics simulations
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HQ in Stockholm.
16 offices in Europe, India and USA.
250+ employees.
14 000 licenses, 60 000 users.
COMSOL in Sweden
• Development
– Math & Computer Science
– Numerical Methods
– Rendering & Visualization
– API
– Quality & testing
• Applications
– Physics interfaces
– Modules
– Model library
• Support
• Sales
Traditional approach to modeling
Electromagnetic
Fields
Chemical
Reactions
Fluid Flow
Acoustics
Heat Transfer
Structural
Mechanics
The COMSOL Multiphysics approach
Electromagnetic
Fields
Acoustics
Heat Transfer
Chemical
Reactions
Structural
Mechanics
Fluid Flow
User Defined
Equations
COMSOL 4.2a Product Line
Modeling steps
• Define geometry
– With a LiveLink to CAD program, interactively or by CAD file import
• Select physics (and/or mathematics)
– Through application tailored interfaces (and/or user defined equations)
• Generate mesh
– Automatically, interactively, mesh import (NASTRAN)
• Specify details
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Material properties
Boundary conditions
Sources, sinks,...
Multiphysics couplings
• Select “Study” to perform and compute
– Generate solver settings automatically or manually
• Result processing
Study
• Study step
– Analysis type
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Stationary
Time-dependent
Eigenfrequency (eigenvalue problem)
Frequency domain (harmonic assumption)
– Physics to use
– Mesh to use (for each geometry)
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• Multi Study step
– Modal analysis
– Small signal analysis
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Our basic method for PDE’s
• Galerkin FEM discretization
– With optional artificial stabilization (SD, GLS-stabilization,…)
– Lagrange elements, Edge elements, ...
• Standard studies
– Stationary -> AE
• f(u,x) = 0
– Time dependent -> DAE
• f(du/dt,u,t,x) = 0
– Eigenfrequency/Eigenvalue -> GAEP
• (E*lambda^2 + D*lambda + K)*u=0
– Frequency dependent (Helmholtz eq.) -> parametric
• K(k)*u = L(k)
... and the basic solvers
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Stationary
– Fully coupled (Newton)
• Automatic and Constant damping
– Segregated (solve for subset of variables, iterate)
– Pseudo time stepping (CFD)
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Time-dependent
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BDF solver (SUNDIALS/IDA, 1st-5th order, implicit, adaptive)
Generalized alpha (2nd order, implicit, tunable damping, adaptive)
Runge-Kutta (1st-4th order, explicit, manual step length)
Time discrete (for CFD projection schemes)
Modal solver (uses eigenfunction expansion)
Algebraic eigenvalue
– ARPACK using shift and invert mode
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Frequency domain
– Plain sweep (solve for each wave number k)
– AWE (Taylor or Padé expansion)
– Modal Solver (uses eigenfunction expansion)
Extensions
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Sensitivity (forward and adjoint)
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Optimization (NLP and LSQ)
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Fixed mesh in sub time-intervals
Uses a physics (or user) controlled error indicator function
Moving meshes
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L2-norm
Goal oriented (dual weighted residual)
h-adaption (for Time-dependent problems)
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SNOPT (Stanford)
Levenberg-Marquardt
For stationary and time-dependent problems (4.3)
h-adaption (for Stationary, Parametric and Eigenvalue problems)
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For stationary and time-dependent (4.3) problems
ALE (Arbitrary Lagrange-Eulerian)
Automatic re-meshing (Parametric and Time-dependent)
Model control (Jobs)
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Parametric sweep (vary any parameters in a systematic way)
Batch (a detachable - external process - job)
Cluster computing (MPI)
Extensions and more methods...
• Particle dynamics
– Large system of independent ODE’s
• Field to particle effects (one-way coupled)
• Boundary interaction (bounce, stick, dissaper, ...)
• Explicit and implicit time-stepping methods
• Far-field evaluation
– BEM formulation
• Nodal Discontinuous Galerkin method (work in progress)
– For wave equations in the time-domain
– High order, very memory lean, scalable, ...
– Fully explicit time-stepping
• Other general methods ... (work in progress)
Core algorithms
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Linearization, evaluation and symbolic differentiation
– Used by all the basic solvers
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Parallel FE assembly
– OpenMP and MPI
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Parallel sparse matrix lib
– OpenMP and MPI
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Sparse linear systems
– Direct; MUMPS, PARDISO, SPOOLES
– Iterative; GMRES, FGMRES, BiCGSTAB, CG
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Multilevel methods; AMG, GMG(hp)
SOR, Jacobi (standard)
SOR Vector (vector element Helmholtz equation)
SOR Gauge (ungauged magnetostatics)
SOR Line (boundary layer meshes)
Vanka (saddle point problems)
Krylov (Helmholtz equations)
LAPACK
– BLAS; MKL, ACML
Performance example 1
• Ahmed body (CFD benchmark model, Re>1e6)
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k-eps Reynolds stress turbulence model
Mixed structured-unstructured-boundary layer mesh.
Size: 2.16M dofs (linear Lagrange elements on 1.6M mesh elements)
Solver: Segregated, GMRES/GMG/SOR Line
Memory: ~10GB
CPU time: 42h (-np 1), 7.5h (-np 16)
Accuracy C_d (drag): 2% within experimental results
Performance example 2
• Balanced Patch Antenna for 6GHz (for cell phones, GPS etc.)
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Study of the efficiency over a freq. range
No. Elems: 77k
Solver: BiCGStab/GMG/SOR Vector (blocked version)
Size: 0.47M complex valued dofs (2nd order edge elements)
Memory: ~2GB
CPU time: 307 sec (-np 4), 694 sec (-np 1)
Accuracy: 10-20% (est.)
COMSOL Multiphysics
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Facilitates all steps in the modeling
process − defining your geometry,
meshing, specifying your physics,
solving, and then visualizing your
results.
Needed in order to run all add-ons.
Interfaces for:
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Heat transfer
Structural analysis
Electromagnetics
CFD
Acoustics
Diffusion
PDEs
Unlimited multiphysics couplings
Heat Transfer Module
• Handles:
– Convection
– Conduction
– Radiation
• Interfaces for:
– Surface-to-surface radiation
– Non-isothermal flow
– Heat transfer in thin layers
– Heat transfer in biological tissue
Model courtesy Continental Corporation.
AC/DC Module
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Capacitors
Inductors
Motors & Generators
Cables
Sensors
EMC
Model courtesy Comet AG, Switzerland.
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Capacitors
Inductors
Motors & Generators
Cables
Sensors
EMC
RF Module
• Antennas
• Waveguides
• Microwave & optical
components
• Plasmonics
• Metamaterials
• Seabed logging
• Transmission lines
Plasma Module
• All types of non-nuclear plasma
reactors.
• Inductively coupled plasmas (ICP)
• DC discharges
• Wave heated discharges
(Microwave plasmas)
• Capacitively coupled plasmas (CCP)
Structural Mechanics Module
Model courtesy Metelli S.p.A.
• Linear and nonlinear stress-strain
analysis
• Thermal strains and stresses
• Elastoplasticity and hyperelasticity
• Contact analysis and friction
• Buckling
• Viscoelasticity, viscoplasticity and
creep
• Piezoelectric effects
Geomechanics Module
• A specialized add-on to the Structural
Mechanics Module aimed at
modeling and simulating
geotechnical applications.
• Interfaces to study plasticity,
deformation, and failure of soils and
rocks, as well as their interaction with
concrete and human-made
structures.
MEMS Module
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Model courtesy VTT Microtechnologies Anturit.
Resonators
Actuators
Sensors
Piezoelectric devices
Accelerometers
Lab-on-chips
Transducers
BAW/SAW devices
Acoustics Module
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Speakers
Microphones
Transducers
Mufflers
Sound barriers
Building acoustics
CFD Module
• Laminar flow
• K- turbulence model, including
low Re
• Single- and multiphase flow
• Porous media flow
• High Mach Number flow
• Thin Film flow
• Rotating machinery
• K-omega (4.2a - October)
• Euler-Euler (4.2a - October)
Microfluidics Module
• Electrokinetic flow
• Creeping flow
• Two-phase flow with level set
and phase field
• Wetted walls
• Surface tension effects
• Fluid-Structure Interaction
Subsurface Flow Module
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Model courtesy VTT Technical
Research Centre of Finland.
Oil& Gas flow in porous media
Groundwater flow
Pollution through soil
Petroleum extraction analysis
Poroelastic compaction
Chemical Reaction Engineering Module
• Is tailor-made to study reacting
systems including the effects of
material and energy transport.
• The Chemical Engineering
Module and the Reaction
Engineering Module have been
replaced with the new Chemical
Reaction Engineering Module.
Batteries & Fuel Cells Module
• Fuel cells
• Alkaline
• Molten Carbonate (MCFC)
• Direct Methanol (DMFC)
• Proton Exchange Membrane
(PEMFC)
• Solid Oxid (SOFC)
• Batteries
• Lithium ion
• Nickel hydride
• Lead acid
Electrodeposition Module
• Enhancement of electrical and
thermal conductivity
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Printed circuit boards, electrical contacts, and cooling devices
• Protection of metal parts
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Corrosion protection of nuts, bolts, and other components
Wear resistance coatings on bearings and shafts
• Decoration of metals and plastics
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Chromium coatings of automotive parts
Nobel metals on jewelry and tableware
• Electroforming of parts with thin
complex shapes
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Manufacturing of thin screens and shaver heads
Manufacturing of MEMS devices
Material Library
• 2500 different materials
• Up to 24 different properties per
material.
• Most are temperature dependent.
Optimization Module
• Topology optimization
• Inverse modeling
• Based on SNOPT code by Stanford
University and University of
California San Diego
Particle Tracing Module
• Computes the trajectory of
particles in a fluid or
electromagnetic field, including
particle-field interactions
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Flow visualization
Mixing
Spraying
Particle separation
Mass spectrometry
Ion optics
Beam physics,
Ion energy distribution functions
Acoustic streaming
LiveLink for MATLAB
TM
®
• Enables scripting.
• Save your COMSOL files as MATLAB
M-files.
• Manipulate the M-file and call your
own functions.
• Interface COMSOL Multiphysics
simulations to computations
performed in other simulators.
CAD Import Module
• Brings in all major CAD formats
directly into the COMSOL Desktop:
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ACIS® (.sat, .sab)
Parasolid® (.x_t, .x_b, .xmt_bin)
STEP (.step)
IGES (.igs)
TM
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LiveLink for SolidWorks
• Associative connection between
COMSOL Multiphysics and
SolidWorks.
• Parametric sweeps and design
optimization directly from within
SolidWorks.
Model courtesy Comet AG, Switzerland.
TM
LiveLink for Inventor
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• Associative connection between
COMSOL Multiphysics and Inventor.
• Parametric sweeps and design
optimization directly from within
Inventor.
TM
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LiveLink for Pro/ENGINEER
• Associative connection between
COMSOL Multiphysics and
Pro/ENGINEER.
• Parametric sweeps and design
optimization directly from within
Pro/ENGINEER.
TM
LiveLink for AutoCAD
®
• Associative connection between
COMSOL Multiphysics and
AutoCAD.
• Parametric sweeps and design
optimization directly from within
AutoCAD.
The picture shows a direct currents
simulation where a foil wire conductor
is represented as a surface in AutoCAD.
TM
LiveLink for SpaceClaim
®
• Associative connection between
COMSOL Multiphysics and
SpaceClaim.
• Parametric sweeps and design
optimization directly from within
SpaceClaim.
The picture shows a thermal simulation
of an exhaust manifold where the geometry
is synchronized between COMSOL and
SpaceClaim.
TM
TM
LiveLink for Creo Parametric
• Associative connection between
COMSOL Multiphysics and Creo
Parametric.
• Parametric sweeps and design
optimization directly from within
Creo Parametric.
Streamlines showing the velocity into the impeller and
housing of an industrial fan. Model courtesy of Gianluca
Argentini, Riello Burners, Italy.
COMSOL is Expanding!