Uppsala, November 24, 2011

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Nov 16, 2013 (3 years and 6 months ago)

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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


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

Fluid Flow

Chemical

Reactions

Electromagnetic

Fields

Heat Transfer

Acoustics

Structural

Mechanics

The COMSOL Multiphysics approach

Fluid Flow

Chemical

Reactions

Acoustics

Electromagnetic

Fields

Heat Transfer

Structural

Mechanics

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


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


Stationary


Time
-
dependent


Eigenfrequency

(
eigenvalue

problem)


Frequency domain (harmonic assumption)


Physics to use


Mesh to use (for each geometry)


...


Multi Study step


Modal analysis


Small signal analysis


...









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


Stationary


Fully coupled (Newton)


Automatic and Constant damping


Segregated (solve for subset of variables, iterate)


Pseudo time stepping (CFD)


Time
-
dependent


BDF solver (SUNDIALS/IDA, 1
st
-
5
th

order, implicit, adaptive)


Generalized alpha (2
nd

order, implicit,
tunable

damping, adaptive)


Runge
-
Kutta

(1
st
-
4
th

order, explicit, manual step length)


Time discrete (for CFD projection schemes)


Modal solver (uses
eigenfunction

expansion)


Algebraic eigenvalue


ARPACK using shift and invert mode


Frequency domain


Plain sweep (solve for each wave number k)


AWE (Taylor or
Padé

expansion)


Modal
Solver (uses
eigenfunction

expansion)



Extensions


Sensitivity (
f
orward and
adjoint
)


For stationary and time
-
dependent (4.3) problems


Optimization (NLP and LSQ)


SNOPT (Stanford)


Levenberg
-
Marquardt


For stationary and time
-
dependent problems (4.3)


h
-
adaption (for Stationary, Parametric and Eigenvalue problems)


L2
-
norm


Goal oriented (dual weighted residual)


h
-
adaption (for Time
-
dependent problems)


Fixed mesh in sub time
-
intervals


Uses a physics (or user) controlled error indicator function


Moving meshes


ALE (Arbitrary Lagrange
-
Eulerian
)


Automatic re
-
meshing (Parametric and Time
-
dependent)


Model control (Jobs)


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


Linearization, evaluation and symbolic differentiation


Used by all the basic solvers


Parallel FE
assembly


OpenMP and MPI


Parallel sparse matrix
lib


OpenMP and MPI


Sparse linear systems


Direct; MUMPS, PARDISO, SPOOLES


Iterative; GMRES, FGMRES, BiCGSTAB, CG


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)


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.)


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)


A
ccuracy: 10
-
20% (est.)

COMSOL Multiphysics


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:


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


Capacitors


Inductors


Motors & Generators


Cables


Sensors


EMC



Capacitors


Inductors


Motors & Generators


Cables


Sensors


EMC

Model courtesy Comet AG, Switzerland.


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

Model courtesy VTT Microtechnologies Anturit.


Resonators


Actuators


Sensors


Piezoelectric
devices


Accelerometers


Lab
-
on
-
chips


Transducers


BAW/SAW devices


Acoustics Module


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

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


Printed circuit boards, electrical contacts, and cooling devices


Protection of metal parts


Corrosion protection of nuts, bolts, and other components


Wear resistance coatings on bearings and shafts


Decoration of metals and plastics


Chromium coatings of automotive parts


Nobel metals on jewelry and tableware


Electroforming of parts with thin
complex shapes


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


Applications include:


Flow visualization


Mixing


Spraying


Particle separation


Mass spectrometry


Ion optics


Beam physics,


Ion energy distribution functions


Acoustic streaming

LiveLink
TM

for MATLAB
®


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:


ACIS
®

(.sat, .
sab
)


Parasolid
®

(.
x_t
, .
x_b
, .
xmt_bin
)


STEP (.step)


IGES (.
igs
)

LiveLink
TM

for SolidWorks
®

Model courtesy Comet AG, Switzerland.



Associative connection between
COMSOL Multiphysics and
SolidWorks.


Parametric sweeps and design
optimization directly from within
SolidWorks.

LiveLink
TM

for Inventor
®


Associative connection between
COMSOL Multiphysics and Inventor.


Parametric sweeps and design
optimization directly from within
Inventor.

LiveLink
TM

for Pro/ENGINEER
®


Associative connection between
COMSOL Multiphysics and
Pro/ENGINEER.


Parametric sweeps and design
optimization directly from within
Pro/ENGINEER.

LiveLink
TM

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.

LiveLink
TM

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.

LiveLink
TM

for
Creo
TM

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!