Comsol 2 Day Advanced Day1

8/16/2019 Comsol 2 Day Advanced Day1

1/130

DAY 1

Course presenter: Christiaan Hattingh

MTC

COMSOL South Africa

Course developed by: Niklas Rom, Anders Ekerot, Christiaan Hattingh

COMSOL AB

Advanced 2-day Training Course


2/130

File pack - Trial install

1. Copy all files from the flash drive1. To a folder on the desktop or some other place that is easy to access. We will use these files during the training at

various stages.

2. Please call me and return the flash drive before proceeding, or pass the flash drive on to other attendants who still

need to copy the files. I will then give you a trial pack with the install disc.

2. Install COMSOL – use the install disc in your trial pack.1. You will be prompted to accept the license agreement and then to enter a passcode or license file.

2. Windows/Mac users select the passcode option. Browse to the files you have copied (using file explorer!) and

open the trial license txt file. In the file you will find the passcode. Copy and paste the whole code into the relevant

input box (using Ctrl-V).

3. Users of Linux – select the license file option and then browse and select the file via the button (the file is in the

folder of copied files from the flash drive).

4. Just use the default install options as you proceed through the install wizard, ie click next, next… until you reach

the button “install” – then click on it and the install process will start.5. In the folder you copied from the flash disc there are some hotfix patch files in a folder (4_2_updatesAndHotfixes)

– for windows there are .exe files, for mac dmg‟s and for linux zip files – please install at least the multiphysics

patch from these, the others are not essential for the workshop.

3. You may use the trial pack for install on another computer/for other colleagues at your

company/institution – just use the same passcode that you received today. The license

is valid for about two weeks. The exact date of expiry is listed inside the passcode file.


3/130

Agenda – Day 1

• Geometry, CAD, Import and Meshing – Geometry creation in COMSOL

– CAD import

– Meshing sequences

– Mesh quality and visualization

• Multiphysics couplings, and Result Visualization – Predefined multiphysics couplings

– Different types of couplings

– Datasets and results visualization

• Equation-based modeling – PDE‟s

– PDE‟s and ODE‟s – PDE‟s and distributed ODE‟s

– DAE‟s

– Complex valued equations

• Cluster computing introduction

• News in COMSOL 4.2a


4/130

Structure

1. Presentations

1. Slides

2. Included in your file pack as PDF for reference after the course.

2. Demonstrations (interactive)1. Presenter will demonstrate in COMSOL 4.2a: you can either just follow the

demonstration or you can participate...your choice.

2. Demonstration models are included in your file pack.

3. Exercises

1. On your own laptop follow the exercises step-by-step as outlined in the

document: 2-day_adv_exercises_all_42.pdf. This document also containsadditional information and detailed sections on specific issues.


5/130

COMSOL Multiphysics

• Finite element analysis – Single physics

– Multiphysics

• Flexible Graphical User Interface – Unlimited Multiphysics combination

– All steps in modeling procedure

– Material databases

– Mathematical tools

– Parameterization jobs

• Adaptable – Predefined Multiphysics

– User defined Multiphysics

– Non-linear equations

• PDE

• ODE and DAE

3D mesh of a power

transistor

Visualization of

temperature distribution


6/130

Model just about any physics

• Traditional approach to modeling

– Acoustics

– Structural analysis

– Mass transport

– Electromagnetism – Fluid dynamics

– Heat transfer

• Multiphysics

– Induction heating

– Acoustic-Structure interaction

– Non-isothermal fluids

– Joule heating with thermal expansion

– Fluid-Structure interaction

– User defined

Piezoelectric button for elevators


7/130

Everything can link to everything


8/130

Geometry, CAD Import and Mesh


9/130

Modeling procedure - Geometry

• COMSOL Multiphysics built-in CAD tools.

– Workplanes

– Boolean operators

– Conversions and transforms

– Extrusion and revolution

– Useful for most geometries

• CAD Import

– STEP, IGES, SAT, Parasolid, …

– Repair and defeaturing

– More flexibility in geometry modeling

• Live Links

– SolidWorks

– Pro/E, CREO Parametric

– Autodesk Inventor, AutoCAD

– SpaceClaim

Draw or import the geometry


10/130

Hands-on – Modelling Exercise

• Page 5-27 in exercise PDF

• Creating a 2D and 3D geometry

– Using COMSOL built-in tools

• Parametrization

• Use of basic features and operators

• Workplanes


11/130

• LiveLinks for SolidWorks, Inventor, and Pro/E, CREO,

AutoCAD and Spaceclaim

– Bidirectional Updates of Geometry Dimensions (1-window for

SolidWorks)

• CAD Import Module now supports these formats

– Parasolid (.x_t, .x_b)

– SAT (.sat, .sab)

– STEP (.step, .stp)

– IGES (.igs, .iges)

– Autodesk Inventor part (.ipt)

– Autodesk Inventor assembly (.iam) – Pro/ENGINEER (.prt, .asm)

– SolidWorks (.sldprt, .sldasm)

• Any LiveLink for CAD includes a CAD Import Module

Live Links and CAD Import


12/130

Importing CAD Files

• When you have other

geometry tools


13/130

CAD design for FEA

• During design of parts:

– Apply fillets and chamfers late in theCAD modeling process.

– Remove small features not importantfor the physics.

– Avoid narrow strips of faces.

• During design of assemblies:

– Avoid missalignment of components.

– Avoid separate design of matingfaces.

– Remove all small gaps andclearances from the model.

– Try to build components in the contextof another.


14/130

Automatic Repair During Import

• Removing short edges, small faces, sliver faces

• Healing gaps

• Removing self-intersections, spikes and discontinuities

• Correcting invalid topology• Absolute import tolerance 10-5 m

Remove C5, C6

Modify C1 or C4

C4

C3

C1

C2

C3

C1C2

C5

C6

C4

Example: spike


15/130

Repair Example – Sliver Faces

Remove face and

extend other faces

to fill gap


16/130

Working with 3D CAD files, the wrong way:

Designers Analysis

Staff

CAD File


17/130

Do not work with the fully detailed CAD model

272K DOF

This cannot be

defeatured by

COMSOLDownloaded fromthomasnet.com


18/130

Sometimes, the CAD file has the wrong information

Making the “reverse” of the part is usually much

easier to do in the original CAD program


19/130

Avoid short edges in the CAD file

GOOD

BAD

1637 elements

935 elements


20/130

Avoid sliver and thin faces

12,556 elements


21/130

Fillets, sometimes you want them, sometimes you

don’t


22/130

Tricks for diagnosing CAD

If you are unable to put a 3D mesh on the part

Try interactive

surface meshing

This is a mesh on

the surface only,

but it can visually

guide you to the

problem areas


23/130

Hands-on – CAD import Exercise

• Part 1: Import of 3D CAD file of engine

piston:

– Compare 3D CAD models suitable for

Finite Element Analysis (FEA) versus

design.

– p.28-31 in PDF exercise book.

• Part 2: Import of an IGES file:

– Use repair functionality to create a

solid.

– p.32-36 in PDF exercise book.


24/130

Remember:

Good CAD data has just enough detail to capture the

physics, but not one detail more.


25/130

Meshing Overview

• Various Mesh Algorithms – Free Mesh (see exercise 2)

– Mapped Mesh

– Swept Mesh

– Boundary Layer Mesh

• Interactive Meshing – Click on boundaries/domains/etc. and just

mesh directly from the toolbar

• More Features

– Extrude and Revolve 2D Meshes

– Copy Meshes

– Mesh Import (Nastran)

– Mesh Statistics

– Mesh Visualization


26/130

Mesh – Supported elements

• 3D

– Tetrahedral, hexahedral, prism and pyramid

• 2D

– Triangular and quadrilateral

• 1D

– Discretized domains into intervals


27/130

Automatic and interactive meshing

Free tetrahedral

Boundary layer

Mapped

Swept

Mixed

Adaptive

Model courtesy Metelli S.p.A.


28/130

Live Demo – Meshing techniques

• 3D Geometry Import

• Different features

• Combine different

techniques

Boundary layers

Swept

Free quadFree triangular


29/130

Hands-on – Meshing Exercise

• p.37-45 in PDF exercise book

• Import of a 3D Parasolid file

• Key instructive element

– Learn how to use the meshing

sequence• On a realistic geometry you create a

mesh consisting of different element

types.

• Save your file under a different name

and keep the model open for the next

exercise.


30/130

Live Demo – Mesh statistics and plotting

• Why pyramids?

– Tansitioning element• Combine hexes with tets

• Between domains

• Boundary layers

• At sharp corners/edges• Boundary layers

– But this is handled automatically

by the meshing algorithm

• Plotting techniques for

mesh – Mesh statistics

– Plot different elements

– Mesh quality criteriaCyan – Prism

Green – Pyramid

Hex - Magenta


31/130

Hands-on – Mesh plotting

• Look at the mesh statistics

• Plot the mesh and isolate different

element types.


32/130

Guidelines for meshing refinement…

1. Start with a mesh that you believe will resolve the gradients on the

solution that you expect, use the previously mentioned techniques

to get an answer

2. If it is easy to manually put more elements in regions where youobserve steep gradients in the solution, then do so. Monitor the

convergence of the solution as you proceed

3. Use adaptive mesh refinement to automatically refine the mesh,

but be prepared to devote time and RAM to the solution

4. If the solution itself does not change, to a tolerance that youconsider acceptable, then the solution is converged

5. In 4.2a you can compare solutions using the new “join” dataset.

32


33/130

Meshing notes: The more elements, the better,

but this has some practical limits

P Displacement

0.990

0.995

1.000

0 1 2 3 4 5

Refinement Iteration

N o r m a l i z e d M a

x .

D i s p .

Make sure to study the

solution variable, and

not a derived variable

33


34/130

Review

• By now, you should know

– Different options for drawing a geometry using COMSOL‟s CAD system.

– How to deal with imported CAD geometries, to examine CAD geometries and

repair them. (but alas, the real world awaits...)

– Different meshing options and techniques, and analysing and plotting yourmesh.

– The impact of geometry quality and features on the discretization of the model

(mesh), and consequently/additionally...

– The impact of mesh size and quality on simulation time and the results of the

simulation (relative error).


35/130

BREAK?

End of first session


36/130

Multiphysics couplings and Result

Visualisation


37/130

Lets start by considering a real

multiphysics example


38/130

Multiphysics example - Automotive Fuse

• Made of Aluminum Alloy

• Acrylic plastic cover

• Resistive heating from the

electric currents

• Involved physics

– Electric currents DC

– Heat Transfer

– Thermal expansion


39/130

Part 1 – Electric currents

• Single physics

• Linear

• No source terms

Electric currents

V

0)( V e

Ground15 A


40/130

Part 2 – Electric currents and Heat transfer

Electric currents

V

Heat transfer

T

Q = e|V |2

0)( V e

QT T T ))((

T = 20 C

)( amb flux T T hq T = ?

• One way coupled multiphysics

• Coupling through Load

• Non-linear problem, σT(T)


41/130

Part 3 – Electric currents and Heat transfer

Electric currents

V

Heat transfer

T

Q = e|V |2

0)( V e

QT T T ))((

T e

T = 20 C

)( amb flux T T hq T = ?

• Two way coupled

• Non-linear

Couplings through load (strong) and

material property (weak)


42/130

Part 4 – Thermal stress

Electric currents

V

Heat transfer

T

Q = e|V |2

0)( V e

QT T T ))((

T e

Solid Mechanics

u, v, w

Fixed

Free

ref T T

Fv

• One way coupling

• Can be solved separately


43/130

Definitions of various types of couplings

• One-way coupled – Information passes from one physics to the next, in one direction

• Two-way coupled – Information gets passed back and forth between physics

• Load coupled – The results from one physics affect only the loading on the other physics. In an equation

this is the source term (right-hand side).• Material coupled

– The results from one physics affect the material properties of other physics – most oftenthis is temperature.

• Non-linear coupled – The results of one physics affects both that, and other, physics

• Fully coupled – All of the above

• Weakly coupled – The physics do not strongly affect the loads/properties in other physics

• Strongly coupled – The opposite of weakly coupled

46


44/130

Achieving convergence for multiphysics

problems

• Set up the coupled problem and try solving it with a direct solver

• If it is not converging:

– Check initial conditions

– Ramp the loads up

– Ramp up the non-linear effects

– Make sure that the problem is well posed (this can be very difficult!)

• If you are running out of memory, or the solution time is very long:

– Try an iterative solver

– Use the segregated solver and select the optimal solver (direct or iterative) for

each physics, or group of physics, in the problem. FOR 3D, START HERE! – Upgrade hardware

• Perform a mesh refinement and/or error refinement study to

validate your solution

47


45/130

Results Visualization and data sets

• All solutions are stored in data sets. Several data sets can be stored from a single study or frommultiple studies.

• When visualizing data you can plot in 1D, 2D or 3D depending on the data set and application

thereof to the plot group.

• You can also create “special” data sets which refer to other data sets:

– On a specified selection of geometric entities in the model or by creating your own

geometry intersecting with the domain/boundaries.

– By combining data sets with the join feature.• The „Derived Values‟ section allow for scalar evaluations of quantities that either exist in the

default variable list or as created by yourself. Probe evaluations will also be stored here.

• The evaluations will also be stored in the tables section and can be plotted or exported. If you

do a manual point and click evaluation on a surface plot, for example, it will also be stored in a

table.

• In the export section you can define various ways of exporting data referring to a specific plot

group – so once it is set up it is easy to export in a specific format with a single click. Some ofthese export options are available directly above the graphics window, in the case where you

just want to quickly export an image, for example.

• Finally, there is the automated report generator – you can also customize the template to export

exactly the data you want.


46/130

Pick your own visualization exercise example

• Pick one of the following model exercises(open the solved problem from the model library if necessary, and just explore visualization)

– Busbar

– Power transistor

– Boat radar cross section

– Plot exercise in the PDF exercise book – p.46-62

• You can also browse in the Model library for other models


47/130

Exercise - Busbar

• Electric conductor, typically found in high

power applications

• Parameterized Geometry

• Joule Heating

• Thermal Expansion

• Flow and Cooling

• All files needed on product DVD in Model

Library


48/130

Exercise - Power Transistor

• Predefined interface – Joule Heating

• Find the operating temperature of the power transistor

• One way coupled problem

Electric currents

V

Heat transfer

T

Joule heating

Q = |V |2

Applied current


49/130

Exercise - Radar Cross Section

• Boat hit by a radar

– background field in an electromagnetic scattering problem.

Incident field Response field (top) Response field (norm)


50/130

Exercise – Result Vizualisation

• Volume

• Surface

• Contour

• Plot Scalar Quantities


51/130

BREAK?

End of session 2


52/130

Equation-Based Modeling:

PDEs, ODEs, and Algebraic Equations

f auuuuct

ud

t

ue aa

)(

2

2


53/130

Content

• Partial Differential Equations (PDEs) – PDE Interfaces

– Boundary Conditions

• Ordinary Differential Equations (ODEs)

– Global ODEs – Distributed ODEs

• Algebraic Equations – Global algebraic equations

– Distributed algebraic equations


54/130

When is Equation-based Modeling Needed?

• Try to avoid equation-based modeling if possible

– Using built-in physics interfaces enables ready-made post processing variables

and other tools for faster model setup and much lower risk of human error

– Long-time users sometimes use equation-based modeling even though it is not

needed any longer. It may have been needed in the past but not any longer,examples:

• Thin Thermally Resistive Layer (contact resistance) boundary condition for Heat

Transfer in Solids. In older versions this required manual “gluing” of two physics

interfaces using equations on the boundary.

• Adsorption (physics interface in in 4.2). Previously required weak form modeling.

• and many more…


55/130

When is Equation-based Modeling Needed?

• But: we don‟t have every imaginable physics equation built-into

COMSOL (yet!). So there is sometimes a need for custom

modeling.

• Or you might be deriving a new mathematical model, or using a

particular/unique model from literature.

• Also – if you cannot afford all the modules you need to simulate a

particular model, then you could get by modeling certain

phenomena directly from the equations. (time vs. money?)

• You can combine equation based modeling with any physics

interface as if it is just another physics interface.


56/130

Custom-Modeling in COMSOL

• COMSOL Multiphysics allows you to model with PDEs

or ODEs directly:

– use one of the equation-template user interfaces

• You do *not* need to write “user -subroutines” in

COMSOL to implement your own equation!

– Benefit: COMSOL‟s nonlinear solver gets all the nonlinear info

with gradients and all. Faster and more robust convergence.


57/130


58/130

PDEs


59/130

Linear Model Problems: Fundamental Phenomena

• Laplace‟s equation

• Heat equation

• Wave equation

• Helmholtz equation

• Convective Transport equation

0 u

0)( uk ut

0)( uutt

For inhomogeneous versions, replace 0 with a functiondepending on the independent variables

uu )(

0 xt buu


60/130

COMSOL PDE Modes: Graphical User Interfaces

• Can be used for scalar equations or systems

– Note: coefficients may become operators of higher degree

• Coefficient form

– Coefficients correspond to common physical parameters (e.g., diffusion,

advection, etc.)

• General form

– Very flexible and compact

• Weak form

– PDE form that is the foundation of the FEM

– Integral form that gives even more flexibility

– Requires more expert knowledge

• Q: Which to use?

• A: Whichever is more convenient for you and your simulation.


61/130


62/130


63/130

d(u,x) with no Recover smoothing

d(u,x) with Recover smoothing

The Recover feature applies

“polynomial-preserving recovery” on

the partial derivatives (gradients).

Higher-order approximation of the

solution on a patch of mesh

elements around each mesh vertex.


64/130

Coefficient Form, Interpretations

mass damping/mass

diffusion

convection

source

convection

absorption

source

f auuuuct

ud

t

ue aa

)(

2

2


65/130

mass dampedmass

elastic stress initial/thermalstress

body force(gravitation)

a

ae

d

c

c

u

2

2( )a ae d c a f

t t

u u

u u u u

Coefficient Form, Structural Analysis Wave

Equation

density

damping coefficient

stress, u= displacement vector

stiffness, “spring constant”


66/130

2

2( )a a

u ue d c u u u au f

u t

accumulation/storage

diffusion

convection

source

convection

absorption

source

Coefficient Form, Transport Diffusion Equation


67/130

2

2( )a a

u ue d c u u u au f

u t

0

0

2

2

t

u

t

u

Coefficient Form, Steady-State Equation


68/130

2

2

( )a au u

e d c u u u au f u t

diffusion Helmholtz term

source2

2

( )

2

c u k u f

a k

k

Helmholtz equation:

Coefficient Form, Frequency-Response Wave

Equation

Wave number

Wave length


69/130

Demo:

lambda=2.5

k=2*pi/lambda

a= - k^2

f=0

u=1 one end

u=0 other end

file: Helmholtz.mph


70/130

2

2

( )a au u

e d c u u u au f u t

accumulation/storage

diffusion

source

Transient Diffusion Equation ~ Heat Equation

sourceheatvolume

f

k c

C d a


71/130

“Heat Source” f=1

“Cooling” u=0 at ends

Demo:

c=1

da=1

f=0

Transient 0->100 s

file: Transient_Diffusion.mph


72/130

General Form – A more compact formulation

• inside domain

• on domain boundary

• For Poisson‟s equation, the corresponding general form implies

• All other coefficients are 0

R

u

RG

T

0

n

uyux .u R

1 F

F t

ud

t

ue aa

2

2


73/130

Weak Form

• General form

• Multiply by test function v and integrate

• Use Green‟s first identity on the terms involving “del” expressions

• Rearranged

• Subdomain integral above is entered in the “weak” field:-test(ux)*ux - test(uy)*uy + test(u)*F – da*test(u)*ut

On the boundary, set constr: u

a

ud v dA v dA vFdA

t

au

d v dA v ds v dA vFdAt

n

0 au

v vF d v dA v ds

t

n

a

ud F t


74/130


75/130

PDEs+ODEs


76/130

2

2( )a a

u ue d c u u u au f

u t

Transient Diffusion Equation + ODE

integralvolumeof integrale tim

solutionof integral volume

dt U w

dV uU

t

V

What if we wish to measure the global accumulation of “heat” over time?


77/130

2

2( )a a

u ue d c u u u au f

u t

Transient Diffusion Equation + ODE

0

],[ 10

U wt

U dt

dwdt U w

dV uU

t t t

V

=> This is a “Global” ODE in w

What if we wish to measure the global accumulation of “heat” over time?


78/130

Setting up a spatial integration operand

Global Equation ODE:


79/130

Same time-dependent problem as

earlier

Time-dependent 0,10,100

Volume integration of u

ODE: wt-U


80/130

file: Transient_Diffusion_with_ODE.mph


81/130

Demo

• Compute total mass

• You set up this integration in two steps:1. An Integration model coupling is added under the Definitions node in the model

tree to make a space-integral for the mass flow rate m-dot.

2. Next, you need to add an ordinary differential equation (ODE) to integrate the

flowrate with respect to time. The ODE

Solves for the total mass that has exited at time t.

3. In COMSOL rearrange terms to left-handside: Mt-mdot=0.

4. File: fluid_valve_time_int.mph


82/130

PDEs + Distributed ODEs


83/130

2

2( )a a

u ue d c u u u au f

u t

Transient Diffusion Equation + Distributed ODE

solutionof integraltimelocal ),,(),,( dt z y xu z y x P t

What if we get “damage” from local accumulation of “heat”.

Example of real application: bioheating

We want to visualize the P -field to assess local damage.

Let‟s assume damage happens where P>20.


84/130

2

2( )a a

u ue d c u u u au f

u t



What if we get “damage” from local accumulation of “heat”.

Example of real application: bioheating

spacein pointeachatudt

dP


85/130

2

2( )a a

u ue d c u u u au f

u t


solutionof integraltimelocal udt

dP

But this can be seen as a PDE with no spatial derivatives =

= Distributed ODE

Use coefficient form with unknown field P, f = u, da=1

Let all other coefficients be zero


86/130

Volume where P>20 and

we get damage

file: Transient_Diffusion_with_distributed_ODE.mph


87/130

2

2( )a a

u ue d c u u u au f

u t


Let‟s make this more realistic by adding phase change:

1) assume that damage is irreversible

2) assume that for the damage locations the diffusion coefficient takesa different value:

c=1+2.75*(P(x,y,z)>20)



88/130


89/130

Phase Change

Phase change: c=1+2.75*(P(x,y,z)>20)

Also:

Irreversible change!

Negative u’s aren’t allowed to decrease P

Once P>20, the change in diffusion coefficient c from 1 to

3.75 is permanent

)1),,((),,( dt z y xu z y x P t


90/130

Phase Change

More advanced phase change: c=1+2.75*(P(x,y,z)>20)

Also:

For convergence:

inequalities may need smoothing:

P>20 ==> step1(P at 20,ds=5)

u>1 ==> step2(u at 1,ds=0.5)

also: fine enough mesh to resolve phase fronts

)1),,((),,( dt z y xu z y x P

t

Plot c to see phase change!


91/130

Phase Change

More advanced phase change: c=1+2.75*(P(x,y,z)>20)

Also:

For convergence:

inequalities may need smoothing:

P>20 ==> step1(P at 20,ds=5)

u>1 ==> step2(u at 1,ds=0.5)

also: fine enough mesh to resolve phase fronts

)1),,((),,( dt z y xu z y x P

t

Plot c to see phase change!

Diffusion coefficient with phase front clearly visible

for two different mesh cases. c=1 in blue areas


92/130

and c=3.75 in red areas.

file: Transient_Diffusion_with_distributed_ODE_and_pchange.mph


93/130


94/130

Distributed Algebraic Equations


95/130

Example: Ideal gas law

• Assume u =(u,v,w) and p given by Navier-Stokes

• Want to solve Convection-Conduction in gas:

• given by ideal gas law:

• Easy - analytical

0u)(

T C T k

RT

pM


96/130

Example: Non-ideal gas law

• Assume u =(u,v,w) and p given by Navier-Stokes

• Want to solve Convection-Conduction in gas:

• given by non-ideal gas law:

• Needed for high molecular weight at very high pressures

• Difficult – implicit equation

• How to proceed?

0)1)((* 2 DC B p A

0u)( T C T k


97/130

Example: Non-ideal gas law

• How to solve:

• Third order equation in

• Pressure p is function of space

• So: this is an algebraic equation at each point in space!(distributed)

0)1)((* 2 DC B p A


98/130

Distributed Algebraic Equation

• How to solve:

• Third order equation in

• Pressure p is function of space

• So: this is an algebraic equation at each point in space

• See as PDE with no space or time derivatives!

– A*(p+B*rho^2)*(1-C*rho)-D*rho

– or if unknown is u:

– A*(p+B*u^2)*(1-C*u)-D*u

– Here we let: A=1,B=2,C=3, D=4, p=x*y

• How: Put the entire equation in the source (f) term and zero out the rest

0)1)((* 2 DC B p A

The solution u corresponding to theequation A*(p+B*u^2)*(1-C*u)-D*u,

where p=x*y is spatially varying


99/130

where p=x y is spatially varying.

Here the equation is solved for each

point within the unit square.

file: Distributed_Algebraic_State_Law.mph

Di t ib t d Al b i E ti


100/130


• What about nonlinear equations with multiple solutions?

• Which solution do you get?

• For simplicity, consider the equation (u-2)^2-p=0, where p is a constant

• This can be entered as earlier with an f=(u-2)^2-p

• The solution is easy to get analytically: u=2±sqrt(p)

• The solution you get will depend on the Initial Guess given by the PDE

Physics Interface

• If we let p=x*y and let our modeling region be the unit square, then at

(x,y)=(0,0) we should get the unique solution u=2 but at (x,y)=(1,1) we get1 or 3 depending on our starting guess. See next slide.

Di t ib t d Al b i E ti


101/130


u=3

u=2

u=1u=2

file: Distributed_Algebraic_Second_Order.mph


102/130

Distributed Algebraic Transcendental Equation

• How to solve:

• Transcendental equation in

• Same method

0))sin(1)((* 2 DC B p A


103/130

Complex Valued Equations

• COMSOL can also handle complex valued quantities

• Example: Lambert W function with no closed form representation

• Coefficient form with f = w*exp(w)-(x+j*y)

• c=0 and all others zero as well

)*(

)(

yi xwe z we

z ww

iy x z

we z

ww

w


104/130

Complex Arithmetics

• Can compute:

real(w)

imag(w)

abs(w)

arg(w)

conj(w)


105/130

imag(w)

file: Lambert_W.mph


106/130

BREAK?

End of session


107/130

Parallel Computing and Clusters

• Two Ways of Using Clusters for Simulation

– Parameter Sweeps

– Very Large Models


108/130

EM Field: Power Inductor

4 Million DOF / 11 GB RAM / Solution Time 6 Hours


109/130

Structural Analysis: Elbow Bracket of Steel

3.5 Million DOF / 7 GB RAM / Solution Time 0.4 Hours


110/130


111/130

Parallel computing

• Shared memory

– COMSOL uses all available cores

– Mesh, solvers, postprocessing...

– Free of charge

• Distributed memory (Cluster)

– Windows and Linux

– Windows Cluster management

• HPC server 2008

• Compute Cluster 2003

– Uses shared memory on each node

– Free cluster nodes

Core

Host/Computer

COMSOL process


112/130

Clusters

One or severalclients

Client Server/Remote

desktop

Head node

Subnodes


113/130

Running COMSOL in parallel

• COMSOL can run a job on

many cores

in parallel (Shared-memory

processing or multithreading)

• COMSOL can run a job onmany physical nodes (cluster

computing)

• Both parallel operations above

can be used in combination to

maximize parallelizationbenefits

• Cluster computing requires a

floating network license.

Processor core

A COMSOL job can use many

cores in parallel in a node by

Shared-memory processing

Node A COMSOL job can use many nodes in

parallel by cluster computing


114/130

Four Ways to Run a Cluster job

1. Submit batch job from the command line of the headnode

– Direct control through commands,

can be used in shell scripts

– Requires completed and saved

model mph file

– Consumes 1 license seat regardless of number of compute nodes used

– Needed if you use custom schedulers like LSF or PBS

2. Start a cluster-enabled COMSOL desktop GUI on headnode

– Allows interactive modeling and

cluster job submission by the click of a button from

within the COMSOL Deskop GUI. – No command line proficiency needed

– Consumes 1 license seat regardless of number

computer nodes used.

– Not for use with custom schedulers

head:~>

comsol –nn 8 mpd boothead:~>

comsol –nn 8 batch –inputfile in.mphhead:~>

comsol mpd allexit

head:~>

comsol –nn 8 mpd boothead:~>

comsol –nn 8 batch –inputfile in.mphhead:~>

comsol mpd allexit

head:~>

comsol –clustersimple –nn 8ead:~>comsol –clustersimple –nn 8

See comsol h

for details


115/130

Four Ways to Run a Cluster job, cont

3. Start the COMSOL desktop GUI as a normal (non cluster) process on theheadnode. Then add a Cluster Computing feature to the model tree,

which branches off from the GUI a cluster job as a batch job. – Allows interactive modeling, and

cluster job submission as a separated batch job from the COMSOL Deskop GUI.

– No command line proficiency needed

– Allows you to submit and queue multiples jobs (different scenarios) from one

COMSOL Desktop process and continue working while the jobs are computing BUT…

– Consumes 1 or 2 license seats depending on

cluster configuration (regardless of number of compute nodes used).

head:~>

comsolead:~>

comsol


116/130

Four Ways to Run a Cluster job, cont

4. Start the COMSOL desktop GUI locally on a computer, separated fromthe Linux cluster (like a Macintosh or Windows PC). Then start a cluster-

enabled COMSOL server on the cluster. Connect the desktop client to

the COMSOL server – Same as alternative 2 above, except that the COMSOL desktop is on a work computer,

separated from the cluster.

head:~>comsol server -nn 8 –clustersimplehead:~>comsol server -nn 8 –clustersimple client/server


117/130

Two Ways of Using Clusters for Simulation

Parametric sweeps Distributed


118/130

The performance of the cluster

Each NODE contains:

CPU

CoresRAM

Communication Links

(MPI)

More nodes are faster, but performance is also a function of :

• Cores per Node

• Speed of each Core

• RAM per Node

• Communication Link Speed


119/130

Definitions

Host: Hardware physical machine with

network adapter and unique

network address. Part of the cluster.

Listed in mpd.hosts. Sometimes referred

to as physical node.

Core: Processor core.

used in Shared-memory

parallelism by a COMSOL

computational node,

through SMP (Shared-

Memory Processing)

Computational node:

COMSOL process.

Communicates with other

computational nodes through

MPI


120/130

Windows HPC Server 2008

COMSOL

DesktopHead

Node

Windows HPC

Server 2008

Scheduler (job

manager)

nodes

nodes

nodes


121/130


122/130

Which solvers support distribution?

• Parametric sweeps: All default solvers

• Distributed solve: Direct solvers SPOOLES or MUMPS

P i B fit S d (HPCS 2008R2)


123/130

Primary Benefit: Speedup (HPCS 2008R2)

p

pT

T S 1

0

2

4

6

8

10

12

1 2 4 6 8 10 12

S p e e d u

p

Number of Nodes

Definition:

P – number of nodes

T1 – Sequential execution time

Tp – Parallel execution time


124/130

V L M d l


125/130

Very Large Models

Ab b d R di ti i th H B i


126/130

Absorbed Radiation in the Human Brain


127/130

Primar Benefit E tended Memor


128/130

Primary Benefit: Extended Memory

One node: Out of RAM; killed after one hour.

Four nodes: Solution fits in RAM; solves in 5 minutes.


129/130

4PM?

End of Session


130/130

COMSOL 4.2A HIGHLIGHTS

http://www.comsol.com/products/4.2a/
http://www.comsol.com/products/4.2a/http://www.comsol.com/products/4.2a/

Documents

Comsol 2 Day Advanced Day1