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Tuning Free CAE Mechanical Engineering Laboratory, METI Akira TEZUKA March 5, 2001

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Page 1: Tuning Free CAE - AIST

Tuning Free CAE

Mechanical Engineering Laboratory, METI

Akira TEZUKA

March 5, 2001

Page 2: Tuning Free CAE - AIST

 Position of CAEPosition of CAEPosition of CAEPosition of CAE CAD→CAE→Design→。。。

 Property of FEMProperty of FEMProperty of FEMProperty of FEM ArbitraryS h a p e

Inhomogenousmaterial

CommercialS o f t w a r e

P a r a l l e lComputing

MathematicalB a c k g r o u n d

FEM

( S o l i d )

FDM ×

( F l u i d ) ×

BEM × × ×

CAD→FEM software→Design。。。

It is not so simple in reality!

Page 3: Tuning Free CAE - AIST

 HeadacheHeadacheHeadacheHeadache(1)(1)(1)(1)::::3D Mesh Generation3D Mesh Generation3D Mesh Generation3D Mesh Generation  From CAD data・Dilectly TETRA/HEXA mesh generation・Interactively TETRA/HEXA mesh generation

Cause for time eating:Good quality mesh is required

→Accuracy dependent to mesh quality

Two-week task(although reduced to 1/3)(Hitachi’s mesher (JSME prize winner))

→Poor reliability?

→Time consuming

Page 4: Tuning Free CAE - AIST

Many researches as a detour

・Mesh free scheme Only nodes are required. Bad time complexity.

 Element-free Galerkin scheme Partition of Unity scheme hp-cloud scheme          Cells for integration are needed. Free mesh scheme          Locally & temporarily generated elements around a node.

 Voxecell mesh scheme          Large scale FEA with zigzag mesh

Page 5: Tuning Free CAE - AIST

 HeadacheHeadacheHeadacheHeadache(2)(2)(2)(2)::::from from from from FEMFEMFEMFEM((((SimulationSimulationSimulationSimulation)))) to to to to Design(ControlDesign(ControlDesign(ControlDesign(Control)))) 

Interactive deign process by parameter changes on trial & errors(Remeshing is required if shape is drastically changed.)

CAE replaces only experiments. The other is in old fashion.

 Tuning Free CAE 

CAE without special technique and intuition

  HeadacheHeadacheHeadacheHeadache (3)(3)(3)(3)::::No good software for Fluid or Combustion 

  HeadacheHeadacheHeadacheHeadache (4)(4)(4)(4)::::Time eating coding for parallel computation    

Page 6: Tuning Free CAE - AIST

 Seamless CAE from CAD to RP  Voxcell mesh scheme+Optimal topology design

Tuning free based on Massively large scale parallel computation

→Inaccurate compared with conventional CAE?No problems?

 Two possible directions toward tuning free CAE Massively large scale parallel computationImprovement numerical method

→Quantity

→Quality

Page 7: Tuning Free CAE - AIST

TuningTuningTuningTuning----free Computational Mechanicsfree Computational Mechanicsfree Computational Mechanicsfree Computational Mechanics

(1)(1)(1)(1)Tuning FreeTuning FreeTuning FreeTuning Free ((((from Intuition to Technologyfrom Intuition to Technologyfrom Intuition to Technologyfrom Intuition to Technology))))

・・・・Full Automatic Mesh GeneratorFull Automatic Mesh GeneratorFull Automatic Mesh GeneratorFull Automatic Mesh Generator

Interactive process by user was omittedInteractive process by user was omittedInteractive process by user was omittedInteractive process by user was omitted ((((from interactive to fullfrom interactive to fullfrom interactive to fullfrom interactive to full----automaticautomaticautomaticautomatic))))

・・・・Adaptive Finite Element MethodAdaptive Finite Element MethodAdaptive Finite Element MethodAdaptive Finite Element Method

Error control with a posterioriError control with a posterioriError control with a posterioriError control with a posteriori error estimation) error estimation) error estimation) error estimation) ((((free from experiencefree from experiencefree from experiencefree from experience----based mesh generationbased mesh generationbased mesh generationbased mesh generation))))

・・・・Optimal Parameter DesignOptimal Parameter DesignOptimal Parameter DesignOptimal Parameter Design

Optimization under constraintsOptimization under constraintsOptimization under constraintsOptimization under constraints((((Sheet metal formingSheet metal formingSheet metal formingSheet metal forming)))) ((((free from experiencefree from experiencefree from experiencefree from experience----based designbased designbased designbased design))))

・・・・New FEM for New FEM for New FEM for New FEM for DiscontinuousDiscontinuousDiscontinuousDiscontinuous HEXA Mesh HEXA Mesh HEXA Mesh HEXA Mesh

FEM with improved MLS for FEM with improved MLS for FEM with improved MLS for FEM with improved MLS for discontinuousdiscontinuousdiscontinuousdiscontinuous mesh mesh mesh mesh ((((Simplify interactive mesh generationSimplify interactive mesh generationSimplify interactive mesh generationSimplify interactive mesh generation))))

・・・・Common Platform on Parallel ComputationsCommon Platform on Parallel ComputationsCommon Platform on Parallel ComputationsCommon Platform on Parallel Computations ((((Free from coding for parallel computation.)Free from coding for parallel computation.)Free from coding for parallel computation.)Free from coding for parallel computation.)

Common template for parallel FEM/FDM/FVM. Common template for parallel FEM/FDM/FVM. Common template for parallel FEM/FDM/FVM. Common template for parallel FEM/FDM/FVM.

(2)(2)(2)(2) Numerical Method ahead of HardwareNumerical Method ahead of HardwareNumerical Method ahead of HardwareNumerical Method ahead of Hardware’’’’s Progress s Progress s Progress s Progress ((((hardware<softwarehardware<softwarehardware<softwarehardware<software))))

・・・・SpacSpacSpacSpaceeee----Time Time Time Time StabilizedStabilizedStabilizedStabilized Adaptive Fluid FEM Adaptive Fluid FEM Adaptive Fluid FEM Adaptive Fluid FEM

Exponential effects with adaptive meshExponential effects with adaptive meshExponential effects with adaptive meshExponential effects with adaptive mesh

Page 8: Tuning Free CAE - AIST

    Adaptive Space-time Stabilized FEMAdaptive Space-time Stabilized FEMAdaptive Space-time Stabilized FEMAdaptive Space-time Stabilized FEM    Stabilized FEM : Numerically stable steady FEM even with coarse mesh (T.Hughes)Stabilized FEM : Numerically stable steady FEM even with coarse mesh (T.Hughes)Stabilized FEM : Numerically stable steady FEM even with coarse mesh (T.Hughes)Stabilized FEM : Numerically stable steady FEM even with coarse mesh (T.Hughes)

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

GGGGaaaalllleeeerrrrkkkkiiiinnnnGGGG LLLL SSSS

φ

x-coordinate

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

GGGGaaaalllleeeerrrrkkkkiiiinnnnGGGG LLLL SSSS

φ

x-coordinate

????φφφφ

xxxx

uuuu uuuukkkk

1111

0000

Advection-diffusion steady problem in 1D(u=50, k=1)

mesh with 100 elements mesh with 10 elements

Page 9: Tuning Free CAE - AIST

tttt0000====0000:::: IIIInnnnppppuuuutttt iiiinnnniiiittttiiiiaaaallll ccccoooonnnnddddiiiittttiiiioooonnnn

uuuunnnniiiiffffoooorrrrmmmm mmmmeeeesssshhhhSSSSppppaaaacccceeee----ttttiiiimmmmeeee GGGGLLLLSSSS FFFFEEEE aaaannnnaaaallllyyyyssssiiiissss wwwwiiiitttthhhh

AAAA ppppoooosssstttteeeerrrriiiioooorrrriiii eeeerrrrrrrroooorrrr eeeessssttttiiiimmmmaaaatttteeee

AAAAddddaaaappppttttiiiivvvveeee mmmmeeeesssshhhh ccccoooonnnnttttrrrroooollll iiiinnnn xxxxyyyy----ddddiiiirrrreeeeccccttttiiiioooonnnn

SSSSppppaaaacccceeee----ttttiiiimmmmeeee GGGGLLLLSSSS FFFFEEEE aaaannnnaaaallllyyyyssssiiiissss wwwwiiiitttthhhh

ttttnnnn++++1111 ==== ttttnnnn++++ddddtttt

ttttnnnn++++1111>>>>ttttmmmmaaaaxxxx OOOOuuuuttttppppuuuutttt tttthhhheeee rrrreeeessssuuuullllttttyyyyeeeessss

nnnn oooo

aaaaddddaaaappppttttiiiivvvveeee mmmmeeeesssshhhh

PPPPr rrro oooj jjje eeec ccct ttti iiio ooon nnn

Algorithm

・Space-time scheme :Stable unsteady treatment with mesh in time-direction (T.Hughes)

∆∆∆∆ttttttttnnnn++++1111

----

ttttnnnn++++

ttttnnnn----hhhhjjjj----1111 hhhhjjjj

jjjj----1111 jjjj jjjj++++1111

tttt

xxxx yyyyh: mesh size in y-direction; ∆t: mesh size in t-direction

Space-time mesh

・Adaptive remeshing:Mesh improvement with a posteriori error estimate (A.Tezuka, etc)

Page 10: Tuning Free CAE - AIST

(-0.5,0.5)

(-0.5,-0.5)

y

x

φ =0

φ =0 φ =0

φ=0

u1=-yu2= x

A

A FLOWDIRECTION

VIEWINGDIRECTION

(0.5,0.5)

(0.5,-0.5)

A A

(t=0)

0.0

1.0 φ

k=0

Lotating cone problem   (Benchmarch)

Initial condition on φ

Application to Advection-Diffusion Problem (Direct mapping scheme)                              (A.Tezuka)

max= 1.0min= 0.0

Page 11: Tuning Free CAE - AIST

Profile of φ after one rotation

History of max & min of φ

HEXA850*50 meshdt=0.066695 steps

HEXA8h-adap.dt=0.066695 steps

CPUtime375sec@Sparc Ultra 2

CPUtime 165sec@Sparc Ultra 2

max= 0.9937min=-0.0076

max= 1.0089min=-0.0072

Page 12: Tuning Free CAE - AIST

 Optimal Parameter DesignOptimal Parameter DesignOptimal Parameter DesignOptimal Parameter Design 

Sheet Metal Forming・Used at consumer products, automobile・To avoid tearingControlled by draw bead forces

Ordinary & Inverse Problem・Ordinary Problem(FEA)

・Inverse Problem(Optimal Design)

Conventional Process・By experiments based experience andintuition・By trial and error with FEA

Optimal Parameter DesignOptimal choice of draw bead forceRigid-plastic FEA with modifiedmembrane elementOptimal search(Response SurfaceMethod)Evaluated at deep drawing

Input DataInput DataInput DataInput Data Fixed Process Parameters (Blank etc.) Variable Process Parameters (Bead Force)

FE AnalysisDeformed Shape and Strain

Objective Function and Constraints

Minimum Search Searching of the Optimal Values

Converge??

ParameterUpdate

Page 13: Tuning Free CAE - AIST

Optimal Search EngineOptimal Search EngineOptimal Search EngineOptimal Search Engine1.Based on sensitivity(SQP, BFGS,etc) (1) By finite difference approximation2n+1 times FEA for n design variables

(2) By direct differentiation

2.Based on response of model (1) By genetic algorithm (GA) (2) By response surface ・Globally approximated quadratic function against real response・Valid for discretized values・Previous data can be added in database・Less possibility for local minimum convergence・Easy for implementation・Approximated scheme, but sufficient in engineering

i

ii

i ppp

p ∆∆−−∆+=

∂∂

2)()( pp φφφ

・Problems on sensitivity1) Possible local minimumconvergence2) Bad convergence w/ many designvariables3) Bad time complexity at FDA4) Implementation needed at directapproach

・Problems on GADisaster with large number of variables

00 =∂∂+

∂∂+

∂∂→=−+=

pX

XR

pU

UR

pRFQQR bm

dd

dd

Page 14: Tuning Free CAE - AIST

Bead Force Optimization Bead Force Optimization Bead Force Optimization Bead Force Optimization ((((square cup drawing)))) (S.H.Kim & A.Tezuka)

・AssumptionConstant draw bead forces during the process

・Optimal target

Weak Part

mesh

Optimization Region Draw-bead

Model and mesh

Additional strain needed at weak part

stress-strain               MpaLankford values (r0,r45,r90)=(1.833,1.434 ,2.016)Thickness : t = 0.69 mmBlank size: 130mm×170mm

Coulomb friction coeff. : 0.11

274.0)0009.0(576 εσ +=

Page 15: Tuning Free CAE - AIST

Object FunctionObject FunctionObject FunctionObject Function

0p ≥CEE ~

1 <UUUU: displacement、XXXX: coordinates、pppp: process parameter(eq. draw bead force)

 : major principal strain

0E if EEE~ , 0E if EEE~ 2O212O21 >+=≤+−=

0E if EEE~ , 0E if EEE~ 2cO2c2cO2c >+=≤+−=

1E

1~E

Subject to

( ) Ω−=Φ ∫Ω dEEEopt

2

11~)),),(),(((.min pppXpU

(bead force must be positive)

(to avoid tearing)

:Target value

:boundary line for the fracture regionCE~

0

10

20

30

40

50

60

-20 -10 0 10 20Minor Principal Strain (%)

Maj

or

Pri

ncip

al S

trai

n (

%)

Constraint Line

Target Lin

Target line and constraintline on the forming limitdiagram

Page 16: Tuning Free CAE - AIST

0

5

10

15

20

-10 -5 0 5 10

Minor Strain (%)

Maj

or

Str

ain (

%)

Target LineOptimum ValueInitial Guess

Principal strain distributionbefore/after optimization process

Optimization Region Draw-bead

-20

30

80

130

180

0 10 20 30 40

Y coordinate of Bead Points (mm)

Bea

d Pre

ssur

e (

N/m

m)

initial guess25t28t31t45t

mesh

Equivalent bead forces during optimization

Page 17: Tuning Free CAE - AIST

Response Surface MethodologyResponse Surface MethodologyResponse Surface MethodologyResponse Surface Methodology・2n+1 FEA are needed to generate quadratic response surface・Perturbation at each draw bead point around initial value,50 N/mm

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

1 2 3 4 5 6 7 8 9 1 0 1 1

Pr o c e s s Pa r a me t e r Nu mb e r

Sens

itiv

ity

of t

he O

bjec

tive

Fun

ctio

n(m

m**4

/N)

p e r t u r b a t i o n =1 0 * * - 2p e r t u r b a t i o n =1 0 * * - 3p e r t u r b a t i o n =1 0 * * - 4

- 6 . E- 0 2

- 4 . E- 0 2

- 2 . E- 0 2

0 . E+0 0

2 . E- 0 2

4 . E- 0 2

6 . E- 0 2

8 . E- 0 2

1 2 3 4 5 6 7 8 9 1 0 1 1

Pr o c e s s Pa r a me t e r Nu mb e r

Sens

itiv

ity

of t

he c

onst

rain

t (1

/N)

p e r t u r b a t i o n =1 0 * * - 2p e r t u r b a t i o n =1 0 * * - 3p e r t u r b a t i o n =1 0 * * - 4

Sensitivity on object function and constraints

Page 18: Tuning Free CAE - AIST

 Discontinuous meshed mesh (DCMM) FEM  (C. Oishi, A.Tezuka & N. Asano) 

Element-Free Galerkin Method               (T. Belytschko)

・ Integration unit in FEM and EFGM

  (a) FEM         (b)EFGM

・Differences between FEM and EFGM

F E MF E MF E MF E M E F G ME F G ME F G ME F G M

Weak formWeak formWeak formWeak form Galerkin methodGalerkin methodGalerkin methodGalerkin method Galerkin methodGalerkin methodGalerkin methodGalerkin method

ApproximationApproximationApproximationApproximation

function function function function

InterpolationInterpolationInterpolationInterpolation

functionfunctionfunctionfunction

defined in elementdefined in elementdefined in elementdefined in element

MLS functionMLS functionMLS functionMLS function

defined at defined at defined at defined at

integrationintegrationintegrationintegration point point point point

Integration unitIntegration unitIntegration unitIntegration unit ElementElementElementElement Background cellBackground cellBackground cellBackground cell

Nodal valueNodal valueNodal valueNodal value iiih UxU =))))(((( iii

h UxU ≠))))((((

RequiredRequiredRequiredRequired

informationinformationinformationinformation

Elements and nodesElements and nodesElements and nodesElements and nodes Nodes onlyNodes onlyNodes onlyNodes only

Time Time Time Time complexitycomplexitycomplexitycomplexity GoodGoodGoodGood BadBadBadBad

Page 19: Tuning Free CAE - AIST

Moving Least Squares Method(MLSM)Derived only with info. of nodes around an evaluation point

(a) EFGM     (b) FEM

    Interpolation by nodes in support domain

  m : number of basis in pj, n : number of nodes in support domain

  φI: approximation function in MLS

Coefficients aJ are decided in minimization of J

・Exponential weight function

node × evaluation point interpolation

domain of influence

2

1

)()()(

−−= ∑∑

=I

m

JJJI

n

II uapwJ xxxx

∑∑==

≡=n

IIIJ

m

JJ

h uapu11

)()()(( xxxx) φ

( )=2II dw ( )

,1

2

22

)/(

)/()/(

mII

mIIcd

cdcd

dd

dde

eemI

mII

>0

≤−

−−

−−

|||| II xxd −=

Page 20: Tuning Free CAE - AIST

Upper part fixed Yong’s modulus 2.1×105 MPaPulled plate  Poisson’s ratio 0.3

5125 nodes 3955 nodes3520 elements 2490 elements

238 constraints

    

     a)Continuous mesh  b)Discontinuous meshPulled plate with pipe

Example

Page 21: Tuning Free CAE - AIST

Deformation

c) improved EFGM

d) DCMM-FEM

(scaled by 5,000)

a) FEM

b) NLCM

Page 22: Tuning Free CAE - AIST

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1

y-di

spla

cem

ent

[fe

m=1]

FEM

im

DCMM-FEM

FE-改良型EFGM

NLCM

Computational time

00.20.40.60.8

11.21.41.61.8

2

1

Com

puta

tional tim

e[N

LC

M=1] NLCM

DCMM-FEM

FE-改良EFGM

Evaluation

Page 23: Tuning Free CAE - AIST

 Common Platform for Parallel ComputationsCommon Platform for Parallel ComputationsCommon Platform for Parallel ComputationsCommon Platform for Parallel Computations                ((((Collaboration with Fuji Research InstituteCollaboration with Fuji Research InstituteCollaboration with Fuji Research InstituteCollaboration with Fuji Research Institute))))

Target:Researchers on computational mechanics

→Limited with FEM/FDM/FVM

Purpose:Easy shift to parallel computations

→Simple procedure on modification with MPI

Point:Flexible for modification

→Common for FEM/FDM/FVM

Method:General purpose reliable schemes

→Domain de composition. Interface with free software

Page 24: Tuning Free CAE - AIST

Motivations

For fast computation

・I’d like to replace with fast matrix solver

・I’d like to generate stiffness matrix more fast

For large scale computation

・I‘d like to save memory at matrix solver

・I‘d like to save memory at generating stiffness matrix

Problems

・Time consuming task to modify a program with MPI forparallel computations

・Parallel matrix solver such as PETSc, Aztec, and GEOFEMare for professional researchers on parallel computations

・FEM/FDM/FVM are individually developed.

Page 25: Tuning Free CAE - AIST

1.Required data

・Nodal info(num. of element,ndf,coordinates)・Element info(num. of element,connectivity)・Boundary condition(fix,slide,constraint)・Load condition・Subroutine to construct stiffness matrix

2.GMRES and BiCGSTAB are equipped

3.Partitioning by MeTiS

4.Parallel efficiency more than 70% at SR8000@32 nodes

Requirements on parallel platform

Page 26: Tuning Free CAE - AIST

Use of Partitioning ToolUse of Partitioning ToolUse of Partitioning ToolUse of Partitioning Tool

• Interface for partitioning tool(MeTiS)

Mesh data

Partitioning tool (MeTiS) Index for

Partitioning

Parallel platform

User’s program

Page 27: Tuning Free CAE - AIST

How to use Parallel Platform

User’sApplication

Programinfo. of domain de composition

Global stiffness matrix

BC setting

Matrix

Subroutinesin Platform

Method 2

SampleProgram

in Platforminfo. of

node/element

info. of domain de composition

Stiffness matrix

BC setting

User’sSubroutines

Method1

Page 28: Tuning Free CAE - AIST

Modification method for FEM program

• Pattern1– Stiffness matrix

generated at master PE,then solver called

• Pattern2– Stiffness matrix

generated at each PE,then solver called.

DI MENSI ON Ai j () , WORK() , Bi () , I DOMAI N()CALL MPI I NI T( . . . ) ;MPI i ni t i a l i z e d

s e t I DOMAI N( I ) ; Pa r t i t i on i nf o.

DO I =1, 要素数 ; St i f f . Ma t r i xI F( I DOMAI N( I ) . EQ. MYRANK) THEN ; a t Ea c h PE・・・・・Ai j () =END I FEND DO

CALL GM3_SOLVE( Ai j , Bi , I DOMAI N, . . . , WORK) ;Sol ve r

CALL MPI FI NALI ZE( . . . ) ;MPI t e r mi na t e dSTOPEND

DI MENSI ON Ai j () , WORK() , Bi ()CALL MPI _I NI T( . . . ) ;MPI i ni t i a l i z e d

I F( MYRANK. EQ. 0) THEN ;a t Ma s t e r PEDO I =1, 要素数 ; St i f f . Ma t r i x・・・・・Ai j () =END DOEND I F

CALL GM2_SOLVE( Ai j , Bi , . . . , WORK) ;Sol ve r

CALL MPI _FI NALI ZE( . . . ) ;MPI t e r mi na t e dSTOPEND

Page 29: Tuning Free CAE - AIST

  Flow at PlatformFlow at PlatformFlow at PlatformFlow at Platform  

Global Data

Input

Input

Input

Input

MPI

Generate index for matrix solver

Generate matrix

Transfer data to global storage

Matrix solvers

MPI

MPI

MPI

Generate matrix

Generate matrix

Generate matrix

Output

Output

Output

Output

Output Data

・Mesh Data nodes/elements, coordinates, element connectivity, partitioning index(by MeTis)・Control Data boundary conditions, material values, time step, etc

Page 30: Tuning Free CAE - AIST

 Example:3D Crankshaft  ((((by graduate student at Yokohama nationalby graduate student at Yokohama nationalby graduate student at Yokohama nationalby graduate student at Yokohama national Univ Univ Univ Univ. . . . ))))

x

y

3D elastic FEM model with boundary/load conditions

Page 31: Tuning Free CAE - AIST

Elastic model, 79,043 nodes, 62,968 HEXA elementsElastic model, 79,043 nodes, 62,968 HEXA elementsElastic model, 79,043 nodes, 62,968 HEXA elementsElastic model, 79,043 nodes, 62,968 HEXA elements

Partitioning by Partitioning by Partitioning by Partitioning by MeTiS MeTiS MeTiS MeTiS for 8 CPUfor 8 CPUfor 8 CPUfor 8 CPU

Page 32: Tuning Free CAE - AIST

Elapsed time 541 sec , 8 CPUs in Hitachi SR8000

DeformationDeformationDeformationDeformation

One hour modificationOne hour modificationOne hour modificationOne hour modification

Page 33: Tuning Free CAE - AIST

Big projects on computational mechanics in JapanBig projects on computational mechanics in JapanBig projects on computational mechanics in JapanBig projects on computational mechanics in Japan

1.1.1.1.Earth Simulator ProjectEarth Simulator ProjectEarth Simulator ProjectEarth Simulator ProjectWhole earth is modeled and analyzed with CAEWhole earth is modeled and analyzed with CAEWhole earth is modeled and analyzed with CAEWhole earth is modeled and analyzed with CAEPrediction of the global warming phenomenon with 1 km meshPrediction of the global warming phenomenon with 1 km meshPrediction of the global warming phenomenon with 1 km meshPrediction of the global warming phenomenon with 1 km meshParallel computer with 30TFLOPS will be developedParallel computer with 30TFLOPS will be developedParallel computer with 30TFLOPS will be developedParallel computer with 30TFLOPS will be developedAmount of project money is $0.4 billion for 5 yearsAmount of project money is $0.4 billion for 5 yearsAmount of project money is $0.4 billion for 5 yearsAmount of project money is $0.4 billion for 5 years

・・・・GeoFEMGeoFEMGeoFEMGeoFEM (http://(http://(http://(http://geofemgeofemgeofemgeofem....tokyotokyotokyotokyo....ristristristrist.or..or..or..or.jpjpjpjp/index.html)/index.html)/index.html)/index.html)    (1997-2001)(1997-2001)(1997-2001)(1997-2001)

Multi-Purpose Parallel FEM System for Solid EarthMulti-Purpose Parallel FEM System for Solid EarthMulti-Purpose Parallel FEM System for Solid EarthMulti-Purpose Parallel FEM System for Solid EarthFree source code download availableFree source code download availableFree source code download availableFree source code download availablehttp://http://http://http://geofemgeofemgeofemgeofem....tokyotokyotokyotokyo....ristristristrist.or..or..or..or.jpjpjpjp////new_ennew_ennew_ennew_en/index.html/index.html/index.html/index.html

2.2.2.2. Adventure project Adventure project Adventure project Adventure project (http://adventure.q.t.(http://adventure.q.t.(http://adventure.q.t.(http://adventure.q.t.u-tokyou-tokyou-tokyou-tokyo.ac..ac..ac..ac.jpjpjpjp/)/)/)/)

ADVanced ENgineeringADVanced ENgineeringADVanced ENgineeringADVanced ENgineering analysis Tool analysis Tool analysis Tool analysis Tool for Ultra large for Ultra large for Ultra large for Ultra large REal REal REal REal world. world. world. world.Free source code download availableFree source code download availableFree source code download availableFree source code download availablehttp://adventure.q.t.http://adventure.q.t.http://adventure.q.t.http://adventure.q.t.u-tokyou-tokyou-tokyou-tokyo.ac..ac..ac..ac.jpjpjpjp/software/download.html/software/download.html/software/download.html/software/download.html

Page 34: Tuning Free CAE - AIST

Free FEM software for referenceFree FEM software for referenceFree FEM software for referenceFree FEM software for reference

1.1.1.1.for single processorfor single processorfor single processorfor single processor

(1) http://phase.etl.go.jp/mirrors/netlib/ (free code department store)

Recommendationshttp://phase.etl.go.jp/mirrors/netlib/slap/index.html(GMRES, BCG Matrix Solver. by Lawrence Livermore National Lab.)http://phase.etl.go.jp/mirrors/netlib/linalg/spooles/index.html(sparse real and complex direct matrix solver)http://phase.etl.go.jp/mirrors/netlib/voronoi/index.html(2D mesh generation, triangulation, and mesh display at X-Window)http://phase.etl.go.jp/mirrors/netlib/f2c/index.html(Convert Fortran 77 to C or C++)

Page 35: Tuning Free CAE - AIST

1.1.1.1.for single processor (for single processor (for single processor (for single processor (contcontcontcont.).).).)

(2) Information on FEMhttp://www.engr.usask.ca/~macphed/finite/fe_resources/node10.html(Various information of FEM)(My name is listed at http://www- users.informatik.rwthaachen.de/%7Eroberts/peoplelist.html :-)

(3) Etchttp://www.mech.port.ac.uk/sdalby/mbm/CTFRProg.htm(Binary source listed in Prof. Ross’s book)

http://www.quint.co.jp/Japanese/pro/vox/voxdemo/license.htm(VOXELCON developed by Prof. N. Kikuchi at U of Michigan)

Page 36: Tuning Free CAE - AIST

2. 2. 2. 2. for parallel computationfor parallel computationfor parallel computationfor parallel computation

http://www.cs.sandia.gov/CRF/aztec1.html(AZTEC)http://www-fp.mcs.anl.gov/petsc/(PETSc)http://geofem.tokyo.rist.or.jp/new_en/index.html(GEOFEM)http://adventure.q.t.u-tokyo.ac.jp/software/download.html(ADVENTURE)http://www-users.cs.umn.edu/~karypis/metis/(Partitioning software)

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IT related companiesIT related companiesIT related companiesIT related companies

1.1.1.1. INCSINCSINCSINCS (http://www.(http://www.(http://www.(http://www.incsincsincsincs.co..co..co..co.jpjpjpjp/)/)/)/)3D die for cellular phone. Internet driven factory.3D die for cellular phone. Internet driven factory.3D die for cellular phone. Internet driven factory.3D die for cellular phone. Internet driven factory.Averaged age is 24.5. Half are part-time employeesAveraged age is 24.5. Half are part-time employeesAveraged age is 24.5. Half are part-time employeesAveraged age is 24.5. Half are part-time employees.

Intuition & experienceIntuition & experienceIntuition & experienceIntuition & experience→→→→3D CAD+Database3D CAD+Database3D CAD+Database3D CAD+Database(for experts) (not for experts)(for experts) (not for experts)(for experts) (not for experts)(for experts) (not for experts)

2.2.2.2. TOYOTA motorsTOYOTA motorsTOYOTA motorsTOYOTA motorsSmall wagon Small wagon Small wagon Small wagon “bBbBbBbB” was developed only for was developed only for was developed only for was developed only for 12 months12 months12 months12 months

Trial units were not tested. CAE predicted everything.Trial units were not tested. CAE predicted everything.Trial units were not tested. CAE predicted everything.Trial units were not tested. CAE predicted everything.CAECAECAECAE’s result database decides the designs result database decides the designs result database decides the designs result database decides the design

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 Conclusions 

As examples of tuning free CAE,Adaptive space-time stabilized FEMOptimal process parameter designDiscontinuous mapped mesh FEMParallel platform for FEM/FDM/FVMare discussed.

We’d like to extend our research to

Multi-physics FEAMassively parallel computationsOptimal design with complicated constraintsInverse problem with large variablesin near future