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Tuning Free CAE
Mechanical Engineering Laboratory, METI
Akira TEZUKA
March 5, 2001
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!
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
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
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
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
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
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
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)
(-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
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
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
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
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 +=
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
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
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
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
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 −=
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
Deformation
c) improved EFGM
d) DCMM-FEM
(scaled by 5,000)
a) FEM
b) NLCM
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
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
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.
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
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
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
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
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
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
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
Elapsed time 541 sec , 8 CPUs in Hitachi SR8000
DeformationDeformationDeformationDeformation
One hour modificationOne hour modificationOne hour modificationOne hour modification
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
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++)
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)
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)
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
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
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