General Presentation 2007

8/6/2019 General Presentation 2007

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1 J. KORELC, UNIVERSITY OF LJUBLJANA

On-demand numerical code generationand

finite element analysis

AceShareFinite Element FileSharing

AceGenMulti-language, Multi-

environment Numerical CodeGeneration

AceFEMThe Mathematica Finite

Element Environment


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AceGenMulti-language, Multi-environment Numerical CodeGeneration

Key features:

simultaneous derivation of expressions, global optimization ofexpressions and generation of program structure

automatic selection of the appropriate intermediate variables forward and backward mode of automatic differentiation technique

multi-language code generation (Fortran/Fortran90, C, Mathematicalanguage, Matlab language),

the generated codes are higly efficient and portable

symbolic derivation of the characteristic quantities needed in numericalprocedures (e.g. gradients, tangent operators, sensitivity vectors, etc.)

automatic interface to general environments (MathLink connection toMathematica, Matlab) and specialized FEM environments

(AceFEM, FEAP, ELFEN, ABAQUS,...)


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AceGen - highlights

AceGenAceGen

- symbolic input- problem formulation

- user subroutines

- interface code- initialization- numerical integration

-

C FORTRANMathematica

numericalnumerical user subroutinesuser subroutines

MATLAB

AceFEM

CDriver

FEAPELFEN

MDriver ABAQUS

Numerical environmentsNumerical environments

MATLABMathLink

.


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AceGen - highlights

heuristic procedures

random signatures ofexpressions

[ ]K

EIL

EIL

EIL

EIL

EI

L

EI

L

EI

L

EI

LEI

L

EI

L

EI

L

EI

L

EI

L

EI

L

EI

L

EI

L

0

3 2 3 2

2 2

3 2 3 2

2 2

12 6 12 6

6 4 6 2

12 6 12 6

6 2 6 4

=

Original matrix(input for code generator):

AceGen

{ }vEI

L

v L v L=

12

2

2

331 2

vector ofauxiliaryvariables

internaldata base

[ ]K

v v v v

v v vv

v v v v

vv

v v

S

=

1 2 1 2

2 3 23

1 2 1 2

23

2 3

2

2

Result is simplified matrix, expressed with thenew auxiliary variables

Mathematica

Simultaneous optimizations of expressions:

user


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AceGen - highlights

"If" construct

"Do" construct

HInitializationL

SMSInitialize@"test", "Language" >

"C++", "Mode" "Optimal"D;

HDefinition of a new subroutineL

SMSModule@"Test",

Real@x$$, f$$, dfdx$$DD;

HNumericsymbolic interfaceL

x SMSReal@x$$D;

HDerivation of the problemL

Cos@xD;

SMSIf@SMSAbs@D > 1010D;

f Sin@2 2D ;

SMSElse@D;

f SMSFreeze@Limit@

Sin@2 2D , 0D, "Dependency",

88, Limit@D@Sin@2 2D , D

Evaluate, 0D


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AceGen - highlights

differentiation of the whole program

Reverse mode / Forward mode

Enhancements with respect to the standard AD technique: AD procedure can be initiated at any time and at any point of

derivation of the formulas and as many times as required

AD as code-to-code translator is replaced by the method thatconsistently extends current code rather than produce a new one

the results of all previous uses of AD are accounted for when AD isused several times inside the same subroutine

exceptions handling mechanisms

Automatic differentiation technique (AD):


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AceGen - highlights

1. Mathematical description 2. Symbolic description in AceGenSMSInitialize@"test", Language > "C++"D

SMSModule@"Test", 8u1$$@3D, x$$, L$$, g$$@3D


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X[1];

v[31]=es->Data[0];

v[32]=es->Data[1];v[33]=es->Data[2];

v[34]=sqrt(Power(v[35],2)+Power(v[37],2));

subroutine elmt10(d,ul,xl,ix,tl,s,p,ndfe,ndme,nste,isw)

implicit none

include 'sms.h'

integer ix(nen),ndme,ndfe,nste,isw,INTEGRATIONCODE

double precision xl(ndme,nen),d(*),ul(ndfe,nen,*)double precision s(nste,nste),p(nste),tl(nen),sxd(24)

double precision sall(33,33),pall(33),du(24),dh(9)

double precision ul0(ndfe,nen),sg(24),sg0(24)

character*50 SELEM,datades(2),postdes(0)

logical DEBUG

parameter (INTEGRATIONCODE=7,DEBUG=.false.,

# SELEM="Hypersolid")

integer i,j,jj,ll,ii,k,kk,i1,i2,i3,hlen,icode

double precision w,v(5409),gpost(64,0),npost(8,0)

integer ipordl(30)

data (ipordl(i),i=1,30)/1,4,3,2,1,2,6,5,1,2,1,5,8,4,1,

& 4,8,7,3,4,3,7,6,2,3,7,8,5,6,7/

1235 format(i3,">",3g17.9)


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Key features:

hybrid symbolic-numeric FEM environment

AceFEM combines use of Mathematicas features with externalhandling of intensive computations by compiled modules

customized FEM-based applications in Mathematica.

AceFEM combines use of Mathematicas features with externalhandling of intensive computations by compiled modules

support for web-based FEM throught webMathematica

parallel optimisation throught gridMathematica

build-in structured mesh generation and interface to GID generalpreprocessor

fast sparse solvers, exact sensitivity analysis, etc.

AceFEMThe Mathematica FiniteElement Environment


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Key features:

enables browsing and downloading the FE user subroutines fromstandard and third-party on-line libraries

provides mechanism for the formation of the third-party libraries to beposted on the internet

includes symbolic templates for direct and exact sensitivity analysis ofsteady state, transient, coupled and coupled transient problems

available libraries include AceGen templates and user subroutine source

codes for solid, structural, thermal and contact FE for all supportedenvironments (FEAP, ELFEN, AceFEM, AceFEM-MDriver,ABAQUS, )

AceShare is ideal medium for the dissemination and verification ofnew numerical methods

AceShareFinite Element FileSharing


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AceFEM FEM environment

AceFEM

- input data processing- mesh generation- solution strategies- command language- graphic post-processing

General proceduresGeneral procedures

MathematicaMathematica

element 1.dll file

element 2.dll file

element ....dll file

- data base

- evaluation of element quantities- assembly of element contributions- various linear solvers

CDriverCDriver

C languageC language

dynamic link

MathLink

AceShareAceShare

- FEM file sharing system- download .dll or .m files

element 2.m file

element ....m file

MDriverMDriver

element 1.m file

- Mathematica language- data base in MMA- evaluation of element quantities- assembly of element contributions- MMA linear algebra


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AceFEM - highlights: Multi - field problems induction heating

T. utar , C3M - Ljubljana, Slovenia

Magnetic Thermal Mechanical


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AceFEM - highlights: Multi-scale problems

MACRO - elastic properties of contact surface

MICRO - 3D surface roughness

MACRO - thermal properties of contact surfaceMACRO - lubricant flow in contact surface

S. Stupkiewicz, IPPT, Warsaw, Poland


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AceFEM - highlights: structural analysis Sensitivity analysis of single-storey steel building

four node shell elements and large displacement truss elements

A

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50

Roof angle (deg)

Sensitivity

Analitic (elastic)

Finite differeces (elastic)

Analitic (plastic)

Finite differeces (plastic)


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AceFEM - highlights: Simulation of technological process

Two phase forging

J. Lengiewicz, IPPT, Warsaw, Poland


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Ways to use the system AceGen as multi-language code generator

translates MMA input into efficient C, Fortran, Matab code no calls to external subroutines

AD

AceGen as generator of finite elements for specific environments templates provided for some commercial and research environments finite element environments have large user groups (ABAQUS

several 1000) and companies that make specialized elements

finite elements for specific purpose can be expensive

AceFEM (independent finite element environment)

AceGen + AceFEM complete Finite Element System

commercial linear solver (Intel MKL), meshing,

Documents

General Presentation 2007