Introduction & Philosophy - inuTech · Introduction & Philosophy Peter Böhm, inuTech GmbH. Innovative Numerical Technologies 23. CADFEMUsers´ Meeting, Bonn 09.-11. ... ANSYS, CFX,

Innovative Numerical

Technologies

23. CADFEM Users´ Meeting, Bonn 09.-11. November 2005

Introduction & PhilosophyIntroduction & Philosophy

Peter Böhm, inuTech GmbH


Technologies


Outline Diffpack® -Session

14.00-15.00 Introduction & Philosophy

15.00-15.40 Main Steps Developing Your Own Simulator

16.20-16.40 Easy Use of Advanced Numerical Technologies

16.40-17.40 Complementary Use to Main Stream Analysis


Technologies


Outline

• inuTech - Innovative Numerical Technologies

• Diffpack - an overview

• Diffpack - the main philosophy

• Diffpack - how to realize

• Examples

– Heart

– Tsunami

– CFD


Technologies


inuTech


Technologies


FSV Consulting R&D, founded 1995

inuTech GmbH was established in June 2000

Share Holders: Prof. Schittkowski,

CADFEM International AG, F. Vogel

Currently 10 employees

FSV Consulting R&D, founded 1995

inuTech GmbH was established in June 2000

Share Holders: Prof. Schittkowski,

CADFEM International AG, F. Vogel

Currently 10 employees

inuTech - Our History


Technologies


inuTech - Our Objectives

Closing the Gap between

Engineering and Mathematics

to Solve Engineering and

Mathematical Problems

R&D of Numerical Methods Sales and Support of

Software

R&D of Numerical Methods Sales and Support of

Software

Seminars and Training Seminars and Training

Consulting Consulting


Technologies


Structural Optimization Topology Optimization Shape Optimization Sizing- and Parameter Optimization Large Scale Optimization Multi-Disciplinary Optimization Design of Experiments Biological Growth Free Material Optimization

(Composite Design)

Structural Optimization Topology Optimization Shape Optimization Sizing- and Parameter Optimization Large Scale Optimization Multi-Disciplinary Optimization Design of Experiments Biological Growth Free Material Optimization

(Composite Design)

inuTech - Our R&D Experience


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Project Partner

Universität Erlangen


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Diffpack - in general


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Differential Equations inuTech develops and markets the Diffpack Product

Line for the Numerical Modeling and Solution of Differential Equations

inuTech offers Consulting Services around Diffpack; we can deliver customized turn-key solutions for specialized simulation problems

Attention: Diffpack is a development environment, not an application!It allows you to generate asimulator (or to use an already developed simulator!)

Differential Equations inuTech develops and markets the Diffpack Product

Line for the Numerical Modeling and Solution of Differential Equations

inuTech offers Consulting Services around Diffpack; we can deliver customized turn-key solutions for specialized simulation problems

Attention: Diffpack is a development environment, not an application!It allows you to generate asimulator (or to use an already developed simulator!)

inuTech - Our R&D Experience


Technologies


Univ. of Oslo

Univ. of Erlangen

Univ. of Bayreuth

The Diffpack® Team


Technologies


The Diffpack® Distribution

Diffpack Development Framework

Diffpack Kernel(computing/numerics)

Diffpack Toolboxes

Third-Party Pre-/Postprocessors

OpenSource Pre-/PostprocessorsDiffpack

Utility

Programs

Books, Manpages,Reports

Supportphone/e-mail


Technologies


Applications

The Diffpack® Environment

Diffpack Kernel

Ada

ptiv

ity

Par

alle

l LA

Dat

a F

ilter

s

Par

alle

l DD

Mul

tigrid


Technologies


The Diffpack® Documentation


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List of Applications

• electrical activity in the heart (and body)

• continuous casting

• simulation of a solid-oxide fuel cell

• chemical reactor flow

• parasitics in high power electronics

• option pricing in finance

• water waves - structure impact

• hyperspherical black hole simulation

• tsunami simulation

• virtual rock physics laboratory

• heat treatment of cancer

• ...


Technologies


Diffpack - main philosphy


Technologies


Diffpack Kernel

Diffpack Toolboxes(further extensions)

Diffpack Kernel

Diffpack Toolboxes(further extensions)

The Diffpack® Vision

[ ] in

on

u f

u g

κ−∇ ⋅ ∇ = Ω= ∂Ω

“arbitrary” PDE, ODE,

or othernumerical problem

“arbitrary” PDE, ODE,

or othernumerical problem

+ = ownsolver

ownsolver

( ), ,v tt

∂ =∂s

F s


Technologies


The Diffpack® Vision (cont’d)

Structuralmechanics

Porous mediaflow

Aero-dynamics

Incompressibleflow

Other PDEapplications

Waterwaves

Electromagnetics

Heattransfer

Field

Grid

MatrixVector

I/O

Ax=b

FEM

FDM

Observation:Methodology basisindependent of applications


Technologies


• Flexible building blocks to develop solvers for non-standard oder specialized simulation problems

• for building highly customized ”trimmed-down” solverswith minimum overhead of unused functionality andunnecessary complexity

• Complementary to standard FEM-programs (i.e.ANSYS, CFX, etc. ...) to fill in the gaps in functionality

• Benefits are:• Applicable to all simulation problems that can be modeled by Differential Equations

• Exact modeling of physical effects• Control of numerical solution algorithm

Diffpack® – Tailored simulation


Technologies


for complex, new problems who require the abilityto do self-programming

Solverfor PDE1

STRUCT

• Scenario: Build and test (or use existing) solver for PDE1 (STRUCTURAL)

Diffpack® – Flexible Building Blocks


Technologies


for complex, new problems …

STRUCT

Solverfor PDE2

EMAG

•Build (or use existing) solver for PDE2 (Electro Magnetics)•Test EMAG Solver standalone •Couple EMAG Solver with Structural Solver



Technologies



STRUCT EMAG

Add in Heateffects

Heat

•Add in Heat effects to coupled solver



Technologies



STRUCT EMAG

Solverfor PDE3

CFD

Heat

•Build (or use existing) solver for PDE3 (CFD)•Test CFD Solver standalone •Couple CFD Solver



Technologies



STRUCT EMAG

CFD

Heat

Solverfor ODEs

ODEs

•Add ODEs (chemical reactions, kinematic, etc. ...) to the coupled system



Technologies



STRUCT EMAG

CFD

Heat

AddAdaptivity

ADAP

ODEs

•Add Adaptive Functionality



Technologies



STRUCT EMAG

CFD

Heat ADAP

ODEs

Parallel Funct.

PARALLEL

•Add Parallel Functionality



Technologies



STRUCT EMAG Heat ADAP

PARALLEL

•Do numerical experimentation and adjustments

NA1

NA2

Tune Domain Decomposition

NA4

…

Add Criteriafor elementrefinement

NA5

NonlinearSolver Adjustment

Add TissueMaterial model

NA3

Incorporatenew elementformulation

CFDODEs



Technologies



PrePost

Add advancedPre- and

Postprocessing

STRUCT EMAG

CFD

Heat ADAP

ODEsPARALLEL

NA1

NA2

NA3

NA4NA5

•Add advanced Pre- and Postprocessing



Technologies


PrePost


PrePost

Add GraphicalUser Interface

GUI

WB

Could beANSYS

Workbench!

STRUCT EMAG

CFD

Heat ADAP

ODEsPARALLEL

NA1

NA2

NA3

NA4NA5

•Add GUI



Technologies


At the end we have for example a solver to simulate the electrical activity in the human heart (Courtesy Simula Research, Oslo)

PrePostt

GUI

STRUCT EMAG

CFD

Heat ADAP

PARALLEL

NA1

NA3NA5

NA5

Heart Solver

Example – Heart Simulation


Technologies


The Diffpack® Intention

satisfy the criteria of numerical software by using Diffpack

• efficiency

• reliability

• robustness

• extensibility

• portability

• user-friendliness

focus on your own problem-specific parts


Technologies


The Challenge

Software DevelopmentSoftware Development

Num

eric

al M

etho

dsScientific Computing

Speed-Up 1,000,000 over last 50 years

Speed-Up 1,000,000 over last 50 years

Hardw

are Power

getSpeed-Up


Technologies


The Diffpack® Philosophy

• do not reinvent the wheel

• trust (to a certain extend) former developments

• make use of OOP in numerics -> Object Oriented Numerics

– inheritance

– virtual function

– polymorphism

• support high abstraction level

• offer suitable building blocks (modular design)

– stay as close as possible to the math

– avoid translation errors


Technologies


The Diffpack® Philosophy

• do not patronize the developer

– allow for arbitrary equations / combination of equation

– work on weak formulation

– allow for user defined extensions

• user defined new finite elements

• user defined new preconditioners

• user defined new solvers

• avoid bottle-necks of OOP


Technologies


software specialistwrites a program tosolve the problem

The Diffpack® Philosophy - build a common language

engineerhas a

problem

physicisthas a

physical description

comm

unication

mathematician numeric specialist

has a set of equations / solution

methods

software

available

engineer get datawhich tell him how

to solve theinitial problem

comm

unication

system admin / hardware specialisthas computer to run

on the program

comm

unication

comm

unication

comm

unication

communication

Diffpack: common languageDiffpack: common languagegives

defines


Technologies


Diffpack - how realized


Technologies


Diffpack® Implementation - high abstraction level

Example: Solve A*x=b by a CG method:

CALL NSPCP (PREC,ACCEL,NDIM,N,MAXNZ,COEF,JCOEF,P,IP,U,

UBAR,RHS,WKSP,IWKSP,NW,INW,IPARM,RPARM,IER)

Procedural language approach (ITPACK, Netlib):

OON (C++, Diffpack):

//Given Matrix A, Vector x, Vector bLinEqSystem system (A,x,b);LinEqSolver solver (method);

solver.solve(system);


Technologies


C+

+ C

lass

esC

++

Cla

sses

Diffpack® Implementation - inheritance

FEMFEMFEM

Fundamental library class for any simulation

OwnSimulatorOwnSimulatorOwnSimulatorGeneral implementation of the problem. Focus on numerics

Inheritance

SimCaseSimCaseSimCase

Inheritance

Fundamental library class for finite element methods


Technologies


Diffpack® Implementation - inheritance (cont’d)

FEMFEMFEM

OwnFDMSimulatorOwnFDMSimulatorOwnFDMSimulator

SimCaseSimCaseSimCase

FDMFDMFDMFVMFVMFVM

MxFEMMxFEMMxFEM

OwnMxSimulatorOwnMxSimulatorOwnMxSimulator


Technologies


Diffpack® Implementation - use weak formulation

[ ] in

on

u f

u g

κ−∇ ⋅ ∇ = Ω= ∂Ω

solve on operator level ×1

, 1,..., in

on

m

j i j ij

N N d u f N d i m

u g

κ= Ω Ω

∇ ∇ Ω + = Ω = Ω

= ∂Ω

∑ ∫ ∫

Use weak formulation


Technologies


Diffpack® Implementation - important member

global_menu.multipleLoop (S)

S::adm

S::define

S::scan

S::solveProblem

S::integrands

FEM::makeSystem

FEM::calcElmMatVec

FEM::numItgOverElm

S::resultReport


Technologies


bAu

midNfudNNvdNNk i

m

jjijij

=

=Ω=

Ω∇⋅+Ω∇∇ ∫∑ ∫∫

Ω= ΩΩ

,...,1 , 1

Weak Formulation ( ):0=α

ConvDiff:: integrands (numerical kernel)


Technologies


Apply Boundary Conditions:

2 3 4( , ) 0, , , ,u x y x y= ∈Γ Γ Γ “essential conditions”

ConvDiff :: fillEssBC (apply essential boundary Conditions)


Technologies


Examples


Technologies


Courtesy of Simula Research Lab

Accurate 2D solution: 1,000,000 elements, 32 proc essors, 4 hours, 1 Gb Accurate 3D solution: 900.000.000 unknowns, 64 proc essors, 1000s per time step , 312Gb

Accurate 2D solution: 1,000,000 elements, 32 proc essors, 4 hours, 1 Gb Accurate 3D solution: 900.000.000 unknowns, 64 proc essors, 1000s per time step , 312Gb

4 3 coupled PDEs - 1 in torso, 2 in heart4 12 coupled ODEs sitting in each node4 Solved by finite elements using

4Diffpack standard FEM tools4multigrid methods4adaptive gridding (wave front)4Parallel solution using Domain Decomposition

/ODEs solved in parallel4 Sub-problem simulators build and tested

separately. Joined by administration class.4 Dimension independent code4 Around 10,000 lines of code

4 3 coupled PDEs - 1 in torso, 2 in heart4 12 coupled ODEs sitting in each node4 Solved by finite elements using

4Diffpack standard FEM tools4multigrid methods4adaptive gridding (wave front)4Parallel solution using Domain Decomposition

/ODEs solved in parallel4 Sub-problem simulators build and tested

separately. Joined by administration class.4 Dimension independent code4 Around 10,000 lines of code

Diffpack® - Electrical Activity in the Heart

3D Case:440.000.000 nodes in the heart41.000.000 nodes in the body4900.000.000 unknowns update

every time step4About 1000 sec per time step4Optimal preconditioning, 64

processors: 15 days



processors: 15 days


Technologies


( )

( ) ( ) ( )( ) ( )( )eeii

eiim

uMMvM

uMvMsvIt

vC

svFt

s

∇+⋅∇+∇⋅∇=

∇⋅∇+∇⋅∇=+∂∂

=∂∂

0

,

,

ionχχ

ty tensorconductivicellular Extra

ty tensorconductivicellular Intra

ratio volume toarea surface Membrane

ecapacitanc Membrane

current ionic Total

functions Rate

gates) and tions(concentra vector State

potential, aneTransmembr

potentialcellular Extra

where

ion

e

i

m

ei

e

M

M

C

I

F

s

uuvv

u

χ

−=

Courtesy of Simula Research Lab

Diffpack® - Electrical Activity in the Heart



processors: 15 days



processors: 15 days


Technologies


Tsunami Simulation - Storegga (Norway)

• Slides/impact

• Large destructive water waves

Courtesy of International Centre for Geohazards

Diffpack® - Tsunami Simulation


Technologies


Large-eddy simulation of flow around two cylinders in atandem arrangement, Re=22000,

velocity isosurface and pressure distribution

Viscous 3D flow around a cylinder, Re=265,velocity isosurface

Diffpack® - Computational Fluid Dynamics

Courtesy of SINTEF, Applied Mathematics


Technologies


Diffpack® Benchmarks

-251197/

953 s

Origin3800/ Itan.-Clu.(2)

32 /

16

10.4 Mio+ 150 Mio

Electro-cardiac(1)

Simula

(2005)Heart

1 / proc.

1

8

200

RAM

[Gb]

--Origin 3800963 MioVISTA-

Marine CFD

SINTEF

(2004)Flow

23.9/

23.7

725 /

563

Origin2000/

PIII-Clu.

32 /

321 Mio

3D-Nonlin. acoustics

Simula

(2000)Sound

19.4780 sItan.-Clu.2011 MioBoussinesqSimula

(2005)Tsunami

-5263 /

2840 sOrigin3800

32 /

64

84 Mio +

1260 Mio

Electro-cardiac

Simula

(2004)Heart

Speedup

WT(3)

[s]SystemCPU

un-

knownsEquation

Author

(Year)Project

(1)2 PDEs & 30 ODEs, (2)Linux Itanium2 Cluster (1.3 GHz, 64bit), (3)wall clock time (per time-step)


Technologies


Thank you for attention !Thank you for attention !

Documents

Introduction & Philosophy - inuTech · Introduction & Philosophy Peter Böhm, inuTech GmbH. Innovative Numerical Technologies 23. CADFEMUsers´ Meeting, Bonn 09.-11. ... ANSYS, CFX,