ITR/AP: Multiscale Models for Microstructure Simulation and Process Design

Principal Investigators:

Bob Haber (Theor. & Applied Mechs.),

Jonathan Dantzig (Mech. & Ind. Engng.),

Duane Johnson (Matl. Science & Engng.).

University of Illinois at Urbana–Champaign

Principal Investigators: Principal Investigators:

Bob Haber (Bob Haber (TheorTheor. & Applied. & Applied MechsMechs.), .),

JonathanJonathan DantzigDantzig ((MechMech. &. & IndInd.. EngngEngng.), .),

Duane Johnson (Duane Johnson (MatlMatl. Science &. Science & EngngEngng.). .).

University of Illinois atUniversity of Illinois at UrbanaUrbana––ChampaignChampaign

Faculty Investigators

Continuum science• Jonathan Dantzig (Mech. & Ind. Engrg.)

• Eliot Fried (Theor. & Appl. Mechs.)

• Robert Haber (Theor. & Appl. Mechs.)

• Daniel Tortorelli (Mech. & Ind. Engrg.)

Materials (atomistic) science• Duane Johnson (Matl. Sci. & Engnrg.)

Continuum scienceContinuum science•• JonathanJonathan DantzigDantzig ((MechMech. &. & IndInd.. EngrgEngrg.).)

•• Eliot Fried (Eliot Fried (TheorTheor. &. & ApplAppl.. MechsMechs.).)

•• Robert Haber (Robert Haber (TheorTheor. &. & ApplAppl.. MechsMechs.).)

•• DanielDaniel TortorelliTortorelli ((MechMech. &. & IndInd.. EngrgEngrg.).)

Materials (Materials (atomisticatomistic) science) science•• Duane Johnson (Duane Johnson (MatlMatl.. SciSci. &. & EngnrgEngnrg.).)

Faculty InvestigatorsInformation science• Jeff Erickson (Computer Sci.)

• Michael Garland (Computer Sci.)

• Sanjay Kale (Computer Sci.)

• Herbert Edelsbrunner (Computer Sci., Duke)

Mathematics• Robert Jerrard (Mathematics) - pde’s

• John Sullivan (Mathematics) - geometry

• Martin Bendsøe (Mathematics, Danish Tech. U.) - topology opt.

Information scienceInformation science•• Jeff Erickson (Computer Jeff Erickson (Computer SciSci.).)

•• Michael Garland (ComputerMichael Garland (Computer SciSci.).)

•• Sanjay Kale (ComputerSanjay Kale (Computer SciSci.).)

•• Herbert Herbert Edelsbrunner Edelsbrunner (Computer (Computer SciSci., ., DukeDuke))

MathematicsMathematics•• Robert Robert Jerrard Jerrard (Mathematics) (Mathematics) -- pde’spde’s

•• John Sullivan (Mathematics) John Sullivan (Mathematics) -- geometrygeometry

•• Martin Martin Bendsøe Bendsøe (Mathematics, (Mathematics, Danish Tech. U.Danish Tech. U.) ) -- topology opt.topology opt.

A joint effort between two centers

Materials Computation Center• Atomistic models

• Prediction of bulk properties

Center for Process Simulation & Design• Manufacturing processes

• Continuum models

• Simulation and optimization of microstructure properties in manufacturing processes

• Successful experience with interdisciplinary collaborations

Materials Computation CenterMaterials Computation Center•• Atomistic Atomistic modelsmodels

•• Prediction of bulk propertiesPrediction of bulk properties

Center for Process Simulation & DesignCenter for Process Simulation & Design•• Manufacturing processesManufacturing processes

•• Continuum modelsContinuum models

•• Simulation and optimization of microstructure Simulation and optimization of microstructure properties in manufacturing processesproperties in manufacturing processes

•• Successful experience with interdisciplinary Successful experience with interdisciplinary collaborationscollaborations

CPSD Funding HistoryAlcoa (1996 - 2000)

• $20k/yr seed grant

NSF GOALIE grant with Alcoa (1997-2001)• $120k / year NSF; $20k / year Alcoa

NSF-DARPA OPAAL grant (1998-2001)• Math directorates

• ~$800,000 / year over 3 years

NSF ITR grant (2001-2006)• Division of Materials Research,

• Computer and Information Science Engineering

• ~$800,000 / year over 5 years

Alcoa (1996 Alcoa (1996 -- 2000)2000)

•• $20k/$20k/yryr seed grantseed grant

NSF GOALIE grant with Alcoa (1997NSF GOALIE grant with Alcoa (1997--2001)2001)•• $120k / year NSF; $20k / year Alcoa$120k / year NSF; $20k / year Alcoa

NSFNSF--DARPA OPAAL grant (1998DARPA OPAAL grant (1998--2001)2001)•• Math directoratesMath directorates

•• ~$800,000 / year over 3 years~$800,000 / year over 3 years

NSF ITR grant (2001NSF ITR grant (2001--2006)2006)•• Division of Materials Research, Division of Materials Research,

•• Computer and Information Science EngineeringComputer and Information Science Engineering

•• ~$800,000 / year over 5 years~$800,000 / year over 5 years

CPSD/MCCMission I: Manufacturing ScienceImprove product quality through control of microstructure

Simulation tools to predict microstructure evolution during processing• Basic science (atomic to micro scale studies)

• Applied science (micro - macro scale process simulations)

Optimization tools for process design• Use multi-scale process simulations

• Sensitivity analysis, optimization of process parameters

– Tool shapes, process rates, alloy chemistry, quench, ...

Improve product quality through control of Improve product quality through control of microstructuremicrostructure

Simulation tools to predict microstructure Simulation tools to predict microstructure evolution during processingevolution during processing•• Basic science (atomic to micro scale studies)Basic science (atomic to micro scale studies)

•• Applied science (micro Applied science (micro -- macro scale process simulations)macro scale process simulations)

Optimization tools for process designOptimization tools for process design•• Use multiUse multi--scale process simulationsscale process simulations

•• Sensitivity analysis, optimization of process parametersSensitivity analysis, optimization of process parameters

–– Tool shapes, process rates, alloy chemistry, quench, ...Tool shapes, process rates, alloy chemistry, quench, ...

CPSD/MCCMission II: Computational MethodsDevelop new computational techniques to support manufacturing science mission

Common requirements and responses• Multi-scale physics + optimization = large scale problems

– Parallel computation, adaptive analysis, multigrid

• Difficult geometry:

– complex shapes, moving boundaries, variable connectivity,

– Meshing, phase-field, ALE, spacetime methods, “skin”

• Embedded physical models

– Direct : discontinuous Galerkin, quantum-continuum

– Linked hierarchical models: homogenization, etc.

Develop new computational techniques to support Develop new computational techniques to support manufacturing science missionmanufacturing science mission

Common requirements and responsesCommon requirements and responses•• MultiMulti--scale physics + optimization = large scale problemsscale physics + optimization = large scale problems

–– Parallel computation, adaptive analysis,Parallel computation, adaptive analysis, multigridmultigrid

•• Difficult geometry: Difficult geometry:

–– complex shapes, moving boundaries, variable connectivity, complex shapes, moving boundaries, variable connectivity,

–– Meshing, phaseMeshing, phase--field, ALE,field, ALE, spacetimespacetime methods, “skin”methods, “skin”

•• Embedded physical modelsEmbedded physical models

–– Direct : discontinuousDirect : discontinuous GalerkinGalerkin, quantum, quantum--continuumcontinuum

–– Linked hierarchical models: homogenization, etc.Linked hierarchical models: homogenization, etc.

Dendritic Solidification• Jonathan Dantzig, faculty lead

• Controls grain size and morphology in casting

•• Jonathan Jonathan DantzigDantzig, faculty lead, faculty lead

•• Controls grain size and morphology in castingControls grain size and morphology in casting

Scaling with undercooling,grain size

Anisotropy due to convective flow

DantzigDantzig (M&IE),(M&IE), GoldenfeldGoldenfeld (Physics), Kale (CS)(Physics), Kale (CS)

Modeling Dendritic GrowthMicrostructure evolution with flow• Length scales: nm – mm• Phase-field method for microstructure• Parallel, adaptive, Navier-Stokes solver

Microstructure evolution with flowMicrostructure evolution with flow•• Length scales:Length scales: nmnm –– mmmm•• PhasePhase--field method for microstructurefield method for microstructure•• Parallel, adaptive,Parallel, adaptive, NavierNavier--Stokes solverStokes solver

DantzigDantzig (M&IE),(M&IE), GoldenfeldGoldenfeld (Physics), Kale (CS)(Physics), Kale (CS)

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Modeling Dendritic GrowthBinary Alloy Solidification• Important industrial applications• Directional solidification (2D and 3D)• Spacing selection of interest• Flow interactions with

complex structures

Binary Alloy SolidificationBinary Alloy Solidification•• Important industrial applicationsImportant industrial applications•• Directional solidification (2D and 3D)Directional solidification (2D and 3D)•• Spacing selection of interestSpacing selection of interest•• Flow interactions with Flow interactions with

complex structurescomplex structures

DantzigDantzig (M&IE),(M&IE), GoldenfeldGoldenfeld (Physics), Kale (CS)(Physics), Kale (CS)

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Parallelization Infrastructure:

Laxmikant Kale, faculty lead

2-prong approach to user-friendly parallelization• Parallel Objects

• Component Frameworks

Several successful, diverse applications

LaxmikantLaxmikant Kale, faculty lead Kale, faculty lead

22--prong approach to userprong approach to user--friendly friendly parallelizationparallelization•• Parallel ObjectsParallel Objects

•• Component FrameworksComponent Frameworks

Several successful, diverse applicationsSeveral successful, diverse applications

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

Charm Component Frameworks

Automatic Load balancing

Auto. Checkpointing

Flexible use of clusters

Out-of-core execution

Object based decomposition

ReusableSpecialized

Parallel Strucutres

Component Frameworks

FEM / Unstructured Grid

- Collision Detection

- NetFEM visualizer

Multi-block

TaskGraph: supporting space-time meshes

Charm++

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

Object-based Parallelization

User View

System implementationUser is only concerned with interaction between objects

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

FEM Framework

Charm++(Dynamic Load Balancing, Communication)

FEM Framework(Update of Nodal properties, Reductions over nodes or partitions)

FEM Application(Initialize, Registration of Nodal Attributes, Loops Over Elements, Finalize)

METIS I/O

Partitioner Combiner

Collaborators: Jon Dantzig and Coworkers, R. Haber and coworkers, Dan Torterelli and coworkers

Not just FEM:

-Any Unstructured-Grid app

Also being extended for:

-DG method (Haber)

-Implicit solvers (Torterelli)

-Finite Volume (CSAR)

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

Dendritic GrowthStudies evolution of solidification microstructures using a phase-field model computed on an adaptive finite element grid

Adaptive refinement and coarsening of grid involves re-partitioning

Studies evolution of Studies evolution of solidification solidification microstructures using a microstructures using a phasephase--field model field model computed on an adaptive computed on an adaptive finite element gridfinite element grid

Adaptive refinement and Adaptive refinement and coarsening of grid coarsening of grid involves reinvolves re--partitioningpartitioning

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

Load balancer in action

0

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501 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91

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Automatic Load Balancing in FEM1. AdaptiveRefinement 3. Chunks

Migrated

2. Load Balancer Invoked

Res

torin

g Th

roug

hput

L.V. Kale, O.L.V. Kale, O. LawlorLawlor, G., G. KakulapathiKakulapathi, A., A. SinglaSingla, J. Booth, J. Booth

Spacetime discontinuous Galerkinfinite element methods• Bob Haber, faculty lead

• New finite element methods for hyperbolic pde’s– Spacetime formulations

– Eliminates nearly all of the vexing problems of shocks, CFD, etc. ~ w/o special procedures

– Exact balance/conservation at the element level

– O(N) complexity.

• Applications– Dynamic fracture

– Continuum bulk models of microstructure evolution

– Atomistic-continuum coupling strategies

•• Bob Haber, faculty leadBob Haber, faculty lead

•• New finite element methods for hyperbolic New finite element methods for hyperbolic pde’spde’s–– SpacetimeSpacetime formulationsformulations

– Eliminates nearly all of the vexing problems of shocks, CFD, etc. ~ w/o special procedures

– Exact balance/conservation at the element level

– O(N) complexity.

•• ApplicationsApplications–– Dynamic fractureDynamic fracture

–– Continuum bulk models of microstructure evolutionContinuum bulk models of microstructure evolution

–– AtomisticAtomistic--continuum coupling strategiescontinuum coupling strategies

Haber, Yin, Haber, Yin, PalaniappanPalaniappan(T&AM); (T&AM); JerrardJerrard, Sullivan, , Sullivan, KoKo, , JegdicJegdic, , PetrocoviciPetrocovici(Math); (Math); Erickson, Garland, Zhou, Booth, Kale (CS)Erickson, Garland, Zhou, Booth, Kale (CS)

Spacetime discontinuous Galerkinfinite element methods• Eliminates oscillations without stabilization•• Eliminates oscillations without stabilizationEliminates oscillations without stabilization

Position, x

Dis

plac

emen

t,u

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

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80 elements

40 elements

Position, x

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1/h=20

1/h=40

1/h=80

WellWell--known commercial codeknown commercial code Spacetime Spacetime DGDG

Spacetime discontinuous Galerkinfinite element methodsSpace-time DG methods

Nonlinear conservation laws

Elastodynamics

SpaceSpace--time DG methodstime DG methods

Nonlinear conservation lawsNonlinear conservation laws

ElastodynamicsElastodynamics

t

x

P∂Q∫ = 0 ∀ Q ⊂ D

dM + b = 0 in Q

DG Method for First-Order Hyperbolic Problems• Success with linear, first-order problems

– Element-wise conservation

– Scalable element-by-element solutions

– Localized model for subscale physics

• Quench precipitate evolution– Reaction rate kinetics

•• Success with linear, firstSuccess with linear, first--order problemsorder problems–– ElementElement--wise conservationwise conservation

–– Scalable elementScalable element--byby--element solutionselement solutions

–– Localized model for Localized model for subscale subscale physicsphysics

•• Quench precipitate evolutionQuench precipitate evolution–– Reaction rate kineticsReaction rate kinetics

Al-Sc systemInflow temp. = 850 KVelocity = 200 mm/s

0.2 m

3.0 m

0.0035 m

0.04 m

symmetry plane

x, flow direction

y

1.8 m

0.005 m

water-spray quench zone

0.04 mMax. size = 1000;5.12 x 107 unknowns12.5 hrs. on a PC5 mins on 64-processors ofan SGI Power Challenge

N1

N j−1

N j

N j

growth

emission

N1

N j−1

Tent-pitcher algorithm• Cone constraint for space-time grid

• Yields local problem on each element

•• Cone constraint for spaceCone constraint for space--time gridtime grid

•• Yields local problem on each elementYields local problem on each element

1 1 1 12 2 2

3 3 3 3

Q

ˆ x

xd+1

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time

Tent-pitcher algorithm• Cone constraint enables O(N) solution

• Progress constraint eliminates locking

•• Cone constraint enables O(N) solutionCone constraint enables O(N) solution

•• Progress constraint eliminates lockingProgress constraint eliminates locking

Erickson, Erickson, GuoyGuoy, , ShefferSheffer,, UngorUngor (CS); Sullivan(Math); Haber (T&AM)(CS); Sullivan(Math); Haber (T&AM)

Simplifying Volumetric Data

115,000115,000tetrahedratetrahedra

10,00010,000tetrahedratetrahedra

2,0002,000tetrahedratetrahedra

Michael Garland & Yuan Michael Garland & Yuan Zhou Zhou (Computer Science)(Computer Science)

Processing time:Processing time:~15 seconds~15 seconds

(1 GHz Pentium 3)(1 GHz Pentium 3)

Applications:Applications:

•• data compressiondata compression

•• multiscalemultiscale material modelingmaterial modeling

•• progressive network transmissionprogressive network transmission

•• guaranteed interactive display timeguaranteed interactive display time

2D crack-tip wave scattering• 2D x time meshing with “tent-pitcher”

• 2D x time DG implementation

•• 2D x time meshing with “tent2D x time meshing with “tent--pitcher”pitcher”

•• 2D x time DG implementation2D x time DG implementation

p

t

Haber (T&AM); Haber (T&AM); JerrardJerrard, Sullivan(Math); Erickson, Garland, Kale (CS), Sullivan(Math); Erickson, Garland, Kale (CS)

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Monte Carlo Simulations of ElastomersWith Variable Functionality• Eliot Fried & Russell Todres, TAM; David Hardy, CS

• Effects of functionality (# cross-links/polymer chain) on the behavior of an elastomeric network

• simple ball + spring model, randomly remove springs

•• Eliot Fried & RussellEliot Fried & Russell TodresTodres, TAM; David Hardy, CS, TAM; David Hardy, CS

•• Effects of functionality (# crossEffects of functionality (# cross--links/polymer chain) links/polymer chain) on the behavior of anon the behavior of an elastomericelastomeric networknetwork

•• simple ball + spring model, randomly remove springssimple ball + spring model, randomly remove springs

O(N) algorithms for coupling atomisticand continuum models

• Duane Johnson, (MatSE); Bob Haber, (TAM); Brent Kraczek (Phys.)

• Coupling strategy applicable to wide range of atomistic methods

• Maintains O(N) nature of atomistic and continuum models

• Spatial partition leads to energetically consistent interpolation between atomistic and continuum response models.

•• Duane Johnson, (Duane Johnson, (MatSEMatSE); Bob Haber, (TAM); Brent ); Bob Haber, (TAM); Brent Kraczek Kraczek (Phys.)(Phys.)

•• Coupling strategy applicable to wide range ofCoupling strategy applicable to wide range of atomisticatomistic methodsmethods

•• Maintains O(N) nature ofMaintains O(N) nature of atomisticatomistic and continuum modelsand continuum models

•• Spatial partition leads to energetically consistent interpolatioSpatial partition leads to energetically consistent interpolation n betweenbetween atomisticatomistic and continuum response models.and continuum response models.

EnergyPartition

Transducer elements(constrained atoms)

Atomistic Standard FE (constrained atoms)

Standard FE (no atoms)

iα

←atomistic continuum→

Surprising similarity to projection method in topology optimization• Bob Haber, (TAM); Julian Norato, Dan Tortorelli (M&IE)

• Problem involves optimal shape design of structures allowing for changes in topology

• Fictitious domain approach requires smooth phase transitions

•• Bob Haber, (TAM); Julian Bob Haber, (TAM); Julian NoratoNorato, Dan , Dan Tortorelli Tortorelli (M&IE)(M&IE)

•• Problem involves optimal shape design of structures allowing Problem involves optimal shape design of structures allowing for changes in topologyfor changes in topology

•• Fictitious domain approach requires smooth phase transitionsFictitious domain approach requires smooth phase transitions

dball

Volume fraction computation px

py

a

b

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L

sym

sym