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Phase field modelling Phase field modelling Current challenges and opportunities for high performance M P Gururajan computing Preamble Microstructure A few movies P G Tennyson , D Mohan , G Phanikumar , M P Gururajan 1 Phase

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Phase field modelling

Current challenges and opportunities for high performance computing P G Tennyson†, D Mohan‡, G Phanikumar‡, M P Gururajan1

Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076 INDIA †: Tata Research Development and Design Center (TRDDC), Pune ‡: Department of Metallurgical and Materials Engineering, IIT Madras, Chennai

December, 2018

1guru.mp@iitb.ac.in,gururajan.mp@gmail.com

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Acknowledgements

Funding: IRCC, IIT Bombay, DST, Government of India, DRDO and SASE, Ministry of Defence, Government of India, DST-DAAD, Tata Steel, GE India Computational resources: Spinode, Dendrite, Nebula / Space-Time, Param Yuva (C-DAC, Pune) Organisers, specifically, Dr. Shenoy, C-DAC, Pune Teachers, collaborators, students

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Outline

Microstructure and its evolution Phase field modelling Examples: Six-fold anisotropy on morphology / Solidification Way forward!

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Computational Materials Engineering Group

Figure: CMEG: part of materials and process modelling lab

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

The problem

Figure: New material development cycle: 10 to 20 years. Can we bring it down to less than 5 years? Xiong and Olson, npj Computational Materials, 2016

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

ICME

Figure: ICME: The minerals, metals and materials society (TMS) study, 2013

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Tools and techniques

Figure: Computational materials science: tools and techniques

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

What is microstructure?

Figure: Microstructure (a Ni-base superalloy). Xu et al, Met. Mat. Trans. A, 1998

Structure, shapes, sizes and distribution of interfaces

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Microstructural evolution

Figure: Effect of heat treatment. Xu et al, Met. Mat. Trans. A, 1998

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Microstructural evolution

Figure: Dendrites during solidification. David et al, JOM, 2003

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Spinodal decomposition

0.5 Homogeneous system with noise

Figure: A homogeneous alloy with a slighlty noisy composition profile

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Pure material solidification

Undercooled melt Nucleus

Figure: An undercooled melt with insulated sides and nucleus on one of the

walls. The interfacial energy is 4-fold anisotropic.

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Six-fold dendrites

Undercooled melt Nucleus

Figure: An undercooled melt with insulated sides and nucleus at the centre. The interfacial energy is 6-fold anisotropic.

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Spinodal decomposition

Figure: Regions rich in A (B) become richer in A (B) with time. Microstructures at times 0, 100 and 1000 units.

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Issue 1

The phase field method, like many other modeling ap- proaches, is practically limited by the computational expense entailed in running large simulations. The challenge stems from the need to resolve a diffuse interface that has a dif- fuseness that is on a much smaller length scale than a typical microstructural evolution length scale. –Modeling Across Scales: A Roadmapping Study for Con- necting Materials Models and Simulations Across Length and Time Scales, TMS study report, 2015

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Issue 2

Common software: MicressTM, FiPyTM, OpenPhaseTM, and MOOSE (Marmot)TM Compare with VASP, LAMMPS, ParaDIS, ... Phase field: an approach and not a set methodology (like FEM) pfHUB: maintained by NIST

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Phase field models

∂c ∂t = ∇M∇µ = ∇M∇[g(c) − κ∇2c] (1) ∂φ ∂t = −Lµ = L[κ∇2φ − g(φ)] (2) Ginzburg-Landau, Alan Turing (Chemical morphogenesis), ...

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Characteristics of phase field models

Interfaces are not sharp; diffuse interface model No tracking of interface: numerical solutions are easier Gradient energy coefficient: interfacial energy contributions (Gibbs-Thomson, for example) are automatically accounted for Topological singularities (splitting or disappearance of interfaces): naturally taken care of Elastic stress, magnetic and electric field: can be coupled by adding the relevant free energy term!

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

What is phase field modelling?

Some representative viewpoints: An approach to obtain solutions of PDEs that are hard to solve – by introducing artificial regions of continuity where there are discontinuities (Mathematical) Non-linear partial differential equations that lead to solutions which are interesting patterns (Biology) Continuum equations derived from statistical mechanics that lead (as solution) to interesting patterns (Physics) Partial differential equations that describe diffusion (of atoms and heat) as well as phase transformations (Materials science)

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Spectral technique

∂c ∂t = D∇2c (3) Spatial Fourier transform of c: ˜ c =

c(x) exp [−ik · r]dV

Turns the PDE into ODE: d˜ c dt = −Dk2˜ c (4) Semi-implicit Fourier spectral technique ∂c ∂t = ∇M∇µ = ∇M∇[g(c) − κ∇2c] (5) ∂φ ∂t = −Lµ = L[κ∇2φ − g(φ)] (6)

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Advantages of FFT

Periodic boundary conditions: representative volume elements Semi-implicit Fourier spectral technique Good, fast, open source FFT codes: FFTW

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Extended Cahn-Hilliard free energy: anisotropic interfacial energy

µ = g(c) − 2κI

ijcij

− 12βI

ijklcijckcl + 2βIII ijklcijkl

− 30αI

ijklmncijckclcmcn − 2αVII ijklmncijklmn

(7)

For details: E S Nani and M P Gururajan, Philosophical Magazine Letters (2014)

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Six fold anisotropy

Interfacial energy anisotropy / Point effect of diffusion / FG to CG

Att. kinetics anisotropy / SG to CG / Noise and Point Effect of Diff

From unpublished M Tech thesis of Mr. Abhinav Soni

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Profiling on NIVIDIA - K40C GPUs (Ternary alloy code)

Strong scaling Weak scaling

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Profiling

Figure: Profiling of 3D phase-field code Figure:

Ni - 19 Cr - 5 Nb (wt.%) alloy - 3D isothermal dendrite at ∆T = 8.0 K, ∆t = 58.0 ns for ∆x = 50.0 nm. (384 × 384 × 1024)

Mohan and Phanikumar, Unpublished

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Performance

1024 1536 2048 2560 3672 4096 1000 2000 3000 4000 5000 Domain length Time in seconds Time taken for 10000 timesteps

ATI HD5870 MPI 16 MPI 32 MPI 64

P G Tennyson, G M Karthik, and G Phanikumar, Computer Physics Communications, 2015.

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Data Visualization

Data files from each processor written at specific time intervals as unformatted .bin files Data files collated and converted to .mat files by Mat I/O library by Christopher Hulbert Visualization of data output was done in Matlab R

MayaVi, created by Prabhu

Ramachandran, was used for 3- D data visualization

500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

P G Tennyson, G M Karthik, and G Phanikumar, Computer Physics Communications, 2015.

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Summary

Phase field models: highly nonlinear, stiff PDEs Large scale computations solving phase field models: important from an applications point of view There is plenty to explore: including developing standard, open source code and its parallel implementation

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Phase field modelling M P Gururajan Preamble Microstructure A few movies Phase field modelling

Phase field modelling

Current challenges and opportunities for high performance computing P G Tennyson†, D Mohan‡, G Phanikumar‡, M P Gururajan1

December, 2018

Acknowledgements

Outline

Microstructure and its evolution Phase field modelling Examples: Six-fold anisotropy on morphology / Solidification Way forward!

Computational Materials Engineering Group

Figure: CMEG: part of materials and process modelling lab

The problem

Figure: New material development cycle: 10 to 20 years. Can we bring it down to less than 5 years? Xiong and Olson, npj Computational Materials, 2016

ICME

Figure: ICME: The minerals, metals and materials society (TMS) study, 2013

Tools and techniques

Figure: Computational materials science: tools and techniques

What is microstructure?

Figure: Microstructure (a Ni-base superalloy). Xu et al, Met. Mat. Trans. A, 1998

Structure, shapes, sizes and distribution of interfaces

Microstructural evolution

Figure: Effect of heat treatment. Xu et al, Met. Mat. Trans. A, 1998

Microstructural evolution

Figure: Dendrites during solidification. David et al, JOM, 2003

Spinodal decomposition

0.5 Homogeneous system with noise

Figure: A homogeneous alloy with a slighlty noisy composition profile

Pure material solidification

Undercooled melt Nucleus

Figure: An undercooled melt with insulated sides and nucleus on one of the

Six-fold dendrites

Undercooled melt Nucleus

Figure: An undercooled melt with insulated sides and nucleus at the centre. The interfacial energy is 6-fold anisotropic.

Spinodal decomposition

Figure: Regions rich in A (B) become richer in A (B) with time. Microstructures at times 0, 100 and 1000 units.

Issue 1

Issue 2

Common software: MicressTM, FiPyTM, OpenPhaseTM, and MOOSE (Marmot)TM Compare with VASP, LAMMPS, ParaDIS, ... Phase field: an approach and not a set methodology (like FEM) pfHUB: maintained by NIST

Phase field models

∂c ∂t = ∇M∇µ = ∇M∇[g(c) − κ∇2c] (1) ∂φ ∂t = −Lµ = L[κ∇2φ − g(φ)] (2) Ginzburg-Landau, Alan Turing (Chemical morphogenesis), ...

Characteristics of phase field models

What is phase field modelling?

Spectral technique

∂c ∂t = D∇2c (3) Spatial Fourier transform of c: ˜ c =

Turns the PDE into ODE: d˜ c dt = −Dk2˜ c (4) Semi-implicit Fourier spectral technique ∂c ∂t = ∇M∇µ = ∇M∇[g(c) − κ∇2c] (5) ∂φ ∂t = −Lµ = L[κ∇2φ − g(φ)] (6)

Advantages of FFT

Periodic boundary conditions: representative volume elements Semi-implicit Fourier spectral technique Good, fast, open source FFT codes: FFTW

Extended Cahn-Hilliard free energy: anisotropic interfacial energy

µ = g(c) − 2κI

− 12βI

− 30αI

(7)

Six fold anisotropy

Interfacial energy anisotropy / Point effect of diffusion / FG to CG

From unpublished M Tech thesis of Mr. Abhinav Soni

Profiling on NIVIDIA - K40C GPUs (Ternary alloy code)

Strong scaling Weak scaling

Profiling

Figure: Profiling of 3D phase-field code Figure:

Mohan and Phanikumar, Unpublished

Performance

1024 1536 2048 2560 3672 4096 1000 2000 3000 4000 5000 Domain length Time in seconds Time taken for 10000 timesteps

ATI HD5870 MPI 16 MPI 32 MPI 64

P G Tennyson, G M Karthik, and G Phanikumar, Computer Physics Communications, 2015.

Data Visualization

Data files from each processor written at specific time intervals as unformatted .bin files Data files collated and converted to .mat files by Mat I/O library by Christopher Hulbert Visualization of data output was done in Matlab R

Ramachandran, was used for 3- D data visualization

Summary

Phase field models: highly nonlinear, stiff PDEs Large scale computations solving phase field models: important from an applications point of view There is plenty to explore: including developing standard, open source code and its parallel implementation

THANK YOU!