FE2TI: Computational Scale Bridging for Dual-Phase Steels

A scale bridging approach combining the FE method with parallel domain decomposition (FETI) is presented. The FETI approach is used in the project “EXASTEEL Bridging Scales for Multiphase Steels” (within the German priority program “Software for Exascale Computing SPPEXA”) for the simulation of modern dual-phase steels. This approach incorporates phenomena on the microscale into the macroscopic problem by solving many independent microscopic problems on representative volume elements (RVEs). The results on the RVEs replace a phenomenological material law on the macroscale. In order to bring large micro-macro simulations to modern supercomputers, in the FETI approach a highly scalable implementation of the inexact reduced FETI-DP (Finite Element Tearing and Interconnecting Dual Primal) domain decomposition method (scalable up to 786 432 Mira BlueGene/Q cores) is used as a solver on the RVEs. Weak scalability results for the FETI method are presented, filling the complete JUQUEEN at JSC Jülich (458 752 cores) and the complete Mira at Argonne National Laboratory (786 432 cores).

[1]  Timothy A. Davis,et al.  Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2) , 2006 .

[2]  A. Klawonn,et al.  Highly scalable parallel domain decomposition methods with an application to biomechanics , 2010 .

[3]  V. E. Henson,et al.  BoomerAMG: a parallel algebraic multigrid solver and preconditioner , 2002 .

[4]  Patrick Amestoy,et al.  Hybrid scheduling for the parallel solution of linear systems , 2006, Parallel Comput..

[5]  Charbel Farhat,et al.  A scalable dual-primal domain decomposition method , 2000, Numerical Linear Algebra with Applications.

[6]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[7]  Fpt Frank Baaijens,et al.  An approach to micro-macro modeling of heterogeneous materials , 2001 .

[8]  A. Klawonn,et al.  Robust FETI-DP methods for heterogeneous three dimensional elasticity problems , 2007 .

[9]  David E. Keyes,et al.  Nonlinearly Preconditioned Inexact Newton Algorithms , 2002, SIAM J. Sci. Comput..

[10]  Olof B. Widlund,et al.  Dual‐primal FETI methods for linear elasticity , 2006 .

[11]  J. Schröder,et al.  Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials , 1999 .

[12]  Frédéric Feyel,et al.  Multiscale FE2 elastoviscoplastic analysis of composite structures , 1999 .

[13]  Pierre Gosselet,et al.  A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage , 2008 .

[14]  Gerhard Wellein,et al.  Hybrid MPI/OpenMP Parallelization in FETI-DP Methods , 2015 .

[15]  Pierre-Alain Boucard,et al.  Balancing Domain Decomposition with Nonlinear Relocalization: Parallel Implementation for Laminates , 2009 .

[16]  C. Farhat,et al.  The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems , 2000 .

[17]  O. Widlund,et al.  FETI and Neumann--Neumann Iterative Substructuring Methods: Connections and New Results , 1999 .

[18]  Axel Klawonn,et al.  Nonlinear FETI-DP and BDDC Methods , 2014, SIAM J. Sci. Comput..

[19]  Axel Klawonn,et al.  A Nonlinear FETI-DP Method with an Inexact Coarse Problem , 2016 .

[20]  Robert D. Falgout,et al.  The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners , 2006 .

[21]  Olaf Schenk,et al.  Two-level dynamic scheduling in PARDISO: Improved scalability on shared memory multiprocessing systems , 2002, Parallel Comput..

[22]  C. Farhat,et al.  The two-level FETI method for static and dynamic plate problems Part I: An optimal iterative solver for biharmonic systems , 1998 .

[23]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[24]  Jörg Schröder,et al.  Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen , 2000 .

[25]  Daniel Rixen,et al.  Application of the FETI Method to ASCI Problems: Scalability Results on One Thousand Processors and Discussion of Highly Heterogeneous Problems , 1999 .

[26]  W. Brekelmans,et al.  Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling , 1998 .

[27]  Oliver Rheinbach,et al.  Parallel Iterative Substructuring in Structural Mechanics , 2009 .

[28]  Axel Klawonn,et al.  On an Adaptive Coarse Space and on Nonlinear Domain Decomposition , 2014 .

[29]  C. Farhat,et al.  Optimal convergence properties of the FETI domain decomposition method , 1994 .

[30]  Axel Klawonn,et al.  Towards Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equation , 2014 .

[31]  Axel Klawonn,et al.  Inexact FETI‐DP methods , 2007 .