Parallel Solvers for Numerical Upscaling

This contribution deals with numerical upscaling of the elastic material behaviour, namely of geocomposites, from microscale to macroscale through finite element analysis. This computationally demanding task raises many algorithmic and implementation issues related to efficient parallel processing. On the solution of the arising boundary value problem, considered with either Dirichlet or Neumann boundary conditions, we discuss various parallelization strategies, and compare their implementations in the specialized in-house finite element package GEM and through the general numerical solution framework Trilinos.

[1]  Radim Blaheta,et al.  GPCG–generalized preconditioned CG method and its use with non‐linear and non‐symmetric displacement decomposition preconditioners , 2002, Numer. Linear Algebra Appl..

[2]  P. Deuflhard,et al.  Large Scale Scientific Computing , 1987 .

[3]  Owe Axelsson,et al.  Material Parameter Identification with Parallel Processing and Geo-applications , 2011, PPAM.

[4]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[5]  Radim Blaheta,et al.  A multilevel method with overcorrection by aggregation for solving discrete elliptic problems , 1988 .

[6]  Radim Blaheta,et al.  Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems , 1994, Numer. Linear Algebra Appl..

[7]  Pavel B. Bochev,et al.  On the Finite Element Solution of the Pure Neumann Problem , 2005, SIAM Rev..

[8]  Marian Brezina,et al.  Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems , 2005, Computing.

[9]  I. Hlavácek,et al.  Mathematical Theory of Elastic and Elasto Plastic Bodies: An Introduction , 1981 .

[10]  Peter Wriggers,et al.  An Introduction to Computational Micromechanics , 2004 .

[11]  Ondrej Jakl,et al.  GEM - A Platform for Advanced Mathematical Geosimulations , 2009, PPAM.

[12]  Radim Blaheta.  Space Decomposition Preconditioners and Parallel Solvers , 2004 .

[13]  Jonathan J. Hu,et al.  ML 3.1 smoothed aggregation user's guide. , 2004 .

[14]  Jonathan J. Hu,et al.  ML 5.0 Smoothed Aggregation Users's Guide , 2006 .

[15]  Ralph Müller,et al.  A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures , 2008 .

[16]  Radim Blaheta,et al.  Multilevel Solvers with Aggregations for Voxel Based Analysis of Geomaterials , 2011, LSSC.