Comparative Study of Krylov Subspace Method Implementations for a GPU Cluster in Elastoplastic Problems.

As a part of the finite element procedure, it is necessary to solve a system of simultaneous linear algebraic equations. A simulation with a sophisticated material model and a fine mesh requires using an iterative linear solver executed on a grid of computational accelerators. Most of modern iterative methods for linear systems are based on Krylov Subspaces. As there is no universal iterative method for linear equations available, numerous varieties of iterative linear solvers exist. The task of choosing a method best suited for a particular computational system and a physical model is arguably impossible to formalize due to both an unpredictable convergence of iterative methods and a sophisticated memory hierarchy of contemporary data processing systems. Computational experiments are virtually the sole approach to choosing a particular method. The paper presents computational experiment results for a cluster of graphic processor units (GPUs) and a linear system from the finite element analysis of an elastoplastic problem with a large plastic strain rate. It appears that the relatively rarely used methods TFQMR and CGS show the best performance. [ABSTRACT FROM AUTHOR]