Study on performance of Krylov subspace methods at solving large-scale contact problems

Abstract

This paper discusses the performance of preconditioned Krylov subspace methods at solving large-scale finite-element-formulated contact problems based on a finite element analysis program (FEAP) and portable, extensible toolkit for scientific computation (PETSc). Different combinations of the common preconditioners and Krylov subspace methods, namely conjugate gradient, generalized minimal residual, conjugate residual, biconjugate gradient, conjugate gradient square, biconjugate gradient stabilized, and transpose-free quasi-minimal residual method, are tested on the problems with rising size. Numerical experiments are carried out in respect of time consumption, parallelism, memory usage, and stability. The results show time consumption for most of combinations increases linearly with the growth of problem size, and block Jacobi and Jacobi-preconditioned conjugate gradient and conjugate residual methods have better potential for large-scale problems in the given and similar case.