A Parallel GMRES Method for Large Linear System

Solving large linear system is of fundamental importance in engineering and scientific computing. Based on a multi-core CPU cluster, we propose a parallel GMRES (Generalized Minimal Residual) method to solve a large linear system
${Ax}={b}$
, where
$A$
is an
${n}\times {n}$
matrix, and in practice,
${n}$
can be 10
⁵
or even 10
⁶
. We validate the effectiveness of the algorithm with the test problem coming from the finite element discretization of Poisson equation.