A Note on Parallel Finite Element Approximate Inverses Using OpenMP on Multicore Systems

During the last decades, explicit finite element approximate inverse preconditioning methods have been extensively used for solving efficiently sparse linear systems on multiprocessor and multicomputer systems. New parallel computational techniques are proposed for the parallelization of explicit finite element approximate inverse methods, based on the concept of the "fish bone" computational approach, and explicit preconditioned conjugate gradient type methods, implemented in OpenMP for multicore systems. Finally, numerical results for the performance of the finite element explicit approximate inverse preconditioning for solving characteristic two dimensional boundary value problems on multicore computer systems are presented. Theoretical estimates on speedups and efficiency are also presented.