On the design and implementation of parallel finite element approximate inverses using POSIX threads on multicore systems

Purpose - The purpose of this paper is to propose novel parallel computational techniques for the parallelization of explicit finite element generalized approximate inverse methods, based on Portable Operating System Interface for UniX (POSIX) threads, for multicore systems. Design/methodology/approach - The authors' main motive for the derivation of the new Parallel Generalized Approximate Inverse Finite Element Matrix algorithmic techniques is that they can be efficiently used in conjunction with explicit preconditioned conjugate gradient-type schemes on multicore systems. The proposed parallelization technique of the Optimized Banded Generalized Approximate Inverse Finite Element Matrix (OBGAIFEM) algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on the computational complexity of the parallel generalized approximate inverse finite element matrix algorithmic techniques are also derived. Findings - Application of the proposed method on a two-dimensional boundary value problem is discussed and numerical results are given on a multicore system using POSIX threads. These results tend to become optimum and are favorably compared to corresponding results from multiprocessor systems, as presented in recent work by Gravvanis et al Originality/value - The proposed parallel explicit finite element generalized approximate inverse preconditioning, using approximate factorization and approximate inverse algorithms, is an efficient computational method that is valuable for computer scientists and for scientists and engineers in engineering computations.