Higher Order Finite Difference Preconditioned Scheme: A Multithreaded Approach

New parallel computational techniques are introduced for the parallelization of explicit finite difference approximate inverse methods, using higher order approximation schemes, based on Portable Operating System Interface for UniX (POSIX) Threads, for multicore systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Finite Element Matrix algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on speedups and efficiency are also presented. Finally, numerical results for the performance of the POBGAIFEM algorithm as well as the loop level and functional level parallelized Explicit Preconditioned Bi-conjugate Gradient Gradient-STAB method for solving two dimensional boundary value problems on multicore computer systems are presented.