Mathematics and Computers in Simulation
SIAM Journal on Scientific and Statistical Computing
Programming with POSIX threads
Programming with POSIX threads
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Multigrid
Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
International Journal of High Performance Computing Applications
PCI '12 Proceedings of the 2012 16th Panhellenic Conference on Informatics
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New parallel computational techniques are introduced for the parallelization of Generic Approximate Sparse Inverse multigrid methods, based on Portable Operating System Interface for UniX (POSIX) threads, for multicore systems. Parallelization of the Generic Approximate Sparse Inverse Matrix (GenAspI) algorithm is achieved based on a new computational approach, namely "strip," which utilizes the data independence of the rows assigned in each available processor. Additionally, new parallel computational techniques are proposed for the parallelization of a modified multigrid V-Cycle method, based on POSIX Threads, for multicore systems. The modified V-Cycle utilized a Parallel PGenAspI Preconditioned Bi-Conjugate Gradient STABilized (BiCGSTAB) as a coarse solver to ensure better parallel performance of the multigrid method. For parallelization purposes, a replication of the multigrid method function is executed on each processor with different index bands and with proper synchronization points to ensure less thread-creation overhead and to maximize parallel performance. Theoretical estimates on speedups and efficiency are also presented. Finally, numerical results for the performance of the PGenAspI algorithm and the PGenAspI---MGV method for solving classical two-dimensional boundary value problems on multicore computer systems are presented. The implementation issues of the proposed method are also discussed using POSIX threads on multicore systems.