Grid Computing for the Bi-CGSTAB applied to the solution of the Modified Helmholtz Equation

The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation matrix’s red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, interconnected through a 100Mbps and 1Gbps ethernet network, and its performance is presented by speedup measurements included. Keywords— Collocation, Preconditioned Bi-CGSTAB, MPI, Grid and DSM Systems.