Parallel iterative block and direct block methods for 2-space dimension problems on distributed memory architecture

Abstract

In numerical simulations of partial differential equations, it is often the case that we have to solve the matrix equations accrued from finite difference models of the equations. For computational purposes, we can iterate the solution system in such a way that the resulting matrices on the left hand side become easy to handle such as diagonal matrices or small matrices, for example the block systems. This indicates that we can apply various group computational molecules to simulate the partial differential equations numerically. In this paper, we present two problems of group schemes, specifically the Alternating Group Explicit (AGE) method and the Crack Propagation. We offer reasonable assessments and contrasts on behalf of the numerical experiments of these two methods ported to run through Parallel Virtual Machine (PVM) on distributed memory architecture.