Parallel Iterative Methods

In this paper we discuss the implementation of the ITPACK library [Kine 82] in the parallel (//)ELL-PACK environment [Holls 92] and report on its performance on the nCUBE II parallel machine. In this study we are concerned with the numerical solution of second order elliptic partial diITerential equations (PDEs) on rectangular regions with mixed boundary conditions using finite difference approximations. The parallelization methodology applied is based on the domain decomposition of discrete geometric data structures (grids) associated with the numerical solution of the PDE problem[Chri 91]. The implementa-tion of I jITPACK for boundary value problems defined on general 2·0 and 3-D domains for both finite element and difference methods is reported in [Kim 93]. The performance results obtained so far indicate almost optimal computational and space efficiency of the / /ITPACK modules