Modelling of Complexities in PA of Laplace Equation

Abstract

Dominant trends in parallel and distributed computing (parallel computers, parallel algorithms) aim to connect a number of powerful workstations (WS) based on single personal computers (PC) or symmetrical multiprocessor system (SMP) to solve complex problems in a parallel way. Typical representatives of these trends are network of workstation (NOW) and Grid as a high integrated network of NOW modules. In relation to it there is a bad need of unified modelling in traditionally evolved parallel computing and distributed computing as two separate research disciplines. Likewise current trends in high performance computing (HPC) aim to use NOW modules based on SMP parallel computers as cheaper alternatives to the traditionally used massive parallel multiprocessors or supercomputers and to profit from unifying modelling in parallel and distributed computing too. To exploit the parallel processing capability of such cluster, any application program must be paralleled. A way how to do it (decomposition model) belongs to a most important step in developing process of effective parallel algorithm. This article at first discusses the development of effective (optimised) iterative parallel algorithms (IPA) to solve partial differential equations (PDE). By carefully choosing an illustrative typical problem of PDE (Laplace equation) the proposed research has demonstrated the most important complexities in the process of complete modelling of substantial complexities and their optimisation in order to develop an effective PA. Such approach could be used as illustrative example for a complete modelling and effective solution of even other more complex PDE´s in a parallel way.