Parallel numerical modelling of short laser pulse compression

Abstract

In this paper we investigate parallel numerical algorithms for solution of the transient stimulated scattering processes. A new symmetrical splitting scheme is proposed and a parallel version is given. The efficiency of the parallel algorithm is investigated for two cases. The first one describes a case when the computation region is constant during the whole time of computations. The second one describes the initial phase of the process, when the computational region increases linearly in time. In order to distribute more evenly jobs between processors a dynamical the grid redistribution algorithm is is used. We also give a proof of one result about optimal static grid distribution in the case of linearly increased problem complexity. The results of computations are presented. They were obtained on different parallel computers and clusters of workstations.

Nagrinejamas priverstines Brijueno sklaidos fokusuotuose pluoštuose uždavinio lygiagretusis skaitinis sprendimo algoritmas. Sukonstruota simetrinio skaidymo baigtiniu skirtumu schema, kurios tikslumas yra antrosios eiles. Lygiagretusis algoritmas gautas naudojant duomenu lygiagretumo paradigma. Detaliai nagrinejamas dinamiškai didejančio sudetingumo uždavinys, modeliuojantis Brijueno sklaidos procesa, kai neužduodama kraštine salyga Stokso bangai. Irodyta hipoteze apie vieno stacionaraus blokinio duomenu paskirstymo algoritmo op‐timaluma. Eksperimentiškai ištirtas dinaminis duomenu perskirstymo algoritmas, patvirtintas jo efektyvumas net ir fiksuoto dydžio uždaviniams. Darbe pateikti skaitinio eksperimento, atlikto naudojant VGTU 20 procesoriu klasteri, rezultatai. Jie patvirtino gautuosius teorinius rezultatus, išsam us fizikiniai rezultatai bus išspausdinti kituose darbuose.

Key words:

• finite‐difference schemes
• symmetrical splitting method
• parallel algorithms
• grid redistribution
• nonlinear optics