Institute of Mathematics and Informatics , Akademijos 4, Vilnius, 2600, Lithuania ; Vilnius Gediminas Technical University , Sauletekio St. 11, Vilnius, 2054, Lithuania
This paper deals with a system of nonlinear differential equations, which describe the interaction of two focused laser beams in nonlinear media. The system of equations is approximated by a splitting finite difference scheme. A parallel version of the finite‐difference scheme is proposed and the efficiency of this algorithm is investigated. Calculations are performed using clusters of computers, connected via local computer network. The emphasis is made on solving this problem on heterogeneous clusters. In the paper a static distribution scheme is analyzed. The results of several computational experiments are presented. Data redistribution during an initial phase of computation is investigated and the influence of slow communication among the processes is taken into account during this analysis.
Netiesinės optikos uždavinio lygiagretusis skaičiavimo algoritmas
Santrauka. Straipsnyje sprendžiama netiesinių diferencialinių lygčių sistema, aprašanti lazerio spindulių sąveiką netiesinėje terpėje. Sudaryta diskrečioji išskaidymo schema bei pateikta lygiagrečioji algoritmo versija. Ištirtas lygiagrečiojo algoritmo efektyvumas. Skaičiavimai atlikti virtualiajame kompiuterių, sujungtų lokaliuoju tinklu, klasteryje. Išsamiai tiriamas algoritmo efektyvumas heterogeniniams lygiagretiesiems kompiuteriams. Duomenų paskirstymui naudojamas statinis paskirstymo metodas. Pateikti ir išanalizuoti duomenų perskirstymo algoritmai, pagerinantys darbo paskirstymo tolygumą pradinėje skaičiavimu fazėje. Teorinėje analizėje atsižvelgiama į duomenų perdavimo kaštus.
Čiegis, R., Dement’ev, A., & Rate, P. (1999). A parallel algorithm for solving one problem of nonlinear optics. Mathematical Modelling and Analysis, 4(1), 58-69. https://doi.org/10.3846/13926292.1999.9637111
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