Застосування паралельних обчислень у чисельному аналізі задач математичної фізики варіаційними методами

Abstract

Робота присвячена використанню паралельних обчислень при розв’язанні крайових задач для еліптичних рівнянь. We consider the numerical solution of the boundary value problem for the Dirichlet equation in a rectangular region with discontinuous boundary conditions. To solve this problem, a structural-variational method of R-functions was used. As coordinate functions was taken two-dimensional finite splines. Such choice suppose to significantly increase the accuracy of approximation and the minimizing sequence to converge rapidly to the exact solution of the problem. Calculations was made using the mathematical package MATHEMATICA 9. Integrals that was arisen in the solution, was computed by multiple threads.