A parallel algorithm for solving 2D Poisson's equation in the context of nonstationary problems

N. V. Snytnikov

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk

Abstract: A new parallel method to solve the Dirichlet problem for Poisson's equation in the context of nonstationary problems of mathematical physics is proposed. This method is based on a decomposition of a rectangular Cartesian domain in one direction, on a direct method of solving Poisson's equation in each subdomain, and on the coupling of the subdomains using a fast procedure for evaluating a single layer potential. A number of test experiments conducted on supercomputers installed at Joint Supercomputing Center of Russian Academy of Sciences and at Siberian Supercomputing Center show a good weak and strong scalability of the parallel algorithm.

Keywords: Poisson's equation, Dirichlet problem, domain decomposition, gravitational potential, stellar dynamics, parallel programming, scalability of algorithms.

UDC: 519.63

Received: 09.12.2014