Domain decomposition based on a direct method for solving the three-dimensional Poisson's equation in nonstationary astrophysical problems

N. V. Snytnikov

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

Abstract: A new parallel algorithm for solving the three-dimensional Poisson's equation in the context of nonstationary problems of astrophysics is proposed. This algorithm is based on a decomposition of the 3D domain in two directions, on the application of a direct method for solving the Dirichlet problem in each subdomain, and on a combination of subdomains coupling for the screened Poisson's equation with the variable separation method. Test experiments were conducted on supercomputers installed at the Joint Supercomputing Center of Russian Academy of Sciences (Moscow) and at the Siberian Supercomputing Center (Novosibirsk).

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

UDC: 519.63

Received: 02.02.2015