Parallel Algorithm for Numerical Solution of Three-Dimensional Poisson Equation

In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics.

Authors:

• Alibek Issakhov

Keywords:

• MPI
• OpenMP
• three dimensional Poisson equation

References:

[1] V. Ilyin, Numerical analysis. - Novosibirsk: INM and MG , 2004 - p.
71
[2] A. Samarskii, ðÉ. Gulin, Numerical methods. - ð£.: Nauka, 1989. - p.
432
[3] A. Samarskii, Introduction to the theory of difference schemes.-ð£.:
Nauka,1971.- p. 553
[4] Quinn, Michael J., Parallel programming in C with MPI and OpenMP.
McGrawHill, 521, 2004.
[5] G. E. Karniadakis, Parallel Scientific Computing in C++ and MPI,
2000.
[6] Pacheco, P. Parallel Programming with MPI. Morgan Kaufmann, 1996.
[7] Alexey Lastoevsky L., Jack Dongarra. High performance heterogeneous
computing. Published by John Wiley & Sons, Inc., Hoboken, New
Jersey. 269, 2009.
[8] Ananth Grama, George Karypis, Vipin Kumar, Anshul Gupta
Introduction to Parallel Computing. Second edition. Pearson Education
Limited.Edinburgh Gate, Harlow, Essex CM20 2JE, England, 2003.