Parallel solvers of Poisson's equation
Author: J. Krupka and Ivan Šimeček

partial differential equations;sparse system of linear equations;parallel implementation;clusters of workstations;message passing interface


Various problems arising from physical processes are modelled using partial differential equations (PDEs). The Poisson's equation is the example of elliptic PDE, which we use for presenting the finite difference method for transforming the continuous problem to the discrete problem and obtaining sparse system of linear equations (SLEs). This paper discusses possibilities of parallel implementation of numerical methods for solving these special SLEs on clusters of workstations using message passing interface. We present theoretical background and evaluate results of our experiments done with OpenMPI library in parallel environment with which we have achieved reasonable high parallel efficiency for our problem. Superlinear speedup and constant efficiency for certain number of used processors have been achieved.


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BibTex entry:
author = {Krupka, J. and {\v S}ime{\v c}ek, I.},
title = {Parallel solvers of Poisson's equation},
booktitle = {6th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science},
publisher = {NOVPRESS},
address = {Brno},
year = {2010},
pages = {101--108},
ISBN = {978-80-87342-10-7},
language = {English}