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Computing

, Volume 95, Supplement 1, pp 49–60 | Cite as

Different approaches to the numerical solution of the 3D Poisson equation implemented in Python

  • Moritz BraunEmail author
Article

Abstract

The numerical solution of the three-dimensional Poisson equation with Dirichlet boundary conditions, which is of importance for a wide field of applications in Computational Physics and Theoretical Chemistry is considered using the method of finite elements for a model problem. The direct, the iterative and the factorized direct methods for solving the corresponding linear system of equations are discussed and implemented in the scripting language Python http://www.python.org making use of the numpy http://www.numpy.org and pysparse http://pysparse.sourceforge.net extensions. The relative performance of the different approaches is compared and it is shown, that the factorized direct method is vastly superior for larger problem sizes. A formalism for implementing the Dirichlet boundary conditions in the factorization approach is derived and presented in some detail, since it is to the best of our knowledge new.

Keywords

Poisson Equation Finite element method Python  Factorization approach 

Mathematics Subject Classification

31-04 35J05 68N99 

Notes

Acknowledgments

Financial support by the University of South Africa (UNISA) is acknowledged.

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of South Africa PretoriaSouth Africa

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