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

Content Provider	Springer Nature Link
Author	Braun, Moritz
Copyright Year	2013
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.
Ending Page	60
Page Count	12
Starting Page	49
File Format	PDF
ISSN	0010485X
e-ISSN	14365057
Journal	Computing
Issue Number	1
Volume Number	95
Language	English
Publisher	Springer Vienna
Publisher Date	2013-02-01
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Finite element method Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation Software Engineering Computer Application in Administrative Data Processing Poisson Equation Computer Science Factorization approach Artificial Intelligence (incl. Robotics) Information Systems Applications (incl. Internet) Explicit machine computation and programs (not the theory of computation or programming) Computer Communication Networks Python
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics Numerical Analysis Computer Science Applications Software

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