On the Direct Solution of Poisson's Equation on a Non-uniform Grid
A direct method for the numerical solution of two- and three-dimensional Poisson equations on non-staggered and non-uniform grids is presented. The method is an extension of the method of matrix decomposition proposed by Buzbee et al. (SIAM J. Numer. Anal. 7 (1970)). Attention is focussed on the sol...
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| Published in | Journal of computational physics Vol. 104; no. 1; pp. 93 - 98 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
01.01.1993
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1006/jcph.1993.1011 |
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| Abstract | A direct method for the numerical solution of two- and three-dimensional Poisson equations on non-staggered and non-uniform grids is presented. The method is an extension of the method of matrix decomposition proposed by Buzbee et al. (SIAM J. Numer. Anal. 7 (1970)). Attention is focussed on the solution of the Poisson equation subject to Neumann boundary condition and details of the performance of the algorithm including operation counts are presented. |
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| AbstractList | A direct method for the numerical solution of two- and three-dimensional Poisson equations on non-staggered and non-uniform grids is presented. The method is an extension of the method of matrix decomposition proposed by Buzbee et al. (SIAM J. Numer. Anal. 7 (1970)). Attention is focussed on the solution of the Poisson equation subject to Neumann boundary condition and details of the performance of the algorithm including operation counts are presented. The present direct method for numerically solving 2D and 3D Poisson equations on nonstaggered and nonuniform grids is an extension of the Buzbee et al. (1970) matrix-decomposition method. Attention is given to both the Poisson equation 2D solution, subject to the Neumann boundary condition, and details of the performance of the algorithm. It is noted that the symmetrization procedure brings out the integral constraint on the Neumann problem, as a consistency condition on the finite difference equations for both uniform and nonuniform grids. (O.C.) |
| Author | Korpela, Seppo A. Babu, V. |
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| Copyright | 1993 Academic Press 1993 INIST-CNRS |
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| Snippet | A direct method for the numerical solution of two- and three-dimensional Poisson equations on non-staggered and non-uniform grids is presented. The method is... The present direct method for numerically solving 2D and 3D Poisson equations on nonstaggered and nonuniform grids is an extension of the Buzbee et al. (1970)... |
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| SubjectTerms | Exact sciences and technology Mathematical methods in physics Numerical approximation and analysis Physics |
| Title | On the Direct Solution of Poisson's Equation on a Non-uniform Grid |
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