A Non-Iterative Numerical Solver of Poisson and Helmholtz Equations Using High-Order Finite-Element Functions
A non-iterative finite-element solver for n-dimensional Poisson and Helmholtz equations has been developed. The electrostatic potential and the charge-density distributions are expanded in finite-element functions consisting of up to sixth-order Lagrange interpolation functions. The method can also...
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Published in | Advances in Quantum Chemistry Vol. 50; pp. 235 - 247 |
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Main Authors | , |
Format | Book Chapter |
Language | English |
Published |
United States
Elsevier Science & Technology
2005
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Subjects | |
Online Access | Get full text |
ISBN | 9780120348503 0120348500 |
ISSN | 0065-3276 2162-8815 |
DOI | 10.1016/S0065-3276(05)50011-X |
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Summary: | A non-iterative finite-element solver for n-dimensional Poisson and Helmholtz equations has been developed. The electrostatic potential and the charge-density distributions are expanded in finite-element functions consisting of up to sixth-order Lagrange interpolation functions. The method can also be applied to differential equations in more than three-dimensional spaces. It is efficient and well suited for parallel computers, since the innermost loops constitute matrix multiplications and the outer ones can be used as parallelizing index on a parallel computer. The solution of the n-dimensional Poisson and Helmholtz equations scales as N(n+1n), where N=Nin denotes the grid size and Ni is the number of element functions, i.e., the number grid points, in each dimension. |
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ISBN: | 9780120348503 0120348500 |
ISSN: | 0065-3276 2162-8815 |
DOI: | 10.1016/S0065-3276(05)50011-X |