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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Bibliographic Details
Published inAdvances in Quantum Chemistry Vol. 50; pp. 235 - 247
Main Authors Berger, Raphael J.F., Sundholm, Dage
Format Book Chapter
LanguageEnglish
Published United States Elsevier Science & Technology 2005
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ISBN9780120348503
0120348500
ISSN0065-3276
2162-8815
DOI10.1016/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.
ISBN:9780120348503
0120348500
ISSN:0065-3276
2162-8815
DOI:10.1016/S0065-3276(05)50011-X