Abstract
Matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermite bicubics is used to solve Poisson’s equation on the unit square. Like their orthogonal spline collocation counterparts, these MDAs, which require O(N 2logN) operations on an N×N uniform partition, are based on knowledge of the solution of a generalized eigenvalue problem associated with the corresponding discretization of a two-point boundary value problem. The eigenvalues and eigenfunctions are determined for various choices of boundary conditions, and numerical results are presented to demonstrate the efficacy of the MDAs.
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D. Abram Lipman and Gadalia M. Weinberg were supported in part by National Science Foundation grant DMS-9912293.
Que N. Nguyen was supported in part by National Science Foundation grant DGE-0231611.
Weiwei Sun was supported in part by a grant from City University of Hong Kong (Project No. CityU 7002110).
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Bialecki, B., Fairweather, G., Knudson, D.B. et al. Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Numer Algor 52, 1–23 (2009). https://doi.org/10.1007/s11075-008-9255-y
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DOI: https://doi.org/10.1007/s11075-008-9255-y
Keywords
- Elliptic boundary value problems
- Finite element Galerkin method
- Piecewise Hermite cubics
- Generalized eigenvalue problem
- Eigenvalues and eigenfunctions
- Matrix decomposition algorithm