A class of sparse spectral operators for inversion of powers of the Laplacian in \(N\) dimensions (Q1387814)
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scientific article; zbMATH DE number 1160527
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of sparse spectral operators for inversion of powers of the Laplacian in \(N\) dimensions |
scientific article; zbMATH DE number 1160527 |
Statements
A class of sparse spectral operators for inversion of powers of the Laplacian in \(N\) dimensions (English)
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4 March 1999
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The inversion of the \(k\)th power of the Laplacian subject to boundary conditions on the function and its first \(k-1\) derivatives is considered. Sparse symmetric, well-conditioned projections of the operator resulting from an expansion in associated Legendre polynomials are derived. Numerical examples show the efficiency of the proposed methods.
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inversion of powers of the Laplacian
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Poisson equation
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biharmonic equation
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Chebyshev polynomials
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Legendre polynomials
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spectral method
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numerical examples
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