A class of sparse spectral operators for inversion of powers of the Laplacian in N dimensions

For inversion of the Laplacian subject to Dirichlet boundary conditions and, more generally, for the kth power of the Laplacian subject to boundary conditions on the function and its first k − 1 derivatives in the normal coordinate, there is a sparse symmetric, well-conditioned, projection of the op...

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Veröffentlicht in:	Journal of scientific computing 1997-03, Vol.12 (1), p.57-73
1. Verfasser:	IERLEY, G. R
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary conditions Dirichlet problem Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Polynomials Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	For inversion of the Laplacian subject to Dirichlet boundary conditions and, more generally, for the kth power of the Laplacian subject to boundary conditions on the function and its first k − 1 derivatives in the normal coordinate, there is a sparse symmetric, well-conditioned, projection of the operator that results from an expansion in associated Legendre polynomials.
ISSN:	0885-7474 1573-7691
DOI:	10.1023/A:1025658404257