A Class of Sparse Spectral Operators for Inversion of Powers of the Laplacian in N Dimensions

Authors:
Glenn R. Ierley
Affiliations:
Institute for Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego 9500 Gilman Drive, La Jolla 92093-0225. grierley@ucsd.edu
Venue:
Journal of Scientific Computing
Year:
1997

Citing 3
Cited 1

Efficient spectral-Galerkin method I: direct solvers of second-and fourth-order equations using Legendre polynomials

SIAM Journal on Scientific Computing
Efficient spectral-Galerkin method II.: direct solvers of second- and fourth-order equations using Chebyshev polynomials

SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Matrix decomposition algorithms for elliptic boundary value problems: a survey

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.