A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries

DOI10.1006/jcph.1994.1116zbMath0810.65097OpenAlexW2034318967MaRDI QIDQ1335594

V. Pereyra

Publication date: 17 October 1994

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1994.1116

zbMATH Keywords

numerical examplesLaplace equationCantor setsscattering matriceslarge scale problemsdirect solutionfractal boundaries

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices ⋮ On the solution of elliptic partial differential equations on regions with corners ⋮ A high-order, fast algorithm for scattering calculation in two dimensions ⋮ Fast algorithms for spectral collocation with non-periodic boundary conditions ⋮ Wave propagation using bases for bandlimited functions ⋮ Boundary element methods for acoustic scattering by fractal screens ⋮ The method of polarized traces for the 2D Helmholtz equation ⋮ Simulations of particle dynamics in magnetorheological fluids ⋮ Exact solutions to a nonlinear partial differential equation: the Product-of-Curvatures Poisson \((u_{x x} u_{y y} = 1)\) ⋮ Fast spectral projection algorithms for density-matrix computations

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