Matrix Decomposition Algorithms for Modified Spline Collocation for Helmholtz Problems

DOI10.1137/S106482750139964XzbMath1035.65135OpenAlexW1977115610MaRDI QIDQ4442133

Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis

Publication date: 20 January 2004

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s106482750139964x

zbMATH Keywords

algorithmsconvergence ratesDirichlet problemnumerical resultsboundary conditionsfast Fourier transformssuperconvergenceHelmholtz equationperiodic boundary conditionsNeumann problemtensor productspline collocationfast direct method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (10)

Modified nodal cubic spline collocation for elliptic equations ⋮ Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics ⋮ Modified nodal cubic spline collocation for three-dimensional variable coefficient second-order partial differential equations ⋮ High order convergent modified nodal bi‐cubic spline collocation method for elliptic partial differential equation ⋮ Matrix decomposition algorithms for elliptic boundary value problems: A survey ⋮ A fast direct solver for a fourth order finite difference scheme for Poisson's equation on the unit disc in polar coordinates ⋮ A Qualocation Method for Parabolic Partial Integro-Differential Equations in One Space Variable ⋮ Optimal superconvergent one step quadratic spline collocation methods ⋮ A quadratic spline collocation method for the Dirichlet biharmonic problem ⋮ Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method

Uses Software

• FFTPACK

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