A nonoverlapping domain decomposition method for Legendre spectral collocation problems

DOI10.1007/s10915-007-9136-xzbMath1134.65086OpenAlexW2058425883MaRDI QIDQ2385517

Bernard Bialecki, Andreas Karageorghis

Publication date: 12 October 2007

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-007-9136-x

zbMATH Keywords

convergenceDirichlet problemnumerical experimentsPoisson's equationconjugate gradient methodpreconditionernonoverlapping domain decompositionLegendre spectral collocation\(L\)-shaped regionSteklov-Poincaré problem

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Iterative numerical methods for linear systems (65F10)

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Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method, Matrix decomposition algorithms for elliptic boundary value problems: A survey, A modified Chebyshev pseudospectral DD algorithm for the GBH equation, The collocation solution of Poisson problems based on approximate Fekete points, Nonoverlapping domain decomposition with cross points for orthogonal spline collocation

Cites Work

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• Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle
• Preconditioned spectral multi-domain discretization of the incompressible Navier-Stokes equations
• Domain decomposition preconditioners for the spectral collocation method
• Spectral methods for problems in complex geometries
• Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
• A multidomain spectral approximation of elliptic equations
• An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• The Spectral Projection Decomposition Method for Elliptic Equations in Two Dimensions
• A Nonoverlapping Domain Decomposition Method for Orthogonal Spline Collocation Problems