Matrix Decomposition Algorithms in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems

DOI10.1137/0916022zbMath0820.65009OpenAlexW2033867298MaRDI QIDQ4763746

Graeme Fairweather, Bernard Bialecki

Publication date: 17 September 1995

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

Full work available at URL: https://semanticscholar.org/paper/b1cdd1c54f099f6bda1df5cb86e08bd507089ba2

zbMATH Keywords

linear systemsnumerical experimentsgeneralized eigenvalue problemmatrix decompositionfast direct methodssecond-order linear elliptic partial differential equationsfinite element Galerkin equationstensor-product orthogonal spline collocation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Direct numerical methods for linear systems and matrix inversion (65F05)

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Non-asymptotic properties of spectral decomposition of large Gram-type matrices and applications, A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem, Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation, ADI+MDA orthogonal spline collocation for the pressure Poisson reformulation of the Navier-Stokes equation in two space variables, Matrix decomposition algorithms for elliptic boundary value problems: A survey, Orthogonal Spline Collocation for Poisson’S Equation with Neumann Boundary Conditions, Quasi-Trefftz spectral method for separable linear elliptic equations, Orthogonal spline collocation methods for partial differential equations, A high-order fast direct solver for singular Poisson equations, Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions, B-spline Methods in Fluid Dynamics, Almost block diagonal linear systems: sequential and parallel solution techniques, and applications, Efficient MFS algorithms in regular polygonal domains

Uses Software

• ELLPACK
• EISPACK
• COLROW