Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation

DOI10.1007/BF02142689zbMath0817.65093MaRDI QIDQ1344103

Bernard Bialecki

Publication date: 13 August 1995

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

Poisson equationcyclic reductioniterative solutionHermite bicubic 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) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (3)

Orthogonal spline collocation methods for partial differential equations ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ The cyclic reduction algorithm: From Poisson equation to stochastic processes and beyond. In memoriam of Gene H. Golub

Uses Software

• MUDPACK
• MUDPACK-2
• FISHPAK
• COLROW
• ARCELO
• HFFT

Cites Work

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• Recent enhancements in MUDPACK, a multigrid software package for elliptic partial differential equations
• A parallel block cyclic reduction algorithm for the fast solution of elliptic equations
• An alternating direction implicit method for orthogonal spline collocation linear systems
• Direct methods for the solution of the discrete Poisson equation: some comparisons
• A practical guide to splines
• The ordering of tridiagonal matrices in the cyclic reduction method for Poisson's equation
• Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
• A $C^1 $ Finite Element Collocation Method for Elliptic Equations
• FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
• Algorithm 541: Efficient Fortran Subprograms for the Solution of Separable Elliptic Partial Differential Equations [D3]
• Fast Direct Solvers for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations
• A direct Method for the Discrete Solution of Separable Elliptic Equations
• The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
• A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension
• A note on the efficient implementation of certain Padé Methods for linear parabolic problems
• Preconditioned Richardson and Minimal Residual Iterative Methods for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations
• A Fast Domain Decomposition Poisson Solver on a Rectangle for Hermite Bicubic Orthogonal Spline Collocation
• On Direct Methods for Solving Poisson’s Equations

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