ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDE

DOI10.1137/S1064827595281794zbMath0912.65092OpenAlexW2137095065MaRDI QIDQ4389246

P. Tsompanopoulou, E. A. Vavalis

Publication date: 12 May 1998

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

Full work available at URL: https://doi.org/10.1137/s1064827595281794

zbMATH Keywords

numerical experimentselliptic partial differential equationscomputational efficiencyalternating direction implicit methodscubic 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) Iterative numerical methods for linear systems (65F10) Complexity and performance of numerical algorithms (65Y20)

Related Items

Modified nodal cubic spline collocation for elliptic equations ⋮ Optimal alternating direction implicit preconditioners for conjugate gradient methods ⋮ Modified nodal cubic spline collocation for three-dimensional variable coefficient second-order partial differential equations ⋮ ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDE ⋮ Orthogonal spline collocation methods for partial differential equations ⋮ An ADI Petrov-Galerkin method with quadrature for parabolic problems ⋮ The alternating-direction schemes and numerical analysis for the three-dimensional seawater intrusion simulation.

Uses Software

• ELLPACK
• BLAS

Cites Work

• Unnamed Item
• Unnamed Item
• A tensor product generalized ADI method for elliptic problems on cylindrical domains with holes
• An alternating direction implicit method for orthogonal spline collocation linear systems
• On convergence of alternating direction procedures
• Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations
• Tensor Product Generalized ADI Methods for Separable Elliptic Problems
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• A $C^1 $ Finite Element Collocation Method for Elliptic Equations
• On the Asymptotic Convergence of Spline Collocation Methods for Partial Differential Equations
• Convergence of $O(h^4 )$ Cubic Spline Collocation Methods for Elliptic Partial Differential Equations
• A Tensor product generalized ADI method for the method of planes
• Collocation methods for linear elliptic problems
• Efficient Computer Manipulation of Tensor Products
• A set of level 3 basic linear algebra subprograms
• ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDE
• Iterative Line Cubic Spline Collocation Methods for Elliptic Partial Differential Equations in Several Dimensions
• Analysis of Iterative Line Spline Collocation Methods for Elliptic Partial Differential Equations
• On a generalised alternating direction implicit method for solving Laplace's equation