Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

DOI10.1007/BF02832060zbMath1108.65104OpenAlexW2076443122MaRDI QIDQ861489

Samir Karaa, Michel Fournié

Publication date: 29 January 2007

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02832060

zbMATH Keywords

comparison of methodsnumerical examplesfinite difference schemecompact schemeGauss-Seidel iterative methodGMRES iterative methodmultigrid method/ preconditioning

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (7)

Fourth order compact schemes for variable coefficient parabolic problems with mixed derivatives ⋮ A robust higher order compact scheme for solving general second order partial differential equation with derivative source terms on nonuniform curvilinear meshes ⋮ High-Order Compact Schemes for Parabolic Problems with Mixed Derivatives in Multiple Space Dimensions ⋮ Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives ⋮ Compact higher order discretization of 3D generalized convection diffusion equation with variable coefficients in nonuniform grids ⋮ Combined compact difference scheme for linear second-order partial differential equations with mixed derivative ⋮ A new development of sixth order accurate compact scheme for the Helmholtz equation

Uses Software

• ILUT
• Wesseling

Cites Work

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• A compact multigrid solver for convection-diffusion equations
• A stable multigrid strategy for convection-diffusion using high order compact discretization
• Preconditioned iterative methods and finite difference schemes for convection-diffusion
• Analysis of stationary iterative methods for the discrete convection--diffusion equation with a 9-point compact scheme
• Compact \(h^ 4\) finite-difference approximations to operators of Navier- Stokes type
• A note on convergence of line iterative methods for a nine-point matrix
• High order ADI method for solving unsteady convection-diffusion problems
• Convergence and performance of iterative methods for solving variable coefficient convection-diffusion equation with a fourth-order compact difference scheme
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• Extension of high-order compact schemes to time-dependent problems
• A single cell high order scheme for the convection-diffusion equation with variable coefficients
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Accuracy, robustness and efficiency comparison in iterative computation of convection diffusion equation with boundary layers
• A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients
• Formulation and experiments with high‐order compact schemes for nonuniform grids
• A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
• High‐order compact scheme for the steady stream‐function vorticity equations
• ILUT: A dual threshold incomplete LU factorization

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