Multilevel preconditioning for the finite volume method

DOI10.1090/S0025-5718-2012-02582-8zbMath1250.65132OpenAlexW2090813019MaRDI QIDQ2894513

Shi Shu, Yonghai Li, Qingsong Zou, Yuesheng Xu

Publication date: 29 June 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2012-02582-8

zbMATH Keywords

finite volume methodnumerical examplesdiscontinuous coefficientspreconditioningelliptic boundary value problemsmultilevel methodcondition numbersmultilevel preconditionerswavelet preconditioners

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) PDEs with low regular coefficients and/or low regular data (35R05) Preconditioners for iterative methods (65F08) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (14)

A family of quadratic finite volume method for solving the Stokes equation ⋮ Modified hierarchy basis for solving singular boundary value problems ⋮ Robust BDDC algorithms for finite volume element methods ⋮ \(L^2\) error estimates for a family of cubic finite volume methods on triangular meshes ⋮ JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research ⋮ Admissible Regions for Higher-Order Finite Volume Method Grids ⋮ Some recent advances on vertex centered finite volume element methods for elliptic equations ⋮ A Two-Grid Finite-Volume Method for the Schrodinger Equation ⋮ Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations ⋮ Higher-order finite volume methods. II: Inf-sup condition and uniform local ellipticity ⋮ Analysis of linear and quadratic simplicial finite volume methods for elliptic equations ⋮ $L^2$ Error Estimates for High Order Finite Volume Methods on Triangular Meshes ⋮ Conditioning of the finite volume element method for diffusion problems with general simplicial meshes ⋮ A construction of higher-order finite volume methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum: On the multi-level splitting of finite element spaces
• Higher-order finite volume methods for elliptic boundary value problems
• On the finite volume element method
• On function spaces related to finite element approximation theory
• Two preconditioners based on the multi-level splitting of finite element spaces
• Hierarchical error estimates for finite volume approximation solution of elliptic equations
• \(L^{2}\) error estimate of the finite volume element methods on quadrilateral meshes
• Analysis of linear and quadratic simplicial finite volume methods for elliptic equations
• Multilevel preconditioning
• Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence
• Multigrid algorithms for a vertex-centered covolume method for elliptic problems
• Locally supported, piecewise polynomial biorthogonal wavelets on nonuniform meshes
• Nonlinear functionals of wavelet expansions -- adaptive reconstruction and fast evaluation
• A note on the optimal \(L^2\)-estimate of the finite volume element method
• Adaptive wavelet methods for elliptic operator equations with nonlinear terms
• Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems
• Spectral (finite) volume method for conservation laws on unstructured grids. VI: Extension to viscous flow
• Multilevel augmentation methods for differential equations
• Wavelet bases of Hermite cubic splines on the interval
• Tree wavelet approximations with applications
• Generalized Difference Methods for a Nonlinear Dirichlet Problem
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
• The Finite Volume Element Method for Diffusion Equations on General Triangulations
• Parallel Multilevel Preconditioners
• UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Some Error Estimates for the Box Method
• A Preconditioned GMRES Method for Nonsymmetric or Indefinite Problems
• The Accuracy of Cell Vertex Finite Volume Methods on Quadrilateral Meshes
• Iterative Methods by Space Decomposition and Subspace Correction
• The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
• A Covolume Method Based on Rotated Bilinears for the Generalized Stokes Problem
• On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
• Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions

This page was built for publication: Multilevel preconditioning for the finite volume method