Ten lectures on wavelets
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
New coarse grid operators for highly oscillatory coefficient elliptic problems
Journal of Computational Physics
Convergence of a Multigrid Method for Elliptic Equations with Highly Oscillatory Coefficients
SIAM Journal on Numerical Analysis
Wavelet-Based Numerical Homogenization
SIAM Journal on Numerical Analysis
Fast Multigrid Solution of the Advection Problem with Closed Characteristics
SIAM Journal on Scientific Computing
The black box multigrid numerical homogenization algorithm
Journal of Computational Physics
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
Coarse-Grid Correction for Nonelliptic and Singular Perturbation Problems
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Computing
Multigrid
Convergence Analysis of a Multigrid Method for a Convection-Dominated Model Problem
SIAM Journal on Numerical Analysis
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Kernel Preserving Multigrid Methods for Convection-Diffusion Equations
SIAM Journal on Matrix Analysis and Applications
A second generation wavelet based finite elements on triangulations
Computational Mechanics
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The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.