GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
SIAM Journal on Scientific and Statistical Computing
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
SIAM Journal on Numerical Analysis
A posteriori error estimates for elliptic problems in two and three space dimensions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Stable multiscale bases and local error estimation for elliptic problems
Applied Numerical Mathematics - Special issue on multilevel methods
An adaptive wavelet-vaguelette algorithm for the solution of PDEs
Journal of Computational Physics
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
Journal of Computational Physics
A fast adaptive wavelet collocation algorithm for multidimensional PDEs
Journal of Computational Physics
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity
SIAM Journal on Scientific Computing
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
SIAM Journal on Scientific Computing
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Adaptive multiresolution finite element method based on second generation wavelets
Finite Elements in Analysis and Design
Journal of Computational Physics
A new wavelet multigrid method
Journal of Computational and Applied Mathematics
Symplectic wavelet collocation method for Hamiltonian wave equations
Journal of Computational Physics
Simulating 2D Waves Propagation in Elastic Solid Media Using Wavelet Based Adaptive Method
Journal of Scientific Computing
Multi-scale Daubechies wavelet-based method for 2-D elastic problems
Finite Elements in Analysis and Design
Wavelet-based adaptive large-eddy simulation with explicit filtering
Journal of Computational Physics
Algorithm 929: A suite on wavelet differentiation algorithms
ACM Transactions on Mathematical Software (TOMS)
Review: Wavelet-based numerical analysis: A review and classification
Finite Elements in Analysis and Design
Hi-index | 31.47 |
An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is described. The method is based on multi-dimensional second generation wavelets, and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems [Int. J. Comp. Fluid Dyn. 17 (2003) 151]. Wavelet decomposition is used for grid adaptation and interpolation, while a hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid. In order to accelerate the convergence of the solver, an iterative procedure analogous to the multigrid algorithm is developed. The overall computational complexity of the solver is O(N), where N is the number of adapted grid points. The accuracy and computational efficiency of the method are demonstrated for the solution of two- and three-dimensional elliptic test problems.