An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs

Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations Multiscale Wavelet Methods for Pdes

w I n t r o d u c t i o n Adaptive methods are an important tool for numerically solving elliptic equations. Their origins appear in the adaptive grid refinements in finite element methods. Heuristically, adaptive methods are effective when trying to recover solutions u which exhibit singularities. Much impetus to the theory of adaptive finite element methods was provided by the introduction M ...

Parallel adaptive wavelet collocation method for PDEs

a r t i c l e i n f o a b s t r a c t Dynamic load balancing Wavelets Lifting scheme Second generation wavelets Adaptive grid Multiresolution Multilevel method Multigrid method Numerical method Partial differential equations Elliptic problem A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by...

Adaptive tensor product wavelet methods for solving PDEs

An optimal adaptive wavelet method - for strongly elliptic operator equations

An adaptive multilevel wavelet collocation method for elliptic problems

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 fo...