An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems

An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems∗

In this paper, we modify the adaptive wavelet algorithm from [Technical Report 1325, Department of Mathematics, Utrecht University, March 2005] so that it applies directly, i.e., without forming the normal equation, not only to self-adjoint elliptic operators but also to such operators to which generally nonsymmetric lower order terms are added, assuming that the resulting operator equation is ...

Iterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value Problems

The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space Hl (ii) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right h...

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...

A Preconditioned Gmres Method for Nonsymmetric or Indefinite Problems

A preconditioning technique is proposed for nonsymmetric or indefinite linear systems of equations. The main idea in our theory, roughly speaking, is first to use some "coarser mesh" space to correct the nonpositive portion of the eigenvalues of the underlying operator and then switch to use a symmetric positive definite preconditioner. The generality of our theory allows us to apply any known ...