Variants of algebraic wavelet-based multigrid methods: Application to shifted linear systems

Abstract

In this paper, we describe some new variants and applications of the wavelet algebraic multigrid method. This method combines the algebraic multigrid method (a well known family of multilevel techniques for solving linear systems, without use of knowledge of the underlying problem) and the discrete wavelet transform. These two techniques can be combined in several ways, obtaining different methods for solution of linear systems; these can be used alone or as preconditioners for Krylov iterative methods. These methods can be applied for solution of linear systems with shifted matrices of the form A - hI , whose efficient solution is very important for implicit ODE methods, unsteady PDEs, computation of eigenvalues of large sparse matrices and other important problems.