A Wavelet-Based Algebraic Multigrid Preconditioning for Iterative Solvers in Finite-Element Analysis

A new approach for algebraic multigrid, based on wavelets, is presented as an efficient preconditioner for iterative solvers applied to the solution of linear systems issued from finite-element analysis. It can be applied to complex systems in which the coefficient matrix violates the M-matrix property, as those arising from ungauged edge-based $AV$ finite-element formulation. When used as a preconditioner for the biconjugate gradient stabilized method it is shown that the proposed technique is more efficient than incomplete Cholesky preconditioner.