A wavelet-Galerkin scheme for analysis of large-scale problems on simple domains

A waveletÐGalerkin scheme tailored to address the numerical solution of large-scale boundary value problems deÞned on domains of simple geometry is presented. The variation of parameters, e.g. material properties, within the domain is arbitrary but the method is speciÞcally designed to solve problems where parameters vary in raster-like fashion. Boundary conditions are imposed via Lagrange multipliers using a Þctitious domain approach. A preconditioner specially designed for this problem is developed to guarantee that convergence of conjugate gradient algorithms is quick and insensitive to problem size. The strategy is applied to the solution of steady state, heat conduction problems in 2-D, but it can be generalized without conceptual changes to 3-D problems and to problems in linear elasticity. Copyright