Numerical zoom for multiscale problems with an application to flows through porous media

Abstract

We propose a technique for interactive mesh refinement in regions where the solution of a partial differential equation is less regular. Based on the method of harmonic patches, the idea is to bypass an expensive calculation on a fine mesh and yet retain the same accuracy with several much smaller computations. A general numerical zoom method is presented; then it is specialized to the case where the mesh in the zoom is a refinement of the coarse mesh; it is also compared with classic domain decomposition algorithms. Numerical examples are given for a porous flow modeled by Darcy's law.