Multiresolution Representation in Unstructured Meshes

Abstract

In this paper we describe techniques to represent data which originate from discretization of functions in unstructured meshes in terms of their local scale components. To do so we consider a nested sequence of discretization, which corresponds to increasing levels of resolution, and we define the scales as the "difference in information" between any two successive levels. We obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of numerical schemes by solving for the more compact representation of the numerical solution in terms of its significant scale-coefficients.