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MULTIRESOLUTION REPRESENTATION IN UNSTRUCTURED MESHES
 

Summary: MULTIRESOLUTION REPRESENTATION IN
UNSTRUCTURED MESHES
R´EMI ABGRALL AND AMI HARTEN
SIAM J. NUMER. ANAL. c 1998 Society for Industrial and Applied Mathematics
Vol. 35, No. 6, pp. 2128­2146, December 1998 002
Abstract. In this paper we describe techniques to represent data which originate from dis-
cretization 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.
Key words. multiresolution analysis, unstructured meshes, ENO reconstruction
AMS subject classifications. 65D99, 65M99, 41A05
PII. S0036142997315056
1. Introduction. Fourier analysis, which provides a way to represent square-
integrable functions in terms of their sinusoidal scale-components, has contributed
greatly to all fields of science. The main drawback of Fourier analysis is in its globality;
a single irregularity in the function dominates the behavior of the scale-coefficients and
prevents us from getting immediate information about the behavior of the function

  

Source: Abgrall, Rémi - Institut de Mathematiques de Bordeaux, Université Bordeaux
Frey, Pascal - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Mathematics