Abstract. The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.
Introduction à Scilab-exercices pratiques corrigés d'algebre linéaire & Algebre linéaire numérique. Cours et exercices − published by Ellipses-Edition Marketing S.A.
We discuss the use of Padé-Legendre interpolants as an approach for the postprocessing of data contaminated by Gibbs oscillations. A fast interpolation based reconstruction is proposed and its excellent performance illustrated on several problems. Almost non-oscillatory behavior is shown without knowledge of the position of discontinuities. Then we consider the performance for computational data obtained from nontrivial tests, revealing some sensitivity to noisy data. A domain decomposition approach is proposed as a partial resolution to this and illustrated with examples.
We design suitable parallel in time algorithms coupled with reduction methods for the stiff differential systems integration arising in chemical kinetics. We consider linear as well as nonlinear systems. The numerical efficiency of our approach is illustrated by a realistic ozone production model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.