Monday, July 10

Multiscale Methods for Conservation Laws

10:30 AM-12:30 PM
Room: Rio Mar 7

Wavelet decompositions provide a basic tool for developing high performance large-scale computer simulations. Fast multiscale or multiresolution (MR) methods use the wavelet decomposition of the solution to identify regions of large variations. The underlying scheme is then applied only to those regions, leading to a compressed form of the numerical operator. Multiscale methods have been shown to considerably speed up 1-D and 2-D structured grid computations, and very recently, on unstructured grids in 3-D as well. From an applications' perspective, it holds great promise to be a viable alternative to traditional adaptive gridding methods. The speakers in this session will present current trends in both research and applications of the multiscale methods to conservation laws, with special emphasis placed on unstructured grid computations.

Organizers: Barna L. Bihari
Rockwell Science Center, USA
Kevin Amaratunga
Massachusetts Institute of Technology, USA
10:30-10:55 On Multiresolution Schemes for Unstructured Grids
Barna L. Bihari, Organizer; and S. V.. Ramakrishnan, Rockwell Science Center, USA
11:00-11:25 Wavelet Transforms on 3-D Unstructured Grids for the Fast Computation of Integral Equations
Kevin Amaratunga, Organizer; and Julio E. Castrillon-Candas, Massachusetts Intitute of Technology
11:30-11:55 A Fully Adaptive Multiscale Scheme for Conservation Laws
Wolfgang Dahmen, Birgit Gottschlich-Müller, and Siegfried Müller, Institut für Geometrie und Praktische Mathematik, RWTH, Germany
12:00-12:25 Fine Grid Simulations with a Multilevel Algorithm for 2D Conservation Laws
G. Chiavassa, R. Donat and Antonio Marquina, Universitat de Valencia, Spain

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