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Parallel Finite Elements for the Wave Equation

Using finite element for solving the wave equation lets us handle complex geometries in a convenient fashion. Geophysical models require large computational domains, and long simulation times, and the high accuracy required is most efficiently obtained by higher order elements. The ``usual'' Lagrange elements have to be modified in order to obtain an explicit solution scheme, while retaining the higher accuracy. In 2D, elements have been constructed by Cohen, Joly and Tordjman, while 3D elements are being worked on by Hannoyer, Mulder, and Oloui and Kern. Because the resulting method is explicit, it can be easily parallelized using domain decomposition.

The example below shows scattering of a source point by a conic obstacle. The domain is circle of radius 6 m, the velocity is 1 m/s, and the source is a 12 Hz Ricker wavelet. The mesh generator and mesh splitting software are from INRIA. We show several snapshots of the acoustic field, computed on 7 processors of a SGI Origin 2000 at Centre Charles Hermite (Nancy, France).


T = 2 s


T = 6 s


T = 10 s


T = 14 s

Contact

Michel.Kern-at-inria-dot-fr


URL: http://www-roc.inria.fr/who/Francois.Clement/sigma/parallel
Author: François Clément
Creation date: September 8th, 1998