Noniterative overlapping domain decomposition method for acoustic wave propagation

Abstract

A noniterative overlapping domain decomposition technique for a linear acoustic wave equation is presented, based on the concept of regionofdependence of a point P. The field computed in P after a time interval Δt depends on the initial values of the points inside this region, whose extension depends mainly on Δt that in turn depends on the time integration scheme. In practice, the original domain is decomposed into overlapping subdomains containing an interface. The overlaps include the region of dependence of the interface. The numerical solution is then computed separately and concurrently on each subdomain. Finally, the fields on each overlap are updated with the values of the field in the underlying domain. The implementation for an explicit scheme is straightforward. For implicit schemes, great advantage can be gained by using a local spatial interpolation. In this work, the spectral element method and the implicit Newmark method are used, respectively, for spatial and time integration. The overlap region is reduced to a maximum of two elements. Numerical results are shown for 1-D and 2-D cases.