A multiple-patch phase space method for computing trajectories on manifolds with applications to wave propagation problems
2007 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 5, no 3, 617-648 p.Article in journal (Refereed) Published
We present a multiple-patch phase space method for computing trajectories on two-dimensional manifolds possibly embedded in a higher-dimensional space. The dynamics of trajectories are given by systems of ordinary differential equations (ODEs). We split the manifold into multiple patches where each patch has a well-defined regular parameterization. The ODEs are formulated as escape equations, which are hyperbolic partial differential equations (PDEs) in a three- dimensional phase space. The escape equations are solved in each patch, individually. The solutions of individual patches are then connected using suitable inter-patch boundary conditions. Properties for particular families of trajectories are obtained through a fast post-processing. We apply the method to two different problems : the creeping ray contribution to mono-static radar cross section computations and the multivalued travel-time of seismic waves in multi-layered media. We present numerical examples to illustrate the accuracy and efficiency of the method.
Place, publisher, year, edition, pages
2007. Vol. 5, no 3, 617-648 p.
ODEs on a manifold, phase space method, escape equations, high frequency wave, propagation, geodesics, creeping rays, seismic waves, travel-time, partial-differential equations, dielectric coated cylinder, high-frequency, creeping waves, travel-times, computation, rays, rcs
IdentifiersURN: urn:nbn:se:kth:diva-16973ISI: 000249723400006ScopusID: 2-s2.0-35349024163OAI: oai:DiVA.org:kth-16973DiVA: diva2:335016
QC 201005252010-08-052010-08-052010-11-19Bibliographically approved