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A multiple-patch phase space method for computing trajectories on manifolds with applications to wave propagation problemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2007 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 5, no 3, p. 617-648Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2007. Vol. 5, no 3, p. 617-648
##### Keywords [en]

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
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-16973ISI: 000249723400006Scopus ID: 2-s2.0-35349024163OAI: oai:DiVA.org:kth-16973DiVA, id: diva2:335016
#####

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##### Note

QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
##### In thesis

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.

1. Topics in Analysis and Computation of Linear Wave Propagation$(function(){PrimeFaces.cw("OverlayPanel","overlay13586",{id:"formSmash:j_idt1181:0:j_idt1185",widgetVar:"overlay13586",target:"formSmash:j_idt1181:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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