Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimensions

dc.contributor.authorAmbikasaran, Sivaram
dc.contributor.authorBorges, Carlos
dc.contributor.authorImbert-Gerard, Lise-Marie
dc.contributor.authorGreengard, Leslie
dc.contributor.departmentApplied Mathematics
dc.description.abstractWe present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered eld using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial di erential equation, we obtain an integral equation of the Lippmann-Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad tree data structure which provides rapid access to arbitrary elements of the discretized system matrix. This permits the straightforward application of state-of-the-art algorithms for constructing compressed versions of the solution operator. These solvers typically require O(N3=2) work, where N denotes the number of degrees of freedom. We demonstrate the performance of the method for a variety of problems in both the low and high frequency regimes.en_US
dc.description.sponsorshipThis work was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DEFGO288ER25053 and by the O ce of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program Award FA9550-10-1-0180.en_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorAcoustic scatteringen_US
dc.subject.authorelectromagnetic scatteringen_US
dc.subject.authorpenetrable mediaen_US
dc.subject.authorfast direct solveren_US
dc.subject.authorintegral equationen_US
dc.subject.authorLippmann-Schwinger equationen_US
dc.subject.authorhigh order accuracyen_US
dc.titleFast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimensionsen_US