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

Loading...
Thumbnail Image
Authors
Ambikasaran, Sivaram
Borges, Carlos
Imbert-Gerard, Lise-Marie
Greengard, Leslie
Subjects
Acoustic scattering
electromagnetic scattering
penetrable media
fast direct solver
integral equation
Lippmann-Schwinger equation
high order accuracy
adaptivity
Advisors
Date of Issue
2015-05-26
Date
Publisher
Language
Abstract
We 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.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
Other Units
Identifiers
NPS Report Number
Sponsors
This 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.
Funder
Format
Citation
Distribution Statement
Rights
This 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.
Collections