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 field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of 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 low and high frequency regimes.
Original language | English (US) |
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Pages (from-to) | A1770-A1787 |
Journal | SIAM Journal on Scientific Computing |
Volume | 38 |
Issue number | 3 |
DOIs | |
State | Published - 2016 |
Keywords
- Acoustic scattering
- Adaptivity
- Electromagnetic scattering
- Fast direct solver
- High-order accuracy
- Integral equation
- Lippmann-schwinger equation
- Penetrable media
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics