Author: Lise-Marie Imbert-Gerard
Requested Type: Poster
Submitted: 2016-02-14 17:49:29
Co-authors: S. Ambikasaran, C. Borges, L. Greengard
Courant Institute - NYU
251 mercer street
New York, 10012
We are interested in the propagation of the Ordinary mode in the cold plasma model, corresponding to the Helmholtz equation with a variable coefficient, proportional to the electron density.
We present a fast direct solver for the corresponding two dimensional scattering problem, 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 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. The work required by these solvers is typically of the order N to the power 3/2, where N denotes the number of degrees of freedom.