Numerical Analysis and Scientific Computing Seminar

Direct solvers for integral equations in broadband applications

Speaker: Abi Gopal, Yale University

Location: Warren Weaver Hall 1302

Date: March 11, 2022, 10 a.m.

Synopsis:

In recent years there have been many advances in the development of fast direct solvers for the linear systems arising from the discretization of integral equations. In this talk I present a new technique for accelerating the application of a particular class of these solvers to scattering problems where multiple frequencies are of interest. The technique works by accelerating the "compression stage" of direct solvers by precomputing bases that approximately span the column and row spaces of various off-diagonal blocks of all coefficient matrices corresponding to a range of different wavenumbers. The key observation is that the ranks when this is done are often comparable to those in the single frequency case at the highest frequency considered. This is joint work with Per-Gunnar Martinsson at UT Austin.