Event Date
Speaker: Abi Gopal, Assistant Professor, Department of Mathematics, UC Davis
Title: Direct solvers for scattering problems
Abstract: Problems involving acoustic or electromagnetic wave scattering often possess features that complicate their numerical solution, such as highly oscillatory solutions and unbounded domains. One effective approach is to first reformulate the relevant partial differential equation as an integral equation with much more favorable mathematical properties. The main trade-off is that discretizing the integral equation yields a linear system with a coefficient matrix that is dense (i.e., most entries are nonzero), making efficient solution nontrivial. Fortunately, the matrices that arise in these applications are highly structured, since the majority of their entries are given by evaluating certain translationally invariant kernel functions. This structure can be exploited to efficiently compute approximate inverses, which can then be rapidly applied to the right-hand sides. In this talk, I will discuss some recently developed solvers that proceed in this manner for variable-coefficient problems in acoustics and optical metasurface design.
Faculty website (links to Github): https://abigopal.github.io/