Projects

This is a (non-exhaustive) list of things I've worked on. If you would like to talk about any of them, just send me an email.

Fast NLA and BIEs

I am working with Prof. Heather Wilber on fast numerical linear algebra for acoustic scattering problems solved using boundary integral equations. Our work combines rational approximation and classical BIE analysis to quickly locate scattering resonances across wide frequency bands and solve the scattering problem. A manuscript is in preparation.

Laplace BIE Solver

The Laplace problem on a separated domain, normally written with the differential operator, can be rewritten as a boundary integral equation (BIE). This leads to several analytic and numerical niceties. In this project, given Dirichlet boundary data, I solve the resulting integral equation for the unknown density layer and evaluate inside the domain. Specialized quadrature called quadrature by expansion (QBX) is used to improve accuracy near and on the boundary which requires the evaluation of a nearly-singular or singular integral. See this GitHub repository for code. And here are some slides for a presentation I gave on BIEs and QBX at UW's NARC.