Past Event: Oden Institute Seminar

The ultraspherical spectral method

Alex Townsend, Assistant Professor, Cornell University

Abstract

Pseudospectral methods, based on high degree polynomials, have spectral accuracy when solving differential equations but typically lead to dense and ill-conditioned matrices. The ultraspherical spectral method is a numerical technique to solve ordinary and partial differential equations, leading to almost banded well-conditioned linear systems while maintaining spectral accuracy. In this talk, we introduce the ultraspherical spectral method and develop it into a spectral element method using a modification to a hierarchical Poincaré-Steklov domain decomposition method. Bio Prof. Alex Townsend is an assistant professor at Cornell University in the Mathematics Department. His research is in Applied Mathematics and focuses on spectral methods, low-rank techniques, orthogonal polynomials, and fast transforms. Prior to Cornell, he was an Applied Math instructor at MIT (2014-2016) and a DPhil student at the University of Oxford (2010-2014). He was awarded a SIGEST paper award in 2019, the SIAG/LA Early Career Prize in applicable linear algebra in 2018, and the Leslie Fox Prize in numerical analysis in 2015.