Past Event: Oden Institute Seminar

Computing with Calderón projectors – Adventures in Rust

Prof. Timo Betcke, UCL, Dept of Math

Abstract

Calderón projectors are fundamental building blocks in the design of boundary integral equations. They encode the relationship between Dirichlet and Neumann data on the boundary of an obstacle and play a crucial role in the design of well-conditioned formulations for the solution of electrostatic, electromagnetic and acoustic scattering problems.

In the first half of the talk we present an overview of Calderón projectors and their practical applications. We show a number of concrete examples for their use to design well-conditioned and efficient solvers across topics as diverse as atmospheric simulations, virus scale electrostatic simulations, and high-intensity focused ultrasound.

In the second half of the talk we venture into software design. While our previous software developments were focused on Python, we have started developing a new simulation environment for boundary integral equations using Rust. We will discuss our motivation, and show current progress across the various software components, from numerical linear algebra in Rust, to grid management, and Fast Multipole Methods.

Biography

Prof Timo Betcke is Professor of Computational Mathematics in the Department of Mathematics at University College London (UCL), and Associate Director of the UCL Advanced Research Computing Centre (ARC).

Prof Betcke studied computational engineering at Hamburg University of Technology in Germany, followed by a DPhil in Numerical Analysis at the University of Oxford. After his DPhil he held postdoc positions in Germany and the UK. In 2009 he was awarded an EPSRC Career Acceleration Fellowship at the University of Reading, and in 2011 moved as Lecturer to UCL. He was later promoted to Reader and in 2018 to Professor of Computational Mathematics. He researches at the interface of computational mathematics, research software, and applications in the physical and engineering sciences. He is currently the UCL PI of two ongoing UK ExCALIBUR projects on integrated simulations at exascale and software generation for system level simulations at exascale.