401-5003-71L  At the Interface Between Semiclassical Analysis and Numerical Analysis of Wave-Scattering Problems

SemesterAutumn Semester 2021
LecturersE. Spence
Periodicitynon-recurring course
Language of instructionEnglish

AbstractPostgraduate degree lecture
ContentSemiclassical analysis (SCA) is a branch of microlocal analysis concerned with rigorously analysing PDEs with large (or small) parameters. On the other hand, numerical analysis (NA) seeks to design numerical methods that are accurate, efficient, and robust, with theorems guaranteeing these properties.

In the context of high-frequency wave scattering, both SCA and NA share the same goal – that of understanding the behaviour of the scattered wave – but these two fields have operated largely in isolation, mainly because the tools and techniques of the two fields are somewhat disjoint.

This by-and-large self-contained course focuses on the Helmholtz equation, which is arguably the simplest possible model of wave propagation. Our first goal will be to show how even relatively-simple tools from semiclassical analysis can be used to prove fundamental results about the numerical analysis of finite-element method applied to the high-frequency Helmholtz equation.
Prerequisites / NoticeThe course will aim at being accessible both to students coming from a numerical-analysis/applied-maths background and to students coming from an analysis background.