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401-5003-71L 4 Credits DR , MSC D-MATH

At the Interface Between Semiclassical Analysis and Numerical Analysis of Wave-Scattering Problems

Lecturers: Prof. Dr. Euan Alastair Spence
Examiners: Prof. Dr. Ralf Hiptmair, Prof. Dr. Euan Alastair Spence
VVZ CR n/a

Last Updated: 2026-02-05 15:47:37

Abstract

Postgraduate degree lecture

Content

Semiclassical 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.

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes
Offered in the Winter 2021/22 and Summer 2022 Examination Sessions only.

Registration & Places

Signup End
27.09.2021

Course Components

Type Title Time & Place Hours
lecture At the Interface Between Semiclassical Analysis and Numerical Analysis of Wave-Scattering Problems
Fridays, 10:15 - 12:00 First lecture: 1 October More information and registration (registration deadline: 27 September)
  • Fri 10:15-12:00 (HG G 43)
2 h weekly

Offered In