Seminar in Numerical Analysis: Erik Burman (University College London)

High order finite element methods for inverse initial value problems and wave propagation in heterogeneous media

In many applications both in medical science and in the geosciences the accurate approximation of solutions to wave equations is an important component for optimisation or inverse identification. Examples include thermoacoustic imaging or high frequency ultrasound treatments in medicine (HIFU) or fault slip analysis in seismology. These problems have in common the need for computational solution of an inverse problem where the forward problem is set in a heterogeneous domain. Indeed typically the sound speed in the bulk domain jumps over material interfaces. Sometimes there is even a need for coupling of the acoustic and elastodynamic equations in the presence of liquid inclusions. In this talk we will give a snapshot of our ongoing work in these topics, motivated by two such applications: HIFU and the propagation of seismic waves. After a brief introduction of the applications we will first discuss the analysis of some approximation methods for inverse initial value problems subject to the wave equation. We will then consider a hybrid high order method for the approximation of wave propagation in heterogeneous media, using cut element techniques to avoid meshing of interfaces. Finally we will discuss some open problems that remain in order to understand the approximation of the inverse initial value problem in heterogeneous media using high order methods.

For further information about the seminar, please visit this webpage.

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