**MACSI **at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar

**Date: Friday 26 ^{th} October 2018, 16:00 **

**Speaker: Prof. Ivan Graham (Department of Mathematical Sciences, University of Bath, UK).**

**Title: Solving frequency domain wave equations at high frequency.**

**Abstract:** In several important applications - e.g. seismic exploration or earthquake prediction - one seeks to infer unknown material properties

of the earth's subsurface by sending seismic waves down and measuring the scattered field which comes back. In the process of solving

the inverse problem (so-called "full-waveform inversion") one needs to iteratively solve the forward scattering problem, each time

using an improved guess of the unknown material properties.

In industry practice, each step is usually done by solving the appropriate wave equation (elastic or acoustic) using explicit time stepping.

However in many applications it would be more efficient to solve in the frequency domain, except for the fact that the linear systems which arise in this case are extremely difficult

to solve iteratively.

In the simplest (acoustic) case the frequency domain problem is the Helmholtz equation. Its iterative solution is of great current interest. To understand the problem we use a combination

of linear algebra (iterative methods for non-normal complex linear systems) and PDE theory (stability theory for highly oscillatory non-self-adjoint PDEs).

In the talk I'll describe progress in this area with concentration on the use of parallel domain decompositon methods in a non-standard setting, aiming to solve discrete

Helmholtz problems of dimension N in order N time.

The techniques which I'll describe also can be used for the elastic wave equation and Maxwell's equations in

the frequency domain and I'll give some examples of this as well.

If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email romina.gaburro@ul.ie and Clifford Nolan (061 202766), __clifford.nolan@ul.ie__).

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.