Projects per year

## Personal profile

### Personal Statement

My main areas of **research** are:

- numerical approximation of the time dependent boundary integral equation (TDBIE) formulation of scattering problems
- elastic stability and biomechanical modelling

Approx total** funding** of £130k as PI and £790k as Co-I from EPSRC and other sources for research projects, organising workshops, Taught Course Centre, etc

In 2014/5 I am **teaching** classes MM103 (mathematical modelling), MM300 (Laplace and Fourier transforms), MM406 (approximation theory), and the continuum mechanics part of the SMSTC Mathematical Models stream.

My current departmental **administration** load includes convening the academic committee and convening the Athena SWAN self assessment team (we submitted an application for a bronze award in Nov 2014).

**Professional activities** in 2014/15 include:

- co-opted member of CMS (Council for the Mathematical Sciences)
- chair of LMS (London Mathematical Society) nominating committee
- member of CMS and EPSRC working groups on the mathematical sciences people pipeline
- member of editorial boards of J Integral Eqn Appl and Roy Soc Open Science

Past **highlights** include being President of the Edinburgh Mathematical Society (EMS) in 2009-11 and being awarded an OBE for service to mathematics in the 2014 Birthday Honours list

**Research details**

Wave propagation and scattering is an important area which despite its long history (the "wave equation'' was derived by d'Alembert in 1747) still provides significant challenges in analysis and computation. Wave propagation has many important applications such as telecommunications, non-destructive testing, geological exploration, tomography, radar, sonar, and other military uses. It is very important for the applications areas to use reliable and efficient computational techniques, and developing these typically involves a combination of applied and numerical analysis.

One of my main research interests is the numerical approximation of time domain wave scattering problems which are formulated as boundary integral equations. These problems are computationally challenging: convolution quadrature methods which use global time basis functions are numerically stable (but involve dense system matrices and are hence computationally expensive), and it is known that methods which use local time basis functions are much less stable (any perturbations such as induced by numerical quadrature can result in an exponentially unstable approximation). Recent collaborative work is focused on the development of methods which share some of the desirable characteristics of convolution quadrature but the underlying basis functions have narrow support, which means that these new approximation methods are computationally efficient.alysis.

Another area of interest is the development of mathematical models (using elasticity) for the mechanical properties of various materials, and associated problems in elastic stability.

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## Projects 2005 2013

- 2 Finished

## Roberts Funding / Skills Training / RA4373

EPSRC (Engineering and Physical Sciences Research Council)

1/10/08 → 31/10/13

Project: Research Studentship - Internally Allocated

## Fast and Accurate Methods for Time Domain Boundry Integral Equations

EPSRC (Engineering and Physical Sciences Research Council)

1/06/05 → 30/06/08

Project: Research

## Research Output 1996 2019

## The MRE inverse problem for the elastic shear modulus

Davies, P. J., Barnhill, E. & Sack, I., 23 Jul 2019, In : SIAM Journal on Applied Mathematics . 79, 4, p. 1367–1388 22 p.Research output: Contribution to journal › Article

## Heterogeneous multifrequency direct inversion (HMDI) for magnetic resonance elastography with application to a clinical brain exam

Barnhill, E., Davies, P. J., Ariyurek, C., Fehlner, A., Braun, J. & Sack, I., 31 May 2018, In : Medical Image Analysis. 46, p. 180-188 9 p.Research output: Contribution to journal › Article

## Prizes

## Awarded OBE for services to mathematics in 2014 Birthday Honours list

Penny Davies (Recipient), Jun 2014

Prize: National/international honour

## Activities 2003 2014

## Royal Society Open Science (Journal)

Penny Davies (Editorial board member)Activity: Publication peer-review and editorial work types › Editorial board member

## External examiner (Hons mathematics)

Penny Davies (External Examiner)Activity: Examination types › Examination