Dr Penny Davies

Senior Lecturer

Mathematics and Statistics

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.

Publications

Numerical approximations of first kind Volterra convolution equations with discontinuous kernels
Davies Penny J, Duncan Dugald B
Journal of Integral Equations and Applications Vol 29, pp. 41-73, (2016)
Convolution spline approximations for time domain boundary integral equations
Davies Penny J., Duncan Dugald B
Journal of Integral Equations and Applications Vol 26, pp. 369-412, (2014)
http://dx.doi.org/10.1216/JIE-2014-26-3-369
Global convergence and local superconvergence of first-kind Volterra integral equation approximations
Brunner Hermann, Davies P.J., Duncan D.B.
IMA Journal of Numerical Analysis Vol 32, pp. 1117-1146, (2012)
http://dx.doi.org/10.1093/imanum/DRR029
The stability of numerical approximations of the time domain current induced on thin wire and strip antennas
Davies P.J., Duncan D.B., Zubik-Kowal B.
Applied Numerical Mathematics Vol 55, pp. 48-68, (2005)
http://dx.doi.org/10.1016/j.apnum.2004.10.007
Stability and convergence of collocation schemes for retarded potential integral equations
Davies P.J., Duncan D.B.
SIAM Journal on Numerical Analysis Vol 42, pp. 1167-1188, (2004)
http://dx.doi.org/10.1137/S0036142901395321
Convergence of collocation methods for time domain boundary integral equations
Davies P.J.
Oberwolfach Reports Vol 1, pp. 579-581, (2004)

more publications

Professional activities

Royal Society Open Science (Journal)
Editorial board member
22/5/2014
External examiner (Hons mathematics)
External Examiner
2014
London Mathematical Society (External organisation)
Chair
11/2012
Research seminar (Cardiff)
Invited speaker
2012
Edinburgh Mathematical Society Presidential address
Keynote/plenary speaker
21/10/2011
Interdisciplinary meeting in Mathematics
Invited speaker
4/2011

more professional activities

Projects

Roberts Funding / Skills Training / RA4373
Davies, Penny (Principal Investigator)
Period 01-Oct-2008 - 31-Oct-2013
Fast and Accurate Methods for Time Domain Boundry Integral Equations
Davies, Penny (Principal Investigator)
Period 01-Jun-2005 - 30-Jun-2008

more projects

Address

Mathematics and Statistics
Livingstone Tower

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