Catherine E. Powell's research page
My research is mainly concerned with numerical linear algebra for solving sparse, structured systems of equations arising in finite element discretisations of partial differential equations. I am currently interested in numerical methods, efficient solvers and preconditioners for PDEs with random data.
Topics: numerical analysis, finite elements, error estimation, mixed finite elements, stochastic finite elements, numerical linear algebra, saddlepoint systems, fast solvers, preconditioning, multigrid, algebraic multigrid
Applications: groundwater flow modelling, fluid flow, image processing
An Introduction to Computational Stochastic PDEs. G. Lord, C.E. Powell and T. Shardlow. Coming soon in 2014.
- PIFISS: Potential Incompressible Flow Software Library
This code illustrates the use of Krylov subspace solvers and preconditioning techniques based on algebraic multigrid for primal and mixed formulations of the steady-state diffusion problem. Test problems are included with discontinuous and anisotropic diffusion coefficients.
- Gaussian random field generators in the NAG Fortran Library
The new routines G05ZMF, G05ZNF, G05ZPF G05ZQF, G05ZRF, G05ZSF and G05ZTF in Mark 24 of the NAG Fortran Library are based on the method of circulant embedding. These were developed during a collaboration between the PhD student Phillip Taylor and NAG (who partially funded the PhD project). The codes can be used to generate realisations of mean zero Gaussian random fields and stochastic processes with both standard and user-defined stationary covariance functions.
Most of the following pieces of work can be obtained from journals or as preprints. Copies of papers which have no active links can be obtained from me by sending me an e-mail and asking nicely.
- A preconditioner for fictitious domain formulations of elliptic PDEs on uncertain parameterized domains (with Andrew Gordon). Submitted. 2013. Preprint
- A posteriori error estimation for parametric operator equations with applications to PDEs with random data (with Alex Bespalov and David Silvester). SIAM Journal Sci. Comp. To appear (2013). Preprint
- Preconditioning steady-state Navier-Stokes equations with random data (with David Silvester). SIAM Journal Sci. Comp. 34(5). (2012) .
- A framework for the development of implicit solvers for incompressible flow problems (with Alex Bespalov and David Silvester). Discrete and Continuous Dynamical Systems - Series S. Vol 5 (6), pp. 1195--1221. (2012). (OPEN ACCESS)
- A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data (with Alex Bespalov and David Silvester). SIAM Journal on Numerical Analysis. 50(4), 2039--2063. (2012)
- Solving Stochastic Collocation Systems with Algebraic Multigrid (with Andrew Gordon). IMA Journal of Numerical Analysis. Volume 32 (3). pp 1051-1070. (2011) .
- Preconditioning Stochastic Galerkin Saddle Point Systems (with Elisabeth Ullmann). SIAM J. Matrix. Anal., 31, pp. 2813--2840 (2010) . (Preprint version) .
- Solving Stochastic Collocation Systems with Algebraic Multigrid (with Andrew Gordon). Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications. Springer.
- H(div) Preconditioning for a Mixed Finite Element Formulation of The Stochastic Diffusion Problem. (With Darran Furnival and Howard Elman). Mathematics of Computation. 79, pp, 733--760 (2010). (Electronic access 2009).
Preprint version .
- Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data. (With O.G. Ernst, E. Ullmann, D.J. Silvester). SIAM Journal Sci. Comp., 31,2, pp. 1424-1447, (2009) .
- Block-diagonal preconditioning for spectral stochastic finite element systems. (With Howard Elman). IMA Journal of Numerical Analysis. 29 (2), pp. 350--375. , April 2009. (Electronic access 2008).
- PIFISS. Potential (Incompressible) Flow & Iterative Solution Software Guide. MIMS Preprint 2007.
- Robust Preconditioning for Second-Order Elliptic PDEs with Random Field Coefficients. MIMS Preprint 2006.
- Parameter-free H(div) preconditioning for mixed finite element formulation of diffusion problems.
IMA J. Numer. Anal., 25(4), pp.783-796, 2005.
- Improving the Forward Solver for the Complete Electrode Model in EIT using Algebraic Multigrid
(with M. Soleimani and N. Polydorides). IEEE Transactions on Medical Imaging, 24(5), pp.577-584, 2005.
- Black-Box Preconditioning for Self-Adjoint Elliptic PDEs (with David Silvester)
Lecture Notes in Computational Science and Engineering, 35, Springer. 2003.
(CISC 2002, Challenges in Scientific Computing.) ( Preprint version)
- Optimal Preconditioning for Raviart-Thomas Mixed Formulation of Second-Order Elliptic Problems (with David Silvester) SIMAX, Vol. 25, No.3, pp.718-738, 2003.
- Optimal Preconditioning for Mixed Finite Element Formulations of Second-Order Elliptic Problems
Ph.D thesis, UMIST, 2003. (Available at MIMS E-print server or request by e-mail.)
- An analysis of a mixed finite element method for the biharmonic equation.
MSc. Dissertation. UMIST, 2000.
Past Research Projects