Catherine E. Powell's research page

Research interests

• 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

Publications

• A posteriori error estimation for parametric operator equations with applications to PDEs with random data (with Alex Bespalov and David Silvester). Submitted. 2013.
  
  
• 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).
  
  
• 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 (2010), 733--760. (Electronic access 2009). Preprint .
  
  
• 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.

Current Research Projects

• Analysis of Numerical Methods for Partial Differential Equations with Random Data. (3 year EPSRC funded)
  
  
• Uncertainty quantification in computer simulations of groundwater flow problems with emphasis on contaminant transport

Software

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.