Catherine 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

• Solving Stochastic Collocation Systems with Algebraic Multigrid (with Andrew Gordon). Submitted to IMAJNA. Preprint . (2010).
  
  
• Preconditioning Stochastic Galerkin Saddle Point Systems (with Elisabeth Ullmann). Submitted to SIMAX. Preprint . (2009).
  
  
• Solving Stochastic Collocation Systems with Algebraic Multigrid (with Andrew Gordon). To appear in 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.
  
  
• 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.