This is a three year EPSRC funded
research project.
Summary
Recently, sophisticated numerical methods for approximating solutions to PDEs with
correlated random data have been proposed. To date, this work has been restricted to
scalar, elliptic PDEs and the question of efficient linear algebra for the resulting linear
systems of equations has been largely overlooked. So-called stochastic Galerkin methods,
in particular, have attractive approximation properties but have been somewhat ignored due
to a lack of robust solvers. More simplistic schemes which require less user know-how but
ultimately more computing time to implement, have been popularised. The aim of this project
is to investigate approximation schemes for quantifying uncertainty in more complex engineering
problems modelled by systems of PDEs with two output variables (e.g. groundwater flow in a
random porous medium). We will extend and test the efficiency of approximation schemes
introduced for scalar PDEs with random data, paying significant attention to the development
of efficient linear algebra techniques for solving the resulting linear systems of equations.
The project builds on work done on a recently completed DAAD/British Council project entitled
Uncertainty quantification in computer simulations of groundwater flow problems with
emphasis on contaminant transport
in collaboration with Oliver Ernst and Elisabeth Ullmann from
Freiberg.
Software
Our open source PIFISS
software for solving deterministic groundwater flow problems is freely available.
PIFISS is a MATLAB toolbox that is written in the IFISS
house-style, but using FEMLAB functions for grid generation.
The package has built-in algebraic multigrid and Krylov subspace solvers and appropriate
preconditioning strategies for each problem.
Page last modified: 13 July 2011
