A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains

Powell, Catherine E. and Gordon, Andrew D. (2013) A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains. [MIMS Preprint]

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Abstract

We consider the numerical solution of elliptic boundary-value problems on uncertain two-dimensional domains via the fictitious domain method. This leads to variational problems of saddle point form. Working under the standard assumption that the domain can be described by a finite number of independent random variables, discretization is achieved by a stochastic collocation mixed finite element method. We focus on the efficient iterative solution of the resulting sequence of indefinite linear systems and introduce a novel and efficient preconditioner for use with the minimal residual method. The challenging task is to construct a matrix that provides a robust approximation to a discrete representation of a trace space norm on a parameterized boundary.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	mixed finite elements, saddle point problems, stochastic collocation, random domains, algebraic multigrid, preconditioning.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Dr C.E. Powell
Date Deposited:	09 Jun 2013
Last Modified:	24 Mar 2021 18:01
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1990

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