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2013.31: A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains

2013.31: Catherine E. Powell and Andrew D. Gordon (2013) A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains.

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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 2000 > 35 Partial differential equations
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MIMS number:2013.31
Deposited By:Dr C.E. Powell
Deposited On:09 June 2013

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