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- DOI: 10.1137/130924202
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A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains
Gordon, Andrew; Powell, Catherine
2014;2(1):622-645.
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Full-text held externally
- DOI: 10.1137/130924202
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.
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