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Sparse Tensor Approximation of Parametric Eigenvalue Problems

Chapter
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 83)

Abstract

We design and analyze algorithms for the efficient sensitivity computation of eigenpairs of parametric elliptic self-adjoint eigenvalue problems on high-dimensional parameter spaces. We quantify the analytic dependence of eigenpairs on the parameters. For the efficient approximate evaluation of parameter sensitivities of isolated eigenpairs on the entire parameter space we propose and analyze a sparse tensor spectral collocation method on an anisotropic sparse grid in the parameter domain. The stable numerical implementation of these methods is discussed and their error analysis is given. Applications to parametric elliptic eigenvalue problems with infinitely many parameters arising from elliptic differential operators with random coefficients are presented.

Keywords

Eigenvalue Problem Collocation Method Collocation Point Selfadjoint Operator Sparse Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

Supported by SNF grant PDFMP2-127034/1 and by ERC AdG grant STAHDPDE 247277.

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Seminar for Applied MathematicsETH ZürichZürichSwitzerland

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