Abstract of Roman Andreev

Sparse tensor approximation of high-dimensional parametric eigenvalue problems
(joint work with Marcel Bieri and Christoph Schwab)
We design and analyse 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 and develop a sparse tensor composite collocation method on a Smolyak grid in the entire parameter space. Stable numerical implementation is discussed and error analysis is performed. Applications to parametric elliptic eigenvalue problems with infinitely many parameters arising from elliptic differential operators with stochastic coefficients are presented.
(Supportes by the Swiss National Science Foundation grants 200021-120290/1 and PDFMP2_127034/1


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)