Low-rank tensor Krylov subspace methods for parametrized linear systems
We consider linear systems A(alpha)x(alpha) - b(alpha) depending on possibly many parameters alpha = (alpha(1), ... , alpha(p)). Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort growing drastically with the number of parameters. We show that a much lower computational effort can be achieved for sufficiently smooth parameter dependencies. For this purpose, computational methods are developed that benefit from the fact that x(alpha) can be well approximated by a tensor of low rank. In particular, low-rank tensor variants of short-recurrence Krylov subspace methods are presented. Numerical experiments for deterministic PDEs with parametrized coefficients and stochastic elliptic PDEs demonstrate the effectiveness of our approach.
Keywords: parametrized linear system ; Tucker decomposition ; tensor ; low-rank approximation ; Krylov subspace methods ; Partial-Differential-Equations ; Stochastic Collocation Method ; Singular-Value Decomposition ; Random Input Data ; Numerical-Solution ; Product Structure ; Elliptic Pdes ; Approximation ; Discretization ; Interpolation
Record created on 2011-05-05, modified on 2016-08-09