Montag, 02. Juli 2012

Kolloquiumsvortrag von Prof. Dr. Christoph Schwab

Sparse adaptive tensor discretizations of nonlinear operator equations with random parameters

Am Montag, dem 2. Juli 2012 hält 

Prof. Dr. Christoph Schwab (ETH Zürich)

um 16:45 Uhr im Hörsaal D2 einen Vortrag mit dem Thema

"Sparse adaptive tensor discretizations of nonlinear operator equations with random parameters"

Zu dieser Veranstaltung sind alle Interessenten herzlich eingeladen.

Um 16:15 Uhr trifft man sich zur Begrüßung des Gastes bei Tee und Kaffee im Besprechungsraum D2.343.

Abstract: 

We consider nonlinear, Fréchet-differentiable operator equations with random inputs. We establish the local solvability of these equations and present a first order, second moment perturbation analysis of the random solutions, based on a suitable (soft) implicit function theorem.

We derive a deterministic tensorized operator equation for the first order approximation of the k-point correlation function of the random solution.We establish its well-posedness and a regularity result in scales of anisotropic Sobolev and Besov spaces of mixed highest derivatives.

Sparse tensor Galerkin discretizations are proved to converge at rates independent of k; wavelet based Galerkin discretization algorithms presented which do not require forming the matrix of the tensorized operators explicitly.

Examples include strongly elliptic and parabolic problems in random domains. Here, Frechet derivatives of the solution involve shape calculus and the linearized operators are pseudodifferential operators on the boundary manifolds of the nominal domains which are discretized by adaptive wavelet methods.

Joint work with A. Chernov (HIM, Bonn, Germany) and H. Harbrecht (Dept. of Mathematics, Basle, Switzerland).


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