# Workshop 5: High-Dimensional Aspects of Stochastic PDEs

**Date:** August 8 - 12, 2011

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

**Organizer:** Christoph Schwab

**Partial Differential Equations with random inputs** are increasingly appearing as models of systems with uncertainty in engineering and in the sciences. Accordingly, numerical methods for their efficient solution are of increasing interest. Among these, sampling methods in connection with standard solvers such as Finite Element (FE) or Finite Volume (FV) methods have limited capability. Novel discretization concepts which simultaneously discretize in physical and in random space are emerging which can be referred to as Sparse Tensor Discretizations.

This workshop presented principal algorithmic directions and their mathematical foundations for these novel solution methods.

In particular, it addressed mathematical formulation and regularity of PDEs with random inputs, sparsity in tensorized discretization schemes, implementations.

Relations to recently emerging concepts around adaptive low rank techniques in multilinear algebra matrix computations were of particular interest.