## Seminar on Modern Scientific Computing Trends

We invite all those interesting in modern scientific computing trends to a free 1-hour seminar taking place February 26th, 2015 from 12:00-13:30 in Building 101, Meeting room 2. Due to limited spaces sign up as soon as possible by sending an email to the organizer (See below).

**Proper Generalized Decomposition Method: algorithms and
applications to several stochastic PDEs**

In this talk, I will present various applications of the Proper Generalized Decompositon (PGD) Method for the approximate solution of Partial Differential Equations involving random (uncertain) parameters, that is SPDEs. The PGD consists in a series of functionals with separated deterministic and stochastic components. The series is sought to minimize the approximation error in a prescribed sense (often the equation resiudal). Starting from the simple case of SPES having energy functionals, e.g. elliptic equations, I will review and compare several algorithms for the approximation of the ideal decomposition. I will subsequently show that these algorithms can be successfully applied to several (moderately) non-linear problems, in particular the incompressible Navier-Stokes equations. Alternative separation formats, needed to further reduce the computational complexity of the PGD algorithms, will also be discussed. Finally, I will present recent PGD results for the uncertain wave equation which requires a multi-resolution framework to effectively deal with the complicated structure of the stochastic functionals.

## Responsible:

The seminar is organized by:

- Assoc. Prof. Allan P. Engsig-Karup, apek@dtu.dk
- Research Assistant, Daniele Bigoni, dabi@dtu.dk