On Sep. 26th, 2016, PhD Candidate Sören Wolfers presented his Proposal Thesis Defense entitled "Sparse methods for the numerical approximation of parametric PDE"
We study the numerical approximation of partial differential equations (PDEs) that depend on a parameter describing uncertain properties of the physical system under consideration. We exploit the algebraic structure of these problems to propose sparse, decomposition-based, algorithms that are able to lift this curse by combining a multilevel approach for the solution of the PDE with sparse grids for the parameter domain in a joint framework.
About
We study the numerical approximation of partial differential equations (PDEs) that depend on a parameter describing uncertain properties of the physical system under consideration. We exploit the algebraic structure of these problems to propose sparse, decomposition-based, algorithms that are able to lift this curse by combining a multilevel approach for the solution of the PDE with sparse grids for the parameter domain in a joint framework. We discuss numerical examples for response surface reconstruction as well as optimization under uncertainty using kernel-based approximation.
