Applied Mathematics

Our research in applied mathematics covers the areas of numerical analysis and inverse problems. In numerical analysis we focus on partial differential equations which typically stem from mathematical physics, mechanical engineering and electromagnetics. We study approximation properties of numerical methods and related problems from numerical linear algebra. Currently, we consider finite and boundary element methods, time-stepping methods, and Petrov-Galerkin schemes for singularly perturbed problems. A specific topic is the development of fast numerical algorthms. We consider the precision and efficiency of algorithms, and develop preconditioning and compression strategies for large linear systems.

In the field of inverse problems our objective is the reconstruction of unknown parameters. This is done by using measurements of data that depend on the corresponding parameter. We consider models that are described by partial differential or integral equations. The unknowns are coefficients of the equation, and the measurements correspond to a partial knowledge of the solution. The objective is to determine the unknown coefficients. The analysis of these problems makes use of techniques from functional analysis and its applications, including partial differential equations, integral equations and the theory of operators.

RESEARCHERS