01.03.2017–28.02.2026
Special Research Program (SFB)
Principal investigator: Jens Markus MELENK (E101-02)

An established tool to describe physical phenomena are Partial Differential Operators, which are local in nature and only suitable to account for certain short-range effects. A classical example are diffusion processes modelled by the Laplace operator. Recent developments in science, such as in material science, financial mathematics, or image processing point at the necessity to account for long-range interaction. The resulting operators are then non-local. A prototype are fractional diffusion processes modelled by the fractional Laplace operator. Equations involving such operators typically cannot be solved explicitly so that numerical methods have to be brought to bear.

The project "non-local operators" in the SFB 65, 'taming complexity in partial differential systems', develops fast and efficient numerical methods for equations involving non-local operators. Efficiency can be achieved in several ways. One focus of the project is to use high order methods with their potential of high accuracy with only a small number of discretization parameters. Another way to obtain an efficient method is to exploit matrix compression techniques to reduce the storage requirement when numerically realizing the discretization of the non-local operator.