Radiation conditions for waves in periodic and stochastic media

• Applicant: Professor Dr. Ben Schweizer
• Subject Area: Mathematics
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 431081410

The project analyzes new radiation conditions for the Helmholtz equation and for the wave equation, we consider periodic and stochastic media. We emphasize that, in heterogeneous media, an artificial boundary should not be a non-reflecting boundary, since the heterogeneous medium in the outer domain creates reflections. For the Helmholtz equation, we want to improve a recently suggested scheme. The scheme demands that the solution is, in so called radiation boxes, a linear combination of outgoing Bloch-waves. The scheme can be transferred to the wave equation, where we can obtain a practical numerical scheme - at least in the homogenization limit. It is a crucial idea of this project to use first order correctors from homogenization theory to improve the numerical scheme. We analyze stochastic media in a third part of the project. We use the recently introduced Taylor-Bloch waves to transfer the above ideas of radiation boxes to the stochastic setting. Our aim is to analyze the new method for large wave-lengths and to test the new method numerically for moderate wave-lengths.

• DFG Programme: Research Grants