18 February – Roland Maier
Wave propagation in heterogeneous and nonlinear media has arisen growing interest in the last years since corresponding materials can lead to unusual and interesting effects and therefore come with a wide range of applications. An important example of such materials is Kerr-type media, where the intensity of a wave directly influences the refractive index. In the time-harmonic regime, this effect can be modeled with a nonlinear Helmholtz equation. If underlying material coefficients are highly oscillatory on a microscopic scale, the numerical approximation of corresponding solutions can be a delicate task.
In this talk, a multiscale technique is presented that allows one to deal with microscopic coefficients in a nonlinear Helmholtz equation without the need for global fine-scale computations. The method is based on an iterative and adaptive construction of appropriate multiscale spaces based on the multiscale method known as Localized Orthogonal Decomposition, which works under minimal structural assumptions.
This talk is based on joint work with Barbara Verfürth (KIT, Karlsruhe)