Seminar in Numerical Analysis: Barbara Verfürth (University of Bonn)

Multiscale wave propagation in time-varying media

In the last years, there has been an increasing interest in time-modulated materials to obtain enhanced properties. As mathematical model, we study the classical wave equation with time-dependent coefficient, which may also include spatial multiscale features.
Based on joint work with Bernhard Maier, we present a numerical multiscale method for spatially multiscale, (slowly) time-evolving coefficients. The method is inspired by the Localized Orthogonal Decomposition (LOD) and entails time-dependent multiscale spaces. We provide a rigorous a priori error analysis for the considered setting. Numerical examples illustrate the theoretical findings and investigate an adaptive approach for the computation of the time-dependent basis functions.
On the other hand, we will also briefly discuss the setting of spatially homogeneous, temporal multiscale coefficients. (Higher-order) multiscale expansions may help to interpret effective physical material properties and are numerically illustrated.

For further information about the seminar, please visit this webpage.

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