Higher-Order Numerical Homogenization for Wave Propagation in Strongly Heterogeneous Media

This thesis is concerned with the numerical solution of the acoustic wave equation, where the wave propagates through a non-smooth, highly heterogeneous medium. This setup poses many challenges for classical methods as the heterogeneity of the medium needs to be resolved, and high regularity is required for higher-order convergence. Herein, we present a novel tailor-made numerical homogenization strategy that builds on coarse piece-wise polynomials and corrects them accordingly such that higher-order convergence can be obtained without globally refining all scales of the medium.
In this thesis, the numerical homogenization strategy is first introduced and analyzed in a prototypical setting providing a basis. Further, the method is fully discretized to obtain a computable method. Finally, it is shown that the calculation of these spaces can be performed localized and fully parallelized on small subdomains without affecting the convergence.