Wave Propagation in Polytopal Domains
Simulation of an acoustic wave diffracting over a re-entrant corner. To capture the point singularity induced by the polygonal corner by a finite-element discretization, the triangulation must be appropriately refined towards all polygonal corners. Similar to a point source, we observe that the corner emits a symmetric signal which is smooth in any neighbourhood far from the corner.
by Dr. Fabian Müller
Additional links:
F. Müller and D. Schötzau and Ch. Schwab Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons, Journal of Scientific Computing (2018), SAM Report 2018-02, external page doi
F. Müller and D. Schötzau and Ch. Schwab Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons, SIAM J. Numer. Anal., 55/5 (2017), pp. 2490-2521, SAM Report 2017-15, external page doi
F. Müller and Ch. Schwab Finite Elements with mesh refinement for elastic wave propagation in polygons, Mathematical Methods in the Applied Sciences, 39/17 (2016), pp. 5027-5042, SAM Report 2014-31, external page doi
F. Müller and Ch. Schwab Finite Elements with mesh refinement for wave equations in polygons, J. Comput. Appl. Math., 283 (2015), pp. 163-181, SAM Report 2013-11, external page doi