Compactification for Wave Equations on Unbounded Domains

Abstract: Wave propagation problems on unbounded domains appear in various disciplines such as seismics, underwater acoustics, electrodynamics, and general relativity. However, numerical calculations typically truncate the unbounded solution domain. This artificial truncation fails to capture radiative fields defined at infinity and introduces numerical outer boundaries that may contaminate the interior solution due to artificial reflections.

I will demonstrate how to map the unbounded physical domain to a compact numerical domain using spacetime transformations. These transformations rely on the unification of space and time by Minkowski and the compactification of spacetime by Penrose. I will list the properties and advantages of compactification and compare it with layer techniques such as Perfectly Matched and Perfectly Absorbing Layers.

Bio: Dr. Anıl Zenginoğlu is an assistant Research Scientist at the Institute for Physical Science & Technology, University of Maryland with broad experience in research, administration, and information technologies. As a researcher, he works on wave equations, black holes, gravitational waves, and null infinity. As an administrator, he brings researchers together in thematically focused but geographically distributed networks. As a technologist, he drives digital transformation to increase the efficiency of business processes that support research and education.