Title: My BYU Journey Riding Waves
Abstract: Computational wave propagation in unbounded regions requires the definition of artificial boundaries to reduce the original regions to bounded ones. This is usually followed by imposing absorbing boundary conditions (ABCs) on these artificial boundaries. These ABCs are based on operators that, approximately or exactly, prevent incoming waves from entering the bounded computational domains while allowing the free exit of outgoing waves through the boundaries. For instance in acoustics, the Sommerfeld radiation operator was commonly used as an ABC until the early 70's. Then, an intense research in this field started and has remained to develop more accurate and efficient conditions in acoustics, electromagnetics, and elastic wave phenomena, among others. My students, senior collaborators and I have contributed to this effort by constructing high order and highly accurate ABCs for acoustic and elastic waves. In this colloquium, I will describe how our research has evolved from single radiation and scattering problems to multiple scattering in acoustics, which have been followed by the extension of these ideas to elastodynamics problems. I will also talk about the key role played by a specific graduate class and a crucial international conference in the flourishing of this research program.