Elwin van 't Wout - Boundary Element Methods for High-Frequency Acoustics with Applications in Biomedical Ultrasound.

The Boundary Element Method (BEM) is a numerical algorithm to solve partial differential equations written in the form of boundary integral equations. Compared to volumetric solvers, the BEM is especially advantageous for exterior scattering problems. For example, radiation conditions in unbounded domains are automatically satisfied. Furthermore, only the boundary of structures needs to be meshed, and Green's functions accurately represent wave phenomena. The dimensionality reduction also considerably lowers the number of degrees of freedom. However, the dense matrix arithmetic has a high computational footprint, which can be alleviated with matrix compression techniques. This talk presents recent advances to improve the computational performance of the BEM at high frequencies, where fine meshes yield large linear systems. Specifically, we designed On-Surface Radiation Condition (OSRC) preconditioners to improve the convergence of GMRES and dedicated boundary integral formulations for high-contrast materials. Other improvements include stable FEM-BEM coupling and nonconforming meshes. These fast algorithms allow us to simulate large-scale problems in biomedical engineering. We simulated the propagation of ultrasound in the human body to understand the effect of bone and soft tissue on the focusing capacity of ultrasound transducers used in non-invasive treatment modalities.