Challenges and insights from the application of spectral/hp methods to problems in computation medicine
Spectral/hp element methods for discretizing engineering-based PDE problems have been lauded for combining geometric (meshing) flexibility with superior convergence behavior. Since their inception in the 1980s, there has been growing interest in their development and usage for solving real-world (i.e. not merely academic) engineering problems. In spite of their relative maturity, each pivot towards trying to solve a new class of problems or towards exploiting newly available hardware opens up the possibility new research into the formulation, development and/or implementation of these methods. In this talk, we will present our work on using spectral/hp element methods to solve problems related to computational medicine. We will focus on three challenge areas: solution positivity, linear system preconditioning, and hardware acceleration. We will show that moving into applications areas not only benefits the area to which one applies spectral/hp element methods, but also provides return benefits on our understanding and implementations of these methods.