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Challenges and insights from the application of spectral/hp methods to problems in computation medicine

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Spectral/hp element methods for discretizing engineering-based PDE problems have been lauded for combining geometric (meshing) flexibility with superior convergence behavior. ÌýSince 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. ÌýIn 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. ÌýIn this talk, we will present our work on using spectral/hp element methods to solve problems related to computational medicine. ÌýWe will focus on three challenge areas: Ìýsolution positivity, linear system preconditioning, and hardware acceleration. ÌýWe 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.