Towards massively-parallel FOURier-based solvers in GEneral Domains – FOURGED

This project concerns the study, development and enhancement of a new class of recently-introduced high-order numerical methods for time-dependent partial differential equations governing wave propagation and diffusion phenomena in solids, fluids and their interactions. Such methods are based on an extension technique for accurate Fourier series representations of non-periodic functions, enabling the construction of fast Fourier transform (FFT-)speed dynamic solvers that provide high-fidelity resolution by means of relatively coarse discretizations and that faithfully preserve the dispersion characteristics of the underlying continuous problems. In order to facilitate broader applicability for real-world complex geometries and extremely large-scale configurations, the work proposes to focus on: 1) fully-controlled, automated construction of boundary-conforming computational domains with appropriate treatment of singularities such as corners and edges; and 2) massive parallelization on CPU and GPU cluster architectures (the latter of which is well-suited for rapid FFT computations). Hence the developments proposed herein are ultimately towards the extremely fast treatment of large-scale, highly dynamic (possibly nonlinear) problems in more complex/realistic configurations, as well as the stable, consistent coupling to other methods/solvers---in an effort to treat previously intractable problems. Indeed, this work is heavily motivated by challenging scientific applications in seismic hazard (earthquake dynamics, long-distance wave propagation, tsunami dynamics) and cardiovascular hemodynamics (fluid-structure blood flow, data-driven advection-diffusion of medical injections), with the spirit of mutually validating simulation and natural, experimental, or clinical data---and potentially providing new insight into each other.