Game-Changing Time Integration of Complex Systems for the Exaflop Era

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It is an exciting time to be a computational scientist. By 2018, some predict we will be in the exaflop era, in which supercomputers will be some 20 times more powerful than the human brain. The enormity of these figures is rivalled only by that of the emergent opportunities for applications of this computing power. Exascale computing would allow us to tackle grand challenge problems in virtual medicine, climate change, renewable energy, advanced materials, resource recovery, and national security. These problems offer a fundamental connection between extreme computing, industrial and economic growth, and societal imperatives. The broad objectives of this research are to develop effective numerical methods and software for the simulation of complex systems that are amenable to current trends in computing hardware, especially those that are envisaged to support exascale computing. The mathematical models for the systems we study are based on evolutionary differential equations. These systems typically have multiple interacting time scales, and accordingly no single time-integration method has the characteristics to handle them all in an effective manner. The specific approach we employ is based on intelligent, fine-scale partitioning strategies combined with the design of optimized time-integration methods. Our present focus is on applying this approach to simulate the electrical activity in the heart. We have proposed novel time-integration methods for such simulations and have already demonstrated performance improvements of up to factors of 300 over current state-of-the-art methods. In the longer term, we plan to tackle whole heart simulations, in which models of electrical activity are further augmented to take into account tissue elasticity and blood flow. The performance gains in heart simulation will bring us closer to simulations that are fast enough to benefit clinical training and practice as well as personalized medicine. This research aims to provide the computational breakthroughs that can ultimately lead to an improvement in the quality of life of millions of people in Canada and around the world who are affected by heart disease.