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

对于计算科学家来说，这是一个激动人心的时代。有人预测，到2018年，我们将进入百亿亿次运算时代，届时超级计算机的运算能力将是人脑的20倍左右。这些数字之巨大，只能与这种计算能力的应用所带来的新机遇相媲美。百亿亿次计算将使我们能够解决虚拟医疗、气候变化、可再生能源、先进材料、资源回收和国家安全等重大挑战问题。这些问题提供了极端计算、工业和经济增长以及社会需求之间的基本联系。这项研究的广泛目标是为复杂系统的模拟开发有效的数值方法和软件，以适应当前计算硬件的趋势，特别是那些设想支持百亿亿次计算的系统。我们研究的系统的数学模型是基于进化微分方程的。这些系统通常具有多个相互作用的时间尺度，因此没有单一的时间积分方法能够有效地处理它们。我们采用的具体方法是基于智能，精细划分策略结合优化时间积分方法的设计。我们目前的重点是应用这种方法来模拟心脏的电活动。我们已经为这种模拟提出了新颖的时间积分方法，并且已经证明了性能比目前最先进的方法提高了300倍。从长远来看，我们计划解决全心脏模拟，其中电活动模型进一步增强，以考虑组织弹性和血流。心脏模拟的性能提升将使我们更接近于足够快的模拟，从而有利于临床培训和实践以及个性化医疗。这项研究旨在提供计算上的突破，最终改善加拿大和世界各地数百万心脏病患者的生活质量。

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.