Public Lecture: Harnessing the Power of Mathematics for High Performance Computing

Mathematics has always played a critical role in scientific discovery through computing. The increasing power and heterogeneity of modern computer architectures provide the opportunity to understand physical systems with higher and higher fidelity. But as the range of length and time scales we want to probe becomes ever greater and the number of different types of physical processes we need to model becomes larger and more varied, the challenge of building effective simulation methodologies grows along with the opportunities. Mathematics provides the key to meeting this challenge. It allows us to decompose complex problems into their core elements and express how these elements are coupled. It allows us to abstract physical processes into equations and design algorithms to solve them. In addition, casting problems in the language of mathematics exposes the commonality between diverse applications. Exploiting this commonality enables us to capture complex algorithms in efficient high-performance software that provides building blocks for new algorithmic exploration and scientific discovery