Numerical simulations are an important tool in understanding complex problems in physics and engineering systems. Many of these phenomena are multi-scale in nature, and are governed by non-linear partial differential equations (PDEs). With a wide range of scales at realistic conditions, like turbulence phenomena in fluid flows, the numerical solution of these equations becomes computationally very expensive. It is known, at extreme scale, that data communication as well as synchronization between PEs pose a major challenge in the scalability of scientific applications. So, there has recently been a major interest in developing numerical methods that minimize communications and relax data synchronization at the mathematical level. This is the main thrust in this NSF-funded project. We have developed asynchrony-tolerant (AT) schemes that will be able to efficiently use future Exascale system with millions or billions of processing elements. The schemes we developed can accurately capture the rich dynamics of turbulence even at the smallest scales (!), while mitigating (or even eliminating) the overheads associated with communication and synchronizations on very large processor counts.
In this project we collaborate with computer scientists to develop the software abstraction layers to implement AT schemes efficiently and in a portable manner through (see here, and here). It is also possible to devise modified equations — proxy equations — that when solved asynchronously, one recovers the solution of the original equation.
Collaborators at Texas A&M: L. Rauchwerger, (Computer Science), R. Bhattacharya (Aerospace Eng.), S. Girimaji (Aerospace Eng.).
Students: Komal Kumari, Bryan Mahoney.