Time‐parallel solution of linear partial differential equations on the Intel Touchstone Delta supercomputer
Nikzad Benny Toomarian, Amir Fijany, Jacob Barmen · Concurrency Practice and Experience · 1994
Abstract The paper presents the implementation of a new class of massively parallel algorithms for solving certain time‐dependent partial differential equations (PDEs) on massively parallel supercomputers. Such PDEs are usually solved numerically, by discretization in time and space, and by applying a time‐stepping procedure to data and algorithms potentially parallelized in the spatial domain. In a radical departure from such a strictly sequential temporal paradigm, we have developed a concept of time‐parallel algorithms, which allows the marching in time to be fully parallelized. This is achieved by using a set of transformations based on eigenvalue‐eigenvector decomposition of the matrices involved in the discrete formalism. Our time‐parallel algorithms possess a highly decoupled structure, and can therefore be efficiently implemented on emerging, massively parallel, high‐performance supercomputers, with a minimum of communication and synchronization overhead. We have successfully carried out a proof‐of‐concept demonstration of the basic ideas using a two‐dimensional heat equation example implemented on the Intel Touchstone Delta supercomputer. Our results indicate that linear, and even superlinear, speed‐up can be achieved and maintained for a very large number of processor nodes.