Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

Author(s)

Schreiber, Martin ; Peixoto, Pedro S. ; Haut, Terry ; Wingate, Beth

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS; v. 32, n. 6, p. 21-pg., 2018-11-01.

Abstract

This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory partial differential equations, which is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale performance for weather prediction is that the strong scaling limit - the parallel performance for a fixed problem size with an increasing number of processors - saturates. A main avenue to circumvent this problem is to introduce new numerical techniques that take advantage of time parallelism. In this paper, we use a time-parallel approximation that retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original problem into a large set of independent terms and (b) solving each of these terms independently of each other which can now be accomplished on a large number of high-performance computing resources. Our results are conducted on up to 3586 cores for problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions in the time-to-solution of 118.3x for spectral methods and 1503.0x for finite-difference methods with the parallelization-in-time approach. A developed and calibrated performance model gives the scalability limitations a priori for this new approach and allows us to extrapolate the performance of the method towards large-scale systems. This work has the potential to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied areas modelling oscillatory dominated problems. (AU)

• FAPESP's process: 14/10750-0 - Numerical modelling of geophysical fluids on geodesic grids
• Grantee: Pedro da Silva Peixoto
• Support Opportunities: Scholarships abroad - Research