Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems. (November 2018)

• Record Type: Journal Article
• Authors: Schreiber, Martin; Peixoto, Pedro S; Haut, Terry; Wingate, Beth
• Other Names: Balaji Pavan guest-editor.; Leung Kai-Cheung guest-editor.; Huang Zhiyi guest-editor.; García-Blas Javier guest-editor.; Brown Christopher guest-editor.
• Is Part Of: International journal of high performance computing applications. Volume 32:Number 6(2018)
• Page Start: 913
• Page End: 933
• Publication Date: 2018-11
• Subjects: Parallelization in time -- oscillatory problem -- exponential integrator -- rational approximation -- scalability limitation; High performance computing -- Periodicals; Supercomputers -- Periodicals; 004.1105
• DOI: 10.1177/1094342016687625
• Languages: English
• ISSNs: 1094-3420

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 118.3× for spectral methods and 1503.0× 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.