{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T01:41:50Z","timestamp":1759542110704,"version":"3.38.0"},"reference-count":29,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2017,2,3]],"date-time":"2017-02-03T00:00:00Z","timestamp":1486080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p> 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 \u2013 the parallel performance for a fixed problem size with an increasing number of processors \u2013 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\u00d7 for spectral methods and 1503.0\u00d7 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. <\/jats:p>","DOI":"10.1177\/1094342016687625","type":"journal-article","created":{"date-parts":[[2017,2,3]],"date-time":"2017-02-03T12:04:06Z","timestamp":1486123446000},"page":"913-933","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems"],"prefix":"10.1177","volume":"32","author":[{"given":"Martin","family":"Schreiber","sequence":"first","affiliation":[{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK"}]},{"given":"Pedro S","family":"Peixoto","sequence":"additional","affiliation":[{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK"},{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo, Brazil"}]},{"given":"Terry","family":"Haut","sequence":"additional","affiliation":[{"name":"Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, USA"}]},{"given":"Beth","family":"Wingate","sequence":"additional","affiliation":[{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK"}]}],"member":"179","published-online":{"date-parts":[[2017,2,3]]},"reference":[{"key":"bibr1-1094342016687625","first-page":"173","volume":"17","author":"Arakawa A","year":"1977","journal-title":"Methods in Computational Physics"},{"key":"bibr2-1094342016687625","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(96)80002-0"},{"key":"bibr3-1094342016687625","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.05.016"},{"key":"bibr4-1094342016687625","unstructured":"Bonaventura L (2015) Local exponential methods: A domain decomposition approach to exponential time integration of PDEs. 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