{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T10:46:54Z","timestamp":1707389214553},"reference-count":19,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2006,10,25]],"date-time":"2006-10-25T00:00:00Z","timestamp":1161734400000},"content-version":"vor","delay-in-days":4346,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Concurrency: Pract. Exper."],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper presents the implementation of a new class of massively parallel algorithms for solving certain time\u2010dependent 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\u2010stepping 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\u2010parallel algorithms, which allows the marching in time to be fully parallelized. This is achieved by using a set of transformations based on eigenvalue\u2010eigenvector decomposition of the matrices involved in the discrete formalism. Our time\u2010parallel algorithms possess a highly decoupled structure, and can therefore be efficiently implemented on emerging, massively parallel, high\u2010performance supercomputers, with a minimum of communication and synchronization overhead. We have successfully carried out a proof\u2010of\u2010concept demonstration of the basic ideas using a two\u2010dimensional heat equation example implemented on the Intel Touchstone Delta supercomputer. Our results indicate that linear, and even superlinear, speed\u2010up can be achieved and maintained for a very large number of processor nodes.<\/jats:p>","DOI":"10.1002\/cpe.4330060803","type":"journal-article","created":{"date-parts":[[2006,11,17]],"date-time":"2006-11-17T15:07:05Z","timestamp":1163776025000},"page":"641-652","source":"Crossref","is-referenced-by-count":2,"title":["Time\u2010parallel solution of linear partial differential equations on the Intel Touchstone Delta supercomputer"],"prefix":"10.1002","volume":"6","author":[{"given":"Nikzad","family":"Toomarian","sequence":"first","affiliation":[]},{"given":"Amir","family":"Fijany","sequence":"additional","affiliation":[]},{"given":"Jacob","family":"Barmen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,25]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Linear and Nonlinear Waves","author":"Whithman G. 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