Geodesic
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
Descombes, Stéphane1 ; Duarte, Max2 ; Dumont, Thierry3 ; Guillet, Thomas4 ; Louvet, Violaine3 ; Massot, Marc5
1 Université Côte d’Azur, CNRS, Inria, LJAD, France
2 CCSE, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd. MS 50A-1148, Berkeley, CA 94720, USA and CD-adapco, 200 Shepherds Bush Road, London W6 7NL, UK
3 Université de Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
4 Intel, Les Montalets, 2 rue de Paris, 92196 Meudon, France, Exascale Computing Research, Campus Teratec, 2 rue de la Piquetterie, 91680 Bruyères-le-Châtel, France
5 CNRS UPR 288, Laboratoire EM2C, CentraleSupélec, Fédération de Mathématiques de l’École Centrale Paris, CNRS FR 3487, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France
The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 29-51

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A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability.

Publié le :
DOI : 10.5802/smai-jcm.19
Classification : 65Y05, 65T60, 65M50, 65L04, 35K57
Keywords: Task-based parallelism, multi-core architectures, multiresolution, adaptive grid, stiff reaction-diffusion equations

Descombes, Stéphane 1 ; Duarte, Max 2 ; Dumont, Thierry 3 ; Guillet, Thomas 4 ; Louvet, Violaine 3 ; Massot, Marc 5

1 Université Côte d’Azur, CNRS, Inria, LJAD, France
2 CCSE, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd. MS 50A-1148, Berkeley, CA 94720, USA and CD-adapco, 200 Shepherds Bush Road, London W6 7NL, UK
3 Université de Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
4 Intel, Les Montalets, 2 rue de Paris, 92196 Meudon, France, Exascale Computing Research, Campus Teratec, 2 rue de la Piquetterie, 91680 Bruyères-le-Châtel, France
5 CNRS UPR 288, Laboratoire EM2C, CentraleSupélec, Fédération de Mathématiques de l’École Centrale Paris, CNRS FR 3487, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France 
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     title = {Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures},
     journal = {The SMAI Journal of computational mathematics},
     pages = {29--51},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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%A Dumont, Thierry
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%A Louvet, Violaine
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Descombes, Stéphane; Duarte, Max; Dumont, Thierry; Guillet, Thomas; Louvet, Violaine; Massot, Marc. Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures. The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 29-51. doi: 10.5802/smai-jcm.19

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