Geodesic
Solving of discontinuous Galerkin method systems on GPU
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 121-131 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Solving systems of equations obtained in Discontinuous Galerkin method by GPU-computing is considered. The direct method and iterative Krylov methods with preconditioning are used. The performance of GPU-computing for these systems of equations is compared with one of multicore CPU.
Keywords: discontinuous Galerkin method, system of linear algebraic equations, Krylov subspaces methods, preconditioner, general purpose сomputing on GPU.
Mots-clés : sparse matrices 
@article{VUU_2011_4_a10,
     author = {S. P. Kopysov and A. K. Novikov and Yu. A. Sagdeeva},
     title = {Solving of discontinuous {Galerkin} method systems on {GPU}},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {121--131},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_4_a10/}
}
TY  - JOUR
AU  - S. P. Kopysov
AU  - A. K. Novikov
AU  - Yu. A. Sagdeeva
TI  - Solving of discontinuous Galerkin method systems on GPU
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 121
EP  - 131
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_4_a10/
LA  - ru
ID  - VUU_2011_4_a10
ER  - 
%0 Journal Article
%A S. P. Kopysov
%A A. K. Novikov
%A Yu. A. Sagdeeva
%T Solving of discontinuous Galerkin method systems on GPU
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 121-131
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2011_4_a10/
%G ru
%F VUU_2011_4_a10
S. P. Kopysov; A. K. Novikov; Yu. A. Sagdeeva. Solving of discontinuous Galerkin method systems on GPU. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 121-131. http://geodesic.mathdoc.fr/item/VUU_2011_4_a10/

[1] Arnold D. N., Brezzi F., Cockburn B., Marini L. D., “Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems”, SIAM J. Numerical Analysis, 39 (2002), 1749–1779 | DOI | MR | Zbl

[2] Klockner A., Warburton T., Bridge J., Hesthaven J. S., “Nodal Discontinuous Galerkin Methods on Graphics Processors”, Journal of Computational Physics, 228:21 (2009), 7863–7882 | DOI | MR | Zbl

[3] Cabel T., Charles J., Lanteri S., Multi-GPU acceleration of a DGTD method for modeling human exposure to electromagnetic waves, Research Report No RR-7592, INRIA Sophia Antipolis–CNRS, 2011

[4] Cecka C., Lew A., Darve E., “Introduction to assembly of finite element methods on graphics processors”, IOP Conf. Ser. Mater. Sci. Eng., 10:1 (2010), 012009 | DOI

[5] Markall G. R., Ham D. A., Kelly P. H. J., “Towards generating optimised finite element solvers for GPUs from high-level specifications”, Procedia Computer Science, 1:1 (2010), 1815–1823 | DOI

[6] Boreskov A. V., Kharlamov A. A., Osnovy raboty s tekhnologiei CUDA, DMK Press, M., 2010, 232 pp.

[7] Saad Y., Iterative Methods for Sparse Linear Systems, SIAM, 2000, 439 pp. | MR

[8] Kopysov S. P., Sagdeeva Yu. A., “Razryvnye metody Galërkina dlya zadach teorii uprugosti”, Sb. statei konferentsii “Aktualnye problemy matematiki, mekhaniki, informatiki”, IMM UrO RAN, Ekaterinburg, 2009, 72–78

[9] Castillo P., “Performance of discontinuous Galerkin methods for elliptic PDE's”, SIAM J. Scientific Computing, 24:2 (2002), 524–547 | DOI | MR | Zbl

[10] CUDA Toolkit 4.0 CUBLAS Library http://developer.download.nvidia.com/compute/cuda/4_0_rc2/toolkit/docs/CUBLAS_Library.pdf

[11] Kopysov S. P., Novikov A. K., “Metod dekompozitsii dlya parallelnogo adaptivnogo konechno-elementnogo metoda”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 3, 141–152

[12] Kopysov S. P., Krasnoperov I. V., Rychkov V. N., “Ob'ektno-orientirovannyi metod dekompozitsii oblasti”, Vychislitelnye metody i programmirovanie, 4:1 (2003), 176–193

[13] Chen K., Matrix Preconditioning Techniques and Applications, Cambridge University Press, 2005, 601 pp. | MR | Zbl

[14] Haase G., Liebmann M., Douglas C., Plank G., “A Parallel Algebraic Multigrid Solver on Graphics Processing Units”, Lecture Notes in Computer Science, 5938, 2010, 38–47 | DOI