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GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems

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GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems

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Lamas Daviña, A.; Román Moltó, JE. (2016). GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems. En Parallel Processing and Applied Mathematics. Springer. 182-191. https://doi.org/10.1007%2F978-3-319-32149-3_18

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/66516

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Title: GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems
Author: Lamas Daviña, Alejandro Román Moltó, José Enrique
UPV Unit: Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació
Issued date:
Abstract:
In an eigenvalue problem defined by one or two matrices with block-tridiagonal structure, if only a few eigenpairs are required it is interesting to consider iterative methods based on Krylov subspaces, even if matrix ...[+]
Subjects: GPU computing , Eigenvalue computation , Krylov methods , Block-tridiagonal linear solvers
Copyrigths: Reserva de todos los derechos
ISBN: 978-3-319-32148-6
Source:
Parallel Processing and Applied Mathematics. (issn: 0302-9743 )
DOI: 10.1007%2F978-3-319-32149-3_18
Publisher:
Springer
Publisher version: http://link.springer.com/chapter/10.1007%2F978-3-319-32149-3_18
Conference name: 11th International Conference on Parallel Processing and Applied Mathematics (PPAM 2015)
Conference place: Krakow, Poland
Conference date: September 6-9, 2015
Series: Lecture Notes in Computer Science;9573
Project ID:
info:eu-repo/grantAgreement/MINECO//TIN2013-41049-P/ES/EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTES/
info:eu-repo/grantAgreement/MECD//FPU13%2F06655/ES/FPU13%2F06655/
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-32149-3_18
Thanks:
This work was partially supported by the Spanish Ministry of Economy and Competitiveness under grant TIN2013-41049-P. Alejandro Lamas was supported by the Spanish Ministry of Education, Culture and Sport through grant FPU13-06655.[+]
Type: Capítulo de libro Comunicación en congreso

References

Baghapour, B., Esfahanian, V., Torabzadeh, M., Darian, H.M.: A discontinuous Galerkin method with block cyclic reduction solver for simulating compressible flows on GPUs. Int. J. Comput. Math. 92(1), 110–131 (2014)

Bientinesi, P., Igual, F.D., Kressner, D., Petschow, M., Quintana-Ortí, E.S.: Condensed forms for the symmetric eigenvalue problem on multi-threaded architectures. Concur. Comput. Pract. Exp. 23, 694–707 (2011)

Haidar, A., Ltaief, H., Dongarra, J.: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem. SIAM J. Sci. Comput. 34(6), C249–C274 (2012) [+]
Baghapour, B., Esfahanian, V., Torabzadeh, M., Darian, H.M.: A discontinuous Galerkin method with block cyclic reduction solver for simulating compressible flows on GPUs. Int. J. Comput. Math. 92(1), 110–131 (2014)

Bientinesi, P., Igual, F.D., Kressner, D., Petschow, M., Quintana-Ortí, E.S.: Condensed forms for the symmetric eigenvalue problem on multi-threaded architectures. Concur. Comput. Pract. Exp. 23, 694–707 (2011)

Haidar, A., Ltaief, H., Dongarra, J.: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem. SIAM J. Sci. Comput. 34(6), C249–C274 (2012)

Heller, D.: Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems. SIAM J. Numer. Anal. 13(4), 484–496 (1976)

Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)

Hirshman, S.P., Perumalla, K.S., Lynch, V.E., Sanchez, R.: BCYCLIC: a parallel block tridiagonal matrix cyclic solver. J. Comput. Phys. 229(18), 6392–6404 (2010)

Minden, V., Smith, B., Knepley, M.G.: Preliminary implementation of PETSc using GPUs. In: Yuen, D.A., Wang, L., Chi, X., Johnsson, L., Ge, W., Shi, Y. (eds.) GPU Solutions to Multi-scale Problems in Science and Engineering. Lecture Notes in Earth System Sciences, pp. 131–140. Springer, Heidelberg (2013)

NVIDIA: CUBLAS Library V7.0. Technical report, DU-06702-001 $$\_$$ v7.0, NVIDIA Corporation (2015)

Park, A.J., Perumalla, K.S.: Efficient heterogeneous execution on large multicore and accelerator platforms: case study using a block tridiagonal solver. J. Parallel and Distrib. Comput. 73(12), 1578–1591 (2013)

Reguly, I., Giles, M.: Efficient sparse matrix-vector multiplication on cache-based GPUs. In: Innovative Parallel Computing (InPar), pp. 1–12 (2012)

Roman, J.E., Vasconcelos, P.B.: Harnessing GPU power from high-level libraries: eigenvalues of integral operators with SLEPc. In: International Conference on Computational Science. Procedia Computer Science, vol. 18, pp. 2591–2594. Elsevier (2013)

Seal, S.K., Perumalla, K.S., Hirshman, S.P.: Revisiting parallel cyclic reduction and parallel prefix-based algorithms for block tridiagonal systems of equations. J. Parallel Distrib. Comput. 73(2), 273–280 (2013)

Stewart, G.W.: A Krylov-Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001)

Tomov, S., Nath, R., Dongarra, J.: Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing. Parallel Comput. 36(12), 645–654 (2010)

Vomel, C., Tomov, S., Dongarra, J.: Divide and conquer on hybrid GPU-accelerated multicore systems. SIAM J. Sci. Comput. 34(2), C70–C82 (2012)

Zhang, Y., Cohen, J., Owens, J.D.: Fast tridiagonal solvers on the GPU. In: Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. PPopp 2010, pp. 127–136 (2010)

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