Source: http://www.teses.usp.br/teses/disponiveis/3/3143/tde-29042015-181255/pt-br.php
Timestamp: 2019-04-21 04:24:53+00:00

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Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.
Este trabalho apresenta a aplicação de técnicas de processamento paralelo na resolução de equações algébricas oriundas do Método de Elementos Finitos aplicado ao Eletromagnetismo, nos regimes estático e harmônico. As técnicas de programação paralelas utilizadas foram OpenMP, CUDA e GPUDirect, sendo esta última para as plataformas do tipo Multi-GPU. Os métodos iterativos abordados incluem aqueles do subespaço Krylov: Gradientes Conjugados, Gradientes Biconjugados, Conjugado Residual, Gradientes Biconjugados Estabilizados, Gradientes Conjugados para equações normais (CGNE e CGNR) e Gradientes Conjugados ao Quadrado. Todas as implementações fizeram uso das bibliotecas CUSP, CUSPARSE e CUBLAS. Para problemas estáticos, os seguintes pré-condicionadores foram adotados, todos eles com implementações paralelizadas e executadas na GPU: Decomposições Incompletas LU e de Cholesky, Multigrid Algébrico, Diagonal e Inversa Aproximada. Para os problemas harmônicos, apenas os dois primeiros pré-condicionadores foram utilizados, porém na sua versão sequencial, com execução na CPU, resultando em uma implementação híbrida CPU-GPU. As ferramentas computacionais desenvolvidas foram testadas na simulação de problemas de aterramento elétrico. No caso do regime harmônico, em que o fenômeno é regido pela Equação de Onda completa com perdas e não homogênea, a formulação adotada foi aquela em dois potenciais, A-V aresta-nodal. Em todas as situações, os aplicativos desenvolvidos para GPU apresentaram speedups apreciáveis, demonstrando a potencialidade dessa tecnologia para a simulação de problemas de larga escala na Engenharia Elétrica, com excelente relação custo-benefício.
Parallel computing on GPU for solving systems of algebraic equations resulting from application of finite element method in electromagnetism.
This work presents the use of parallel processing techniques in Graphics Processing Units (GPU) for the solution of algebraic equations arising from the Finite Element modeling of electromagnetic phenomena, both in steadystate and time-harmonic regime. The techniques used were parallel programming OpenMP, CUDA and GPUDirect, the latter for those platforms of type Multi-GPU. The iterative methods discussed include those of the Krylov subspace: Conjugate Gradients, Bi-conjugate Gradients, Conjugate Residual, Bi-conjugate Gradients Stabilized, Conjugate Gradients for Normal Equations (CGNE and CGNR) and Conjugate Gradients Squared. All implementations have made use of CUSP, CUSPARSE and CUBLAS libraries. For the static problems, the following pre-conditioners were adopted, all with parallelized implementations and executed on the GPU: Incomplete decompositions, both LU and Cholesky, Algebraic Multigrid, Diagonal and Approximate Inverse. For the time-harmonic varying problems, only the first two pre-conditioners were used, but in their sequential version and running in the CPU, which yielded a hybrid CPU-GPU implementation. The developed computational tools were tested in the simulation of electrical grounding systems. In the case of the harmonic regime, in which the phenomenon is governed by the driven, lossy wave equation, the formulation adopted was that in two potential, the ungauged edge A-V formulation. In all cases, the developed GPU-based tools showed considerable speedups, showing that this is a promising technology for the simulation of large-scale Electrical Engineering problems, with excellent cost-benefit.
CAMARGOS, A. F. P., et al. Efficient Parallel Preconditioned Conjugate Gradient Solver on GPU for FE Modeling of Electromagnetic Fields in Highly Dissipative Media [doi:10.1109/TMAG.2013.2285091]. IEEE Transactions on Magnetics [online], 2014, vol. 50, p. 569-572.
CAMARGOS, A. F. P., and SILVA, V. C. GPU-accelerated Iterative Solution of Complex-entry Systems Issued from 3D Edge-FEA of Electromagnetics in the Frequency Domain. The International Journal of High Performance Computing Applications, 2015.
CAMARGOS, A. F. P., and SILVA, V. C. Performance Analysis of Multi-GPU Implementations of Krylov-subspace Methods Applied to FEA of Electromagnetic Phenomena. IEEE Transactions on Magnetics, 2014.
CAMARGOS, A. F. P., et al. Iterative Solution on GPU of Linear Systems Arising from the A-V Edge-FEA of Time-Harmonic Electromagnetic Phenomena [doi:10.1109/PDP.2014.95]. In Parallel, Distributed and Network-Based Processing (PDP), 2014 22nd Euromicro International Conference on, Torino, 2014. Proceedings - 2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing - PDP 2014.Torino : PDP, 2014.
CAMARGOS, A. F. P., and SILVA, V. C. Efficient Conjugate Gradient Parallelization on GPU. In EMF International Symposium on Electric and Magnetic Fields, Bruges, 2013. Proceedings of the 9th International Symposium on Electric and Magnetic Fields.Bruges, 2013. Abstract.
CAMARGOS, A. F. P., and SILVA, V. C. Efficient Preconditioned Conjugate Gradient Parallelization on GPU. In COMPUMAG Conference on the Computation of Electromagnetic Fields, Budapeste, 2013. Proceedings of 19th COMPUMAG Conference on the Computation of Electromagnetic Fields., 2013.
CAMARGOS, A. F. P., and SILVA, V. C. GPU Computing for FEA of Time-harmonic Electromagnetic Problems. In MOMAG 2014, Curitiba, 2014. MOMAG 2014 - 16º SBMO - Simpósio Brasileiro de Micro-ondas e Optoeletrônica e 11º CBMag - Congresso Brasileiro de Eletromagnetismo.Curitiba : UTFPR, 2014.
CAMARGOS, A. F. P., and SILVA, V. C. Krylov Subspace Solvers Using Multi-GPU Computing in FEA of Electromagnetic Phenomena. In The 16th Biennial IEEE Conference on Electromagnetic Field Computation, Annecy, 2014. The 16th Biennial IEEE Conference on Electromagnetic Field Computation Technical Program.Grenoble : G2eLab, 2014. Abstract.

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