Solução Iterativa de Sistemas de Equações do Método dos Elementos Finitos no Computador IBM 3090
Resumo
Este trabalho apresenta uma estratégia de implementação do Método dos Gradientes Conjugados Precondicionado para a solução iterativa de sistemas de equações do Método dos Elementos Finitos, utilizando as facilidades para processamento vetorial disponíveis na arquitetura do computador IBM 3090. Os resultados numéricos obtidos evidenciam a efiência computacional da estratégia adotada.
Referências
Hughes, T.J.R. (1987) "The finite element method-linear static and dynamic finite element analysis", Prentice-Hall Int., Englewood Cliffs, NJ.
Hughes, T.J.R.; Ferencz, R.M. e Hallquist, J.O. (1987) "Large-scale vectorized Implicit calculations in solid mechanics on a CRAY X-MP/48 utilizing EBE preconditioned conjugate gradients", Computer Methods in Applied Mechanics and Engineering, Vol. 61, pp. 215-248.
Fahrat C. e Crivelli L. (1987) "A general approach to nonlinear FE computations on shared memory multiprocessors', Center for Space Structures and controls, University of Colorado, Bouder, USA, Report CU-CSSC - 87-09.
Nour-Omid, B.; Raefsky, A. e Lyzenga, G. (1987) "Solving finite element equations on concurrent computers',Parallel Computations and Their Impact on Mechanics, Edt. by A.K. Noor, ASME, AMD-Vol. 86, pp. 209-228.
Winget, J.M. e Hughes, T.J.R. (1985) "Solution algorithms for nonlinear "transient heat conduction analysis employing element-by-element iterative strategies", Computer Methods in Applied Mechanics and Engineering, Vol. 52, pp. 711-815.
Coutinho, A.L.G.A.; Alves, J.L.D; Landau, L. e Ebecken, N.F.F. (1986) "Um procedimento elemento-por-elemento para a solução de grandes sistemas de equações do MEF pelo método dos gradientes conjugados", Proc. VII Congresso Latino-Americano Sobre Métodos Computacionais em Engenharia, São Carlos, SP, Vol. 1, pp. 243-258.
Coutinho, A.L.G.A.; Alves, J.L.D.; Landau, L.; Lima, E.C.P. e Ebecken, N.F.F. (1987) "On the application of an element-by-element Lanczos solver to large offshore structural engineering problems", Computer and Structures, Vol. 27, pp. 27-37.
Carey, G.F. e Jiang, B.N. (1986) "Element-by-element linear and nonlinear solution schemes", Communications in Applied Numerical Methods, Vol.2, 145-154.
Golub, G.H. e Van Loan, C.F. (1983)"Matrix computations", John Hopkins University Press, USA.
IBM VS FORTRAN Version 2 (1986)"Programming Guide", IBM Corporation SC26-4222-0.
Dubrulle, A.A., Scarborough, R.G. e Kolsky, H.G. (1985) "How to write good vectorizable FORTRAN", IBM Palo Alto Scientific Center, Report G320-3478.
Berger, P.; Brouaye, P.; e Syre, J. (1982) "A mesh coloring method for efficient MIMD processing in finite element problems", Proc. International Conference on Parallel Processing. Edts K.E. Batcher, W.C. Meilander e J.L. Potter, IEEE Computer Society Press, pp. 41-46.
Silvester, D.J. (1988) "Optimizing finite element matrix calculations using the general technique of element vectorization", Parallel Computing, Vol. 6, pp. 157-164.
Coutinho, A.L.G.A., Costa, A.M., Alves, J. L.D., Landau, L. e Ebecken, N.F.F. (1988) - "Pile driving simulation and analysis by the finite element method", 3rd International Conference on the Application of Stress-Wave Theory on Piles, Editor Blugt. H. Fllenius, Ottawa, Canada, pp.197-207.
Hughes, T.J.R.; Ferencz, R.M. e Hallquist, J.O. (1987) "Large-scale vectorized Implicit calculations in solid mechanics on a CRAY X-MP/48 utilizing EBE preconditioned conjugate gradients", Computer Methods in Applied Mechanics and Engineering, Vol. 61, pp. 215-248.
Fahrat C. e Crivelli L. (1987) "A general approach to nonlinear FE computations on shared memory multiprocessors', Center for Space Structures and controls, University of Colorado, Bouder, USA, Report CU-CSSC - 87-09.
Nour-Omid, B.; Raefsky, A. e Lyzenga, G. (1987) "Solving finite element equations on concurrent computers',Parallel Computations and Their Impact on Mechanics, Edt. by A.K. Noor, ASME, AMD-Vol. 86, pp. 209-228.
Winget, J.M. e Hughes, T.J.R. (1985) "Solution algorithms for nonlinear "transient heat conduction analysis employing element-by-element iterative strategies", Computer Methods in Applied Mechanics and Engineering, Vol. 52, pp. 711-815.
Coutinho, A.L.G.A.; Alves, J.L.D; Landau, L. e Ebecken, N.F.F. (1986) "Um procedimento elemento-por-elemento para a solução de grandes sistemas de equações do MEF pelo método dos gradientes conjugados", Proc. VII Congresso Latino-Americano Sobre Métodos Computacionais em Engenharia, São Carlos, SP, Vol. 1, pp. 243-258.
Coutinho, A.L.G.A.; Alves, J.L.D.; Landau, L.; Lima, E.C.P. e Ebecken, N.F.F. (1987) "On the application of an element-by-element Lanczos solver to large offshore structural engineering problems", Computer and Structures, Vol. 27, pp. 27-37.
Carey, G.F. e Jiang, B.N. (1986) "Element-by-element linear and nonlinear solution schemes", Communications in Applied Numerical Methods, Vol.2, 145-154.
Golub, G.H. e Van Loan, C.F. (1983)"Matrix computations", John Hopkins University Press, USA.
IBM VS FORTRAN Version 2 (1986)"Programming Guide", IBM Corporation SC26-4222-0.
Dubrulle, A.A., Scarborough, R.G. e Kolsky, H.G. (1985) "How to write good vectorizable FORTRAN", IBM Palo Alto Scientific Center, Report G320-3478.
Berger, P.; Brouaye, P.; e Syre, J. (1982) "A mesh coloring method for efficient MIMD processing in finite element problems", Proc. International Conference on Parallel Processing. Edts K.E. Batcher, W.C. Meilander e J.L. Potter, IEEE Computer Society Press, pp. 41-46.
Silvester, D.J. (1988) "Optimizing finite element matrix calculations using the general technique of element vectorization", Parallel Computing, Vol. 6, pp. 157-164.
Coutinho, A.L.G.A., Costa, A.M., Alves, J. L.D., Landau, L. e Ebecken, N.F.F. (1988) - "Pile driving simulation and analysis by the finite element method", 3rd International Conference on the Application of Stress-Wave Theory on Piles, Editor Blugt. H. Fllenius, Ottawa, Canada, pp.197-207.
Publicado
26/09/1988
Como Citar
COUTINHO, Álvaro L. G.; ALVES, José L. D.; LANDAU, Luiz; EBECKEN, Nelson F. F..
Solução Iterativa de Sistemas de Equações do Método dos Elementos Finitos no Computador IBM 3090. In: INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE AND HIGH PERFORMANCE COMPUTING (SBAC-PAD), 2. , 1988, São José dos Campos/SP.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
1988
.
p. 243-248.
DOI: https://doi.org/10.5753/sbac-pad.1988.23545.
