MeshTools: uma ferramenta de manipulação de malhas de elementos finitos com foco em alto desempenho
Resumo
Diversos fenômenos físicos e/ou problemas da Engenharia e ciências são modelados por equações diferenciais parciais. Essas equações podem ser solucionadas através de métodos numéricos, tais como, diferenças finitas, elementos finitos e volumes finitos. Em comum, esses métodos requerem alguma forma de discretização de domínio do problema, ou seja, é preciso determinar pontos específicos do domínio onde a solução da equação diferencial será calculada. Discretizações de alta resolução permitem obter soluções com alta precisão numérica. Por outro lado, podem demandar alto poder computacional. Dessa forma, torna-se necessária a utilização do paralelismo para uma execução em tempo hábil. Este trabalho, tem como foco a implementação de um arcabouço computacional que prepara uma malha de elementos finitos para o processamento paralelo em sistemas de memória compartilhada e distribuída. Resultados de desempenho demonstram uma boa escalabilidade paralela.Referências
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Kaushik, D., Knepley, M. G., May, D. A., McInnes, L. C., Mills, R. T., Munson, T., Rupp, K., Sanan, P., Smith, B. F., Zampini, S., Zhang, H., and Zhang, H. (2021). PETSc Web page. https://petsc.org/.
Cuthill, E. and McKee, J. (1969). Reducing the bandwidth of In Proceedings of the 1969 24th National Conference, sparse symmetric matrices. ACM ’69, page 157–172, New York, NY, USA. Association for Computing Machinery.
Fox, A., Diffenderfer, J., Hittinger, J., Sanders, G., and Lindstrom, P. (2020). Stability analysis of inline zfp compression for floating-point data in iterative methods. SIAM Journal on Scientific Computing, 42(5):A2701–A2730.
Garey, M. R. and Johnson, D. S. (1990). Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman Co., USA.
Geuzaine, C. and Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in preand post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11):1309–1331.
Guo, X., Lange, M., Gorman, G., Mitchell, L., and Weiland, M. (2015). Developing a scalable hybrid mpi/openmp unstructured finite element model. Computers Fluids, 110:227–234. ParCFD 2013.
Hanwell, M. D., Martin, K. M., Chaudhary, A., and Avila, L. S. (2015). The visualization toolkit (vtk): Rewriting the rendering code for modern graphics cards. SoftwareX, 1-2:9–12.
Hendrickson, B. and Rothberg, E. (1998). Improving the run time and quality of nested dissection ordering. SIAM Journal on Scientific Computing, 20(2):468–489.
Hughes, T. J. (2012). The finite element method: linear static and dynamic finite element analysis. Courier Corporation.
Karypis, G. and Kumar, V. (1997). Metis: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices.
Netzer, R. H. B. and Miller, B. P. (1992). What are race conditions? some issues and formalizations. ACM Lett. Program. Lang. Syst., 1(1):74–88.
Rodgers, D. P. (1985). Improvements in multiprocessor system design. SIGARCH Comput. Archit. News, 13(3):225–231.
Rokos, G., Gorman, G., and Kelly, P. H. (2015). A fast and scalable In European graph coloring algorithm for multi-core and many-core architectures. Conference on Parallel Processing, pages 414–425. Springer.
Teng, S.-H. (1997). Fast nested dissection for finite element meshes. SIAM Journal on Matrix Analysis and Applications, 18(3):552–565.
Trilinos Project Team (2021). The trilinos project website: https://trilinos.github.io (accessed august 17, 2021).
Cuthill, E. and McKee, J. (1969). Reducing the bandwidth of In Proceedings of the 1969 24th National Conference, sparse symmetric matrices. ACM ’69, page 157–172, New York, NY, USA. Association for Computing Machinery.
Fox, A., Diffenderfer, J., Hittinger, J., Sanders, G., and Lindstrom, P. (2020). Stability analysis of inline zfp compression for floating-point data in iterative methods. SIAM Journal on Scientific Computing, 42(5):A2701–A2730.
Garey, M. R. and Johnson, D. S. (1990). Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman Co., USA.
Geuzaine, C. and Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in preand post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11):1309–1331.
Guo, X., Lange, M., Gorman, G., Mitchell, L., and Weiland, M. (2015). Developing a scalable hybrid mpi/openmp unstructured finite element model. Computers Fluids, 110:227–234. ParCFD 2013.
Hanwell, M. D., Martin, K. M., Chaudhary, A., and Avila, L. S. (2015). The visualization toolkit (vtk): Rewriting the rendering code for modern graphics cards. SoftwareX, 1-2:9–12.
Hendrickson, B. and Rothberg, E. (1998). Improving the run time and quality of nested dissection ordering. SIAM Journal on Scientific Computing, 20(2):468–489.
Hughes, T. J. (2012). The finite element method: linear static and dynamic finite element analysis. Courier Corporation.
Karypis, G. and Kumar, V. (1997). Metis: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices.
Netzer, R. H. B. and Miller, B. P. (1992). What are race conditions? some issues and formalizations. ACM Lett. Program. Lang. Syst., 1(1):74–88.
Rodgers, D. P. (1985). Improvements in multiprocessor system design. SIGARCH Comput. Archit. News, 13(3):225–231.
Rokos, G., Gorman, G., and Kelly, P. H. (2015). A fast and scalable In European graph coloring algorithm for multi-core and many-core architectures. Conference on Parallel Processing, pages 414–425. Springer.
Teng, S.-H. (1997). Fast nested dissection for finite element meshes. SIAM Journal on Matrix Analysis and Applications, 18(3):552–565.
Trilinos Project Team (2021). The trilinos project website: https://trilinos.github.io (accessed august 17, 2021).
Publicado
26/10/2021
Como Citar
SILVA, Guilherme M. F.; CAMATA, José J..
MeshTools: uma ferramenta de manipulação de malhas de elementos finitos com foco em alto desempenho. In: SIMPÓSIO EM SISTEMAS COMPUTACIONAIS DE ALTO DESEMPENHO (SSCAD), 22. , 2021, Belo Horizonte.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2021
.
p. 13-24.
DOI: https://doi.org/10.5753/wscad.2021.18508.