MeshTools: uma ferramenta de manipulação de malhas de elementos finitos com foco em alto desempenho
Abstract
Several physical phenomena and/or problems in engineering and science are modeled by partial differential equations. These equations can be solved using numerical methods, such as finite differences, finite elements, and finite volume. In common, these methods require some form of discretization of the problem domain, that is, it is necessary to determine specific points in the domain where the solution of the differential equation will be calculated. High-resolution discretizations allow obtaining solutions with high numerical precision. On the other hand, they can demand high computational power. Thereby, there is a need to use parallelism for timely execution. In this work, it will be focused on the implementation of computational framework that handles finite element meshes for shared and distributed parallel systems. Performance results demonstrate good parallel scalability.References
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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).
Published
2021-10-26
How to Cite
SILVA, Guilherme M. F.; CAMATA, José J..
MeshTools: uma ferramenta de manipulação de malhas de elementos finitos com foco em alto desempenho. In: BRAZILIAN SYMPOSIUM ON HIGH PERFORMANCE COMPUTING SYSTEMS (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.
