An OpenMP Application for programming with Element By Element Storage in Finite Elements Analysis

Guilherme Piva dos Santos, Eduardo Costa Couto, Aline Ribeiro Paliga, Gerson Geraldo Homrich Cavalheiro, Jansen Avila

Abstract


This article aims to present the solver algorithm, which solves the system of linear equations generated by the Finite Element Method and evaluates its efficiency using a code that analyzes the behavior of a rock mass when a tunnel is excavated. The algorithm was developed for a shared memory platform as it uses the Preconditioned Conjugate Gradient Method paralleled with the OpenMP interface. It was used Element by Element Storage Strategy. A comparison was made between the developed algorithm and another that is sequential and uses the Gaussian Elimination Method, associated with the skyline storage technique. It was found that the developed algorithm was 84.07% faster.


Keywords


Element by Element; OpenMP; Parallel Programming

References


BATHE, KJ. Finite Elements Procedures. 2 Ed., Prentice-Hall, Inc, USA, 2014.

BERNAUD, D., MAGHOUS, S., BUHAN, P., COUTO, E. C. A Numerical Approach for Design of Bolt-Supported Tunnels Regarded as Homogenized Structures. Elsevier, Tunnelling and Underground Space Technology, 24(5), 533-546, 2009.

CHANDRUPATLA, T. R., BELEGUNDU, A. D. Elementos Finitos. Tradução Daniel Vieira. 4 Ed., Pearson, São Paulo, 2014.

CHAPMAN, B., JOST, G., VAN DER PAS, R. Using OpenMP: Portable Shared Memory Parallel Programming. MIT Press, Massachusetts, 2008.

FU, X. D., SHENG, Q., ZHANG, Y. H., CHEN, J. Investigation of Highly Efficient Algorithms for Solving Equations in the Discontinuous Deformation Analysis Method. Wiley, International Journal for Numerical and Analytical Methods in Geomechanics, 40(4), 469-486, 2016.

HESTENES, M. R., STIEFEL, E. Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(4), 409-436, 1952.

LANG, J., RÜGER, G. Dynamic Distribution of Workload Between CPU and GPU for a Parallel Conjugate Gradient Method in an Adaptive FEM. Elsevier, Procedia Computer Science, 18, 299-308, 2013.

PENG, X., CHENG, G., YU, P., ZHANG, Y., GUO, L., WANG, C., CHENG, X., NIU, H. Parallel Computing of Three-Dimensional Discontinuous Deformation Analysis Based on OpenMP. Elsevier, Computers and Geotechnics, 106, 304-313, 2019.

VAZ, L. E. Método dos Elementos Finitos em Análise de Estruturas. Elsevier, Rio de Janeiro, 2011.




DOI: https://doi.org/10.18256/2358-6508.2022.v9i2.4263

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Copyright (c) 2023 Guilherme Piva dos Santos, Eduardo Costa Couto, Aline Ribeiro Paliga, Gerson Geraldo Homrich Cavalheiro, Jansen Avila

Licença Creative Commons
Esta obra da Revista de Engenharia Civil IMED está licenciada com uma Licença Creative Commons Atribuição 4.0 Internacional.

ISSN 2358-6508

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