COMPARAÇÃO ENTRE O MECDR E O MECID NA SOLUÇÃO DE PROBLEMAS DE AUTOVALOR
DOI:
https://doi.org/10.26512/ripe.v2i7.21711Keywords:
Boundary Element Method. Eigenvalue Problem. Radial Basis Function.Abstract
This article compares the performance of two formulations of the BEM to solve acoustic problems, governed by the Helmholtz equation: the formulation of Dual Reciprocity and formulation with Direct Integration. The latter is a new alternative to the Dual Reciprocity technique for solving problems modeled by non-adjoint differential operators. Both method are similar, but, the formulation with Direct Integration is simpler and closely resembles an interpolation procedure. Thus, through the solution of eigenvalue problem,natural frequencies are calculated and their accuracy is taken as a parameter to assessing the quality of the results of each formulation. Examples whose analytical solution is known were chosen for analysis of the results.
Downloads
References
Braga, C. L. R., 2006. Notas de Física Matemática. Editora Livraria da Física, São Paulo.
Brebbia, C. A., Dominguez, J., 1992. Boundary Elements ”“ An Introductory Course, WIT Press.
Brebbia, C. A., Telles, J. C. F., & Wrobel, L. C., 1984. Boundary Element Techniques. Springer-Verlag, Berlin.
Brebbia, C. A., Walker, S., 1980. Boundary Element Techniques in Engineering, Newnes- Butterworths, London.
Buhmann, M. D., 2003. Radial Basis Function: Theory and Implementations. Cambridge Press.
Butkov, E., 1973. Mathematical Physics. Addison-Wesley, Massachusetts.
Cheng, A. H. D., Young, D. L., & Tsai, C. C., 2000. Solution of Poisson’s equation by iterative DRBEM using compactly supported, positive definite radial basis function. Eng. Analysis with Boundary Elements, 24, 549 - 557.
Dominguez, J., 1993. Boundary Elements in Dynamics, Computational Mechanics Publications, Elsevier Applied Science, London.
Franke, R., 1982. Scattered data interpolation. Mathematics of Computation, 38, pp. 181”“200.
Golberg, M. A., Chen, C. S., 1994. The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations, BE Communication 5, 57-61.
Loeffler, C. F., Barcelos, H. M., Mansur, W. J., & Bulcão, A., 2015. Solving Helmholtz Problems using Direct Radial Basis Function Interpolation with the Boundary Element Method. Engineering Analysis with Boundary Elements, vol. 61, pp. 218-225.
Loeffler, C. F., Cruz, A. L., & Bulcão, A. 2015. Direct Use of Radial Basis Interpolation Functions for Modelling Source Terms with the Boundary Element Method. Engineering Analysis with Boundary Elements. vol. 50, p.97-108.
Loeffler, C. F., Mansur W. J., 1986. Vibrações Livres de Barras e Membranas Através do Método dos Elementos de Contorno. Revista Brasileira de Engenharia, caderno de Engenharia Civil, vol. 4, n. 2, pp. 5-23.
Loeffler, C. F., Mansur W. J., 1987. Analysis of time integration schemes for boundary element applications to transient wave propagation problems, in: C.A. Brebbia (Ed.), Boundary Element Techniques: Applications in Stress Analysis and Heat Transfer, Computational Mechanics Publishing, UK, pp. 105-124.
Loeffler, C. F., Pereira, P. V. M., & Barcelos, H. M., 2014. Direct Interpolation Technique using Radial Basis Functions Applied to the Helmholtz Problem. In Mallardo, V., & Aliabadi, F. M. H., eds, 15 International Conference on Boundary Element and Meshless Techniques, pp. 223-228.
Loeffler, C. F., Zamprogno, L., Mansur, W. J., & Bulcão, A., 2016. Performance of Compact Radial Basis Functions in the Direct Interpolation Boundary Element Method for Solving Potential Problems. Computational Methods in Engineering Analysis, no prelo.
Partridge, P. W., Brebbia, C. A., & Wrobel, L. C., 1992. The Dual Reciprocity, Boundary Element Method, Computational Mechanics Publications and Elsevier, London.
Pessolani, R. V., 2002. An hp-adaptive hierarchical formulation for the boundary element method applied to elasticity in two dimensions. Journal of the Brazilian Society of Mechanical Sciences, 24(1): 23-45.
Wendland, H., 1995. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. in Comput. Math., 4, 389-396.
Wrobel, L. C., Aliabadi, M. H., 2002. The Boundary Element Method, Wiley, Chichester.
Wu, Z., 1995. Compactly supported positive definite radial functions. Adv. in Comput. Math., 4, 283-292.
Downloads
Published
How to Cite
Issue
Section
License
Given the public access policy of the journal, the use of the published texts is free, with the obligation of recognizing the original authorship and the first publication in this journal. The authors of the published contributions are entirely and exclusively responsible for their contents.
1. The authors authorize the publication of the article in this journal.
2. The authors guarantee that the contribution is original, and take full responsibility for its content in case of impugnation by third parties.
3. The authors guarantee that the contribution is not under evaluation in another journal.
4. The authors keep the copyright and convey to the journal the right of first publication, the work being licensed under a Creative Commons Attribution License-BY.
5. The authors are allowed and stimulated to publicize and distribute their work on-line after the publication in the journal.
6. The authors of the approved works authorize the journal to distribute their content, after publication, for reproduction in content indexes, virtual libraries and similars.
7. The editors reserve the right to make adjustments to the text and to adequate the article to the editorial rules of the journal.
