Boundary element method solution of stationary advective–diffusive problems: A comparison between the direct interpolation and dual reciprocity technique

Pinheiro, Vitor Pancieri; Loeffler, Carlos Friedrich; Mansur, Webe João

doi:10.1016/j.enganabound.2022.05.003

Cited by 7 publications

(3 citation statements)

References 45 publications

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“…Wu and Wendland functions also were employed successfully (Loeffler et al, 2017c;Frossard et al, 2018). Comparisons with DRBEM and with the FEM in other scalar field problems, as stationary problems and diffusive-advective problems have already Boundary element method been made, pointing out the superior performance of the DIBEM in terms of accuracy of results and numerical robustness (Pinheiro et al, 2022;Loeffler et al, 2018).…”

Section: Boundarymentioning

confidence: 99%

“…More recently, a novel model using radial basis approximation was proposed, named the direct interpolation boundary element method (DIBEM), presenting better performance than DRBEM for solving scalar field problems such as Poisson (Loeffler et al, 2015b) and diffusiveadvective issues (Pinheiro et al, 2022). However, an effective comparison approaching Helmholtz problems is still not done.…”

Section: Introductionmentioning

confidence: 99%

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Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Balista,

Loeffler,

Lara

et al. 2023

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PurposeThis work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.Design/methodology/approachComparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.FindingsAmong the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.Originality/valueThere are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

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Section: Boundarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Balista,

Loeffler,

Lara

et al. 2023

Self Cite

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“…O procedimento MECID foi aplicado com sucesso na solução de problemas de Poisson [17], Helmholtz [18] e Difusão Advecção [19]. Nessas aplicações, o desempenho do MECID foi claramente superior ao MECDR.…”

Section: Introductionunclassified

Um estudo preliminar sobre a estabilidade do Método dos Elementos de Contorno com Interpolação Direta na solução de problemas de propagação de ondas acústicas

Aparecida Romano dos Santos,

Friedrich Loeffler,

de Oliveira Castro Lara

2023

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Este trabalho apresenta a aplicação do Método dos Elementos de Interpolação Direta em problemas de propagação de ondas acústicas, após seu emprego em outros importantes problemas de campo escalar como os problemas de Helmholtz, da Difusão advecção e Poisson. Os testes iniciais mostrados aqui abordam a resposta de uma barra submetida a uma carga de impacto. Este problema clássico, devido às suas dificuldades numéricas, é uma referência apropriada para analisar a consistência, precisão e estabilidade da formulação da técnica de Interpolação Direta. O esquema Houbolt de avanço integra a equação de governo discreta em relação à variável de tempo, devido à sua maior estabilidade numérica.

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Buckling analysis of thin plates using direct interpolation boundary element method

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Albuquerque

et al. 2023

Engineering Analysis with Boundary Elements

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Boundary element method solution of stationary advective–diffusive problems: A comparison between the direct interpolation and dual reciprocity technique

Cited by 7 publications

References 45 publications

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Um estudo preliminar sobre a estabilidade do Método dos Elementos de Contorno com Interpolação Direta na solução de problemas de propagação de ondas acústicas

Buckling analysis of thin plates using direct interpolation boundary element method

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