A new radial basis integration method applied to the boundary element analysis of 2D scalar wave equations

Narváez, A.; Useche, J.

doi:10.1016/j.enganabound.2021.12.005

Cited by 3 publications

(2 citation statements)

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“…In this sense, new proposes for dynamic models are essential and have been continually presented in the literature, such as hybrid models, i.e. the boundary element-Rayleigh integral method (Kirkup et al, 2013); radial basis methods, such as DIBEM and RIM; and meshless-based radial basis integration method (RBIM) (Narvaez and Useche, 2022).…”

Section: Boundary Element Methodsmentioning

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: Boundary Element Methodsmentioning

confidence: 99%

“…the boundary element–Rayleigh integral method (Kirkup et al. , 2013); radial basis methods, such as DIBEM and RIM; and meshless-based radial basis integration method (RBIM) (Narvaez and Useche, 2022).…”

Section: Introductionmentioning

confidence: 99%