Application of radial basis functions augmented by polynomials in the boundary element method to solve problems governed by the Laplace equation Filipe Lopes Cruzeiro, Lucas Silveira Campos, Luciano de Oliveira Castro Lara Engineering Computations Swansea Wales, 2025 Purpose Radial basis function interpolation is a highly valuable tool in the field of numerical methods, and its polynomially augmented version holds promise in addressing some limitations of the traditional formulation. In this article, we aim to analyze the performance of the boundary element method, which employs an alternative approach to traditional boundary discretization with the aid of radial basis functions. Design/methodology/approach This work presents the complete mathematical formulation along with the associated theory, as well as a comparison of errors between the proposed formulation and the traditional formulation, which uses polynomial interpolation. Additionally, a processing time analysis was conducted and is presented. Findings The proposed method yielded the lowest error across all examples with straight geometries. However, its performance was less effective in the problem involving a circular section, likely due to challenges in accurately representing this type of geometry. Originality/value The study presents an interpolation technique that can aid in mesh generation and can be extended to three-dimensional applications. Moreover, the lower errors observed in certain easily identifiable geometries suggest that this approach could be a good option for problems requiring higher accuracy.
TESTING THE USE OF RADIAL BASIS FUNCTION AUGMENTED WITH POLYNOMIALS AS BASIS FUNCTIONS IN THE BOUNDARY ELEMENT METHOD FOR HEAT TRANSFER PROBLEMS Wccm Apcom 2022 15th World Congress on Computational Mechanics and 8th Asian Pacific Congress on Computational Mechanics Pursuing the Infinite Potential of Computational Mechanics, 2022
A Fiber Bragg Grating based Accelerometer for Monitoring the Vibration of an Industrial Engine Prototype: A Preliminary Study Mariana Silveira, Leticia Avellar, Filipe Cruzeiro, Leandro Macedo, Arnaldo Leal-Junior, et al. Journal of Physics Conference Series, 2022 Monitoring the vibration of industrial engines is essential for running diagnostics that can detect faults and point out the feasibility of predictive maintenance. Therefore, this paper describes an optical accelerometer based on a fiber Bragg grating to monitor the vibration of the gearbox of an industrial engine prototype. Experimental tests were performed varying the motor’s rotation speed during normal operation. To validate the proposed system, two electronic accelerometers were attached to the motor’s gearbox and bearing. The natural frequency response of the optical accelerometer was simulated and good agreement with the experimental results was obtained (0.83% of error). The proposed sensor was able to correctly identify the operation speeds of 20, 25, 35, 40, 45 and 50 rps with a maximum error of 0.05%. The mean signal-to-noise ratio (SNR) of the optical accelerometer was 64.05% higher than the SNR of one of the electronic solutions. The experimental results show that the vibration signals have different characteristics when measured at the bearings and at the gearbox, indicating the feasibility of multi-signals analysis for fault detection.