Archives of Acoustics, 45, 4, pp. 647–654, 2020

Selected Aspects of Meshless Method Optimization in the Room Acoustics with Impedance Boundary Conditions

Technical University of Rzeszów

Technical University of Rzeszów

Technical University of Rzeszów

Two optimization aspects of the meshless method (MLM) based on nonsingular radial basis functions (RBFs) are considered in an acoustic indoor problem. The former is based on the minimization of the mean value of the relative error of the solution in the domain. The letter is based on the minimization of the relative error of the solution at the selected points in the domain. In both cases the optimization leads to the finding relations between physical parameters and the approximate solution parameters. The room acoustic field with uniform, impedance walls is considered.

As results, the most effective Hardy’s Radial Basis Function (H-RBF) is pointed out and the number of elements in the series solution as a function of frequency is indicated. Next, for H-RBF and fixed n, distributions of appropriate acoustic fields in the domain are compared. It is shown that both aspects of optimization improve the description of the acoustic field in the domain in a strictly defined sense.
Keywords: architectural acoustics; meshless method; radial basis functions; impedance boundary condition
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Álvarez-Morales L., Galindo M., Girón S., Zamarreño T., Cibrián R.M. (2016), Acoustic characterization by using different room acoustics software tools: A comparative study, Acta Acustica united with Acustica, 102(3): 578–591, doi: 10.3813/AAA.918975

Brański A., Kocan-Krawczyk A., Prędka E. (2017), An influence of the wall acoustic impedance on the room acoustics. The exact solution, Archives of Acoustics, 42(4): 677–687, doi: 10.1515/aoa-2017-0070.

Brański A., Prędka E. (2018), Nonsingular meshless method in an acoustic indoor problem, Archives of Acoustics, 43(1): 75–82, doi: 10.24425/118082.

Chen L, Marburg S., Zhao W., Liu C., Chen H. (2019), Implementation of isogeometric fast multipole boundary element methods for 2D half-space acoustic scattering problems with absorbing boundary condition, Journal of Theoretical and Computational Acoustics, 27(2): 1850024, doi: 10.1142/S259172851850024X.

Chen L., Zhao W., Liu C., Chen H. (2017a), 2D structural acoustic analysis using the FEM/FMBEM with different coupled element types, Archives of Acoustics, 42(1): 37–48, doi: 10.1142/S259172851850024X

Kuttruff H. (2000), Fundamentals of Physical Acoustics, Room Acoustic, WileyInterscience, New York.

Li W., Zhang Q., Gui Q., Chai Y. (2020), A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems, International Journal of Computational Methods, doi: 10.1142/S0219876220410029

Meissner M. (2019), Prediction of low-frequency sound field in rooms with complex valued boundary conditions on walls, Vibrations in Physical Systems, 30(1): 2019127.

Meissner M., Wiśniewski K. (2019), Influence of room modes on low-frequency transients: Theoretical modeling and numerical predictions, Journal of Sound and Vibration, 448: 19–33, doi: 10.1016/j.jsv.2019.02.012.

Pilch A. (2019), Optimization based validation of room acoustic models, AGH University of Science and Technology, Kraków, Poland.

Prędka E., Brański A. (2020), Analysis of the Room Acoustic with Impedance Boundary Conditions in the Full Range of Acoustic Frequencies, Archives of Acoustics, 45(1): 85–92, doi: 10.24425/aoa.2020.132484

Rabisse K., Ducourneau J., Faiz A., Trompette N. (2019), Numerical modelling of sound propagation in rooms bounded by walls with rectangular-shaped irregularities and frequency-dependent impedance, Journal of Sound and Vibration, 440: 291–314, doi: 10.1016/j.jsv.2018.08.059

Shaposhnikov K., Jensen M.J.H. (2018), Panel contribution analysis based on FEM, BEM and numerical Green’s function approaches, Journal of Theoretical and Computational Acoustics, 26(3): 1850037, doi: 10.1142/S2591728518500378.

Shi S., Liu K., Xiao B., Jin G., Liu Z. (2019), Forced acoustic analysis and energy distribution for a theoretical model of coupled rooms with a transparent opening, Journal of Sound and Vibration, 462: 114948, doi: 10.1016/j.jsv.2019.114948.

Van Horssen W.T., Wang Y., Cao G. (2018), On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients, Journal of Sound and Vibration, 424: 263–271,

Wu H., Yu L., Jiang W. (2019), A coupling FEM/BEM method with linear continuous elements for acoustic-structural interaction problems, Applied Acoustics, 150: 44–54, 10.1016/j.apacoust.2019.02.001.

Xiangyu W., Yang X., Jiachi Y. (2018), A meshfree radial point interpolation coupled with infinite acoustic wave envelope element method for computing acoustic fields, Acta Acustica united with Acustica, 104(1): 64–78, doi: 10.3813/AAA.919146.

Xiangyu Y., Wei L., Yingbin C. (2020), A truly meshfree method for solving acoustic problems using local weak form and radial basis functions, Applied Mathematics and Computation, 365: 124694, doi: 10.1016/j.amc.2019.124694.

DOI: 10.24425/aoa.2020.135252

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