Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method

Abstract

SUMMARYAcoustic wave propagation in heterogeneous media is a topic of significant interest in many areas of science and engineering, including aeroacoustics and sound propagation in oceans. In the present work, numerical frequency domain models based on the joint use of the method of fundamental solutions and of the radial basis function collocation method (also known as Kansa's method) are discussed. In this context, the method of fundamental solutions is used to model the homogeneous part of the propagation domain, while Kansa's method is employed to model the presence of heterogeneities. The coupling between the two parts of the propagation domain is performed iteratively, allowing independent spatial discretization between the different subdomains of the model (i.e. matching collocation points at common surfaces are not necessary). Additionally, an optimised algorithm, based on the use of a varying relaxation parameter, is employed to speed up and/or to ensure the convergence of the iterative coupling process. At the end of the paper, numerical results illustrate the applicability and potentialities of the proposed formulations.

Coupled finite element - hierarchical boundary element methods for dynamic soil-structure interaction in the frequency domain

“…Figure 5 shows the real and imaginary part of the radial displacement at r D r o , for the three values of the wave velocity ratio˛. All methods yield accurate results in very good agreement with the analytical solution [44] for all values of the ratio˛, with exception of the sequential Neumann-Dirichlet algorithm, which is unable to retrieve the correct solution within the prescribed number of iterations at (12,(31)(32)(33)(34)(35)(36)(37)(38)(41)(42)46,(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)(62),64-80,82-100) Hz for a wave velocity ratio˛D 1=2. At these particular frequencies, the relative residual norm of the interface displacements and interaction forces still exceeds the specified accuracy of The solutions of the classical direct coupling approach (dashed black line), the iterative Neumann-Dirichlet (grey squares), Dirichlet-Neumann (black plus signs), Neumann-Neumann (grey circles) and Dirichlet-Dirichlet (black crosses) algorithms, and the monolithic coupling procedure (black rhombuses) are compared to the analytical solution (solid grey line) [44].…”

Adaptive Analysis of Acoustic‐Elastodynamic Interacting Models Considering Frequency Domain MFS‐FEM Coupled Formulations

“…For the elastodynamic subdomain, the FEM [8,10] and the newer meshless methods, including the Kansa's method [9,10] and the meshless local Petrov-Galerkin method [10], have been employed with success, while for the acoustic fluid, both the BEM [8,10] and the method of fundamental solutions (MFS) [9,10] have been used in iterative coupling algorithms. Previous works [9][10][11][12] have also shown that the MFS can be particularly well suited for the analysis of the acoustic subdomain, even surpassing the BEM in terms of efficiency and accuracy. Thus, iteratively coupling the MFS with the FEM can be a robust and efficient alternative strategy to handle acoustic-elastodynamic problems in the frequency domain.…”

An Overview of Recent Advances in the Iterative Analysis of Coupled Models for Wave Propagation

“…In the analysis of wave propagation using frequencydomain formulations, iterative coupling procedures can be found in the literature, mostly considering acoustic-acoustic and acoustic-elastodynamic coupling [49][50][51][52][53][54]. As it has been reported, frequency-domain wave propagation analyses usually give rise to ill-posed problems and, in these cases, the convergence of the iterative coupling algorithm can be either too slow or unachievable.…”