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We report results on the synchronization of two organ pipes positioned side by side. Special attention is put on the synchronization of the higher harmonics. As possible explanation, classical theory provides the amplitude death as explanation for the reduction to almost silence of two coupled organ pipes. With our measurements we exclude this scenario. The higher harmonics show a behavior in perfect coincidence with synchronization theory. In addition we investigate the dependence on the coupling of two pipes by varying their distance. In the context of synchronization in networks, a new synchronization effect is observed for extended systems with two distributed, slightly different delays.

A computational procedure is developed for adaptive modeling of transient wave propagation in an unbounded acoustic layer. The adaptivity herein is concerned with controlling the error caused by imperfect modeling of unbounded domains, and the procedure aims at determining the optimal order of the absorbing boundary condition (ABC) under consideration to control the error in the solution within a predetermined tolerance. The perfectly matched layer (PML) is used as an ABC, and the size of the PML domain controls the error associated with modeling unbounded domains. As a key technique in the adaptive method, a local solution procedure is designed based on the method of bicharacteristics to extract, from the computed solution, the information flowing into the computational domain. Numerical experiments show that, under wide circumstances, the maximum pressure associated with the inflow evaluated near the truncated boundary of the PML domain can be related with the maximum error in the pressure and thus can be used as an error estimator. It is demonstrated that a simple adaptive algorithm based on this error estimator can automatically determine the PML domain size to produce solutions with controlled errors.

The benchmark problem of room acoustics, consisting on the determination of the three-dimensional (3D) sound field generated by a point source placed within a closed acoustic space is here addressed by means of the Method of Fundamental Solutions (MFS). The focus of this paper is on the behavior of a MFS numerical frequency domain approach with regards to stability, accuracy, and efficiency. Strategies of improving stability and accuracy of the method such as the use of different distributions of collocation points and virtual sources or an singular value decomposition (SVD) solver are also analyzed. It has been found that these strategies allowed increasing accuracy and attaining stability. Comparison with a classical BEM model was also performed, and has shown that the MFS can reach excellent accuracy making use of smaller-sized equation systems.

We apply the static condensation reduced basis element (scRBE) method to treat the class of parametrized complex Helmholtz partial differential equation. We construct a set of components of interoperable parametrized reference components in a Library to model a family of target models relevant to acoustic devices. The components in the Library are built upon the scRBE method by using reduced basis (RB) formulation, and are compatible to each other by a set of common interfaces, or port. We apply an offline–online computational strategy to achieve rapid and accurate prediction of any parametric systems formed from a set of components in a Library. We demonstrate that the approach can handle large scale models with many parameters and/or topology variations efficiency in several numerical examples. We show that significant computational savings can be obtained by the scRBE method.

The boundary element method (BEM), along with the finite element and finite difference methods, is commonly used to carry out numerical simulations in a wide variety of subjects in science and engineering. The BEM, rooted in classical mathematics of integral equations, started becoming a useful computational tool around 50 years ago. Many researchers have worked on computational aspects of this method during this time.

This paper presents an overview of the BEM and related methods. It has three sections. The first, relatively short section, presents the governing equations for classical applications of the BEM in potential theory, linear elasticity and acoustics. The second describes specialized applications in bodies with thin features including micro-electro-mechanical systems (MEMS). The final section addresses current research. It has three subsections that present the boundary contour, boundary node and fast multipole methods (BCM, BNM and FMM), respectively. Several numerical examples are included in the second and third sections of this paper.

The coefficient matrices of conventional boundary element method (CBEM) are dense and fully populated. Special techniques such as hierarchical matrices (H-matrices) format are required to extent its ability of handling large-scale problems. Adaptive cross approximation (ACA) algorithm is a widely adopted algorithm to obtain the H-matrices. However, the accuracy of the ACA boundary element method (ACABEM) cannot be adjusted by changing the tolerance ${𝜀}^{\prime }$ when it exceeds a certain value. In this paper, the degenerate kernel approximation idea for the low-rank matrices is developed to build a fast BEM for acoustic problems by exploring the multipole expansion of the kernel, which is referred as the multipole expansion H-matrices boundary element method (ME-H-BEM). The newly developed algorithm compresses the far-field submatrices into low rank submatrices with the expansion terms of Green’s function. The obtained H-matrices are applied in conjunction with the generalized minimal residual method (GMRES) to solve acoustic problems. Numerical examples are carefully set up to compare the accuracy, efficiency as well as memory consumption of the CBEM, ACABEM, fast multipole boundary element method (FMBEM) and ME-H-BEM. The results of a pulsating sphere indicate that the ME-H-BEM keeps both storage and operation logarithmic-linear complexity of the H-matrices format as the ACABEM does. Moreover, the ME-H-BEM can achieve better convergence and higher accuracy than the ACABEM. For the analyzed complicated large-scale model, the ME-H-BEM with appropriate number of expansion terms has an advantage in terms of efficiency as compared with the ACABEM. Compared with the FMBEM, the ME-H-BEM is easier to be implemented.