Narrow Results

The process of mesh coarsening describes the reduction and simplification of a highly detailed mesh in such a way that the original geometry is best possible preserved. The earliest coarsening algorithms were developed for real time visualizations in the upcoming field of computer graphics and later on adopted for some element topologies of the finite element method (FEM). An algorithm is presented in this article which applies the mesh decimation process to the requirements of both the FEM and the Boundary Element Method (BEM) in acoustics. The capabilities of the algorithm in order to significantly reduce the CPU times for both numerical methods are shown.

In this paper we investigate the unknown body problem in a waveguide. The Rayleigh conjecture states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. This conjecture is the cornerstone of the intersecting canonical body approximation ICBA for solving the unknown body inverse problem. Therefore, the use of the ICBA requires that an analytical solution be known exterior to the sphere in the waveguide, which leads us to analytically compute the exterior solution for a sphere between two parallel plates. A least-squares matching of theoretical acoustic fields against the measured, scattered field permits a reconstruction of the unknown object.

In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.

In this paper, a new technique is presented for structural acoustic analysis in the case of nonconforming acoustic–solid interface meshes. We first describe a simple method for coupling nonconforming acoustic–acoustic meshes, and then show that a similar approach, together with the coupling operators from conforming analysis, can also be applied to nonconforming structural acoustics. In the case of acoustic–acoustic interfaces, the continuity of acoustic pressure is enforced with a set of linear constraint equations. For structural acoustic interfaces, the same set of linear constraints is used, in conjunction with the weak formulation and the coupling operators that are commonly used in conforming structural acoustics. The constraint equations are subsequently eliminated using a static condensation procedure. We show that our method is equally applicable to time domain, frequency domain, and coupled eigenvalue analysis for structural acoustics. Numerical examples in both the time and frequency domains are presented to verify the methods.

The variational theory of complex rays (VTCR) is a wave-based predictive numerical tool for medium-frequency problems. In order to describe the dynamic field variables within the substructures, this approach uses wave shape functions which are exact solutions of the governing differential equation. The discretized parameters are the number of substructures (h) and the number of wavebands (p) which describe the amplitude portraits. Its capability to produce an accurate solution with only a few degrees of freedom and the absence of pollution error make the VTCR a suitable numerical strategy for the analysis of vibration problems in the medium-frequency range. This approach has been developed for structural and acoustic vibration problems. In this paper, an error indicator which characterizes the accuracy of the solution is introduced and is used to define an adaptive version of the VTCR. Numerical illustrations are given.

In recent years the development of free field radiation conditions in the time domain has become a topic of intensive research. Perfectly matched layer (PML) approaches for the frequency domain are well known. In the time domain, on the other hand, they suffer in many cases from highly increased complexity and instabilities. In this paper, we introduce a PML for the conservation equations of linear acoustics. The used formulation requires three auxiliary variables in 3D and circumvents thereby convolution integrals and higher order time derivatives. Furthermore, we prove the weak stability of the proposed formulation and show their good absorption properties by means of numerical examples.

This paper proposes an extension of the variational theory of complex rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective a priori selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry.

A multipole expansion approximation boundary element method (MEA BEM) based on the hierarchical matrices (H-matrices) and the multipole expansion theory was proposed previously. Though the MEA BEM can obtain higher accuracy than the adaptive cross-approximation BEM (ACA BEM), it demands more CPU time and memory than the ACA BEM does. To alleviate this problem, in this paper, two hybrid BEMs are developed taking advantage of the high efficiency and low memory consumption property of the ACA BEM and the high accuracy advantage of the MEA BEM. Numerical examples are elaborately set up to compare the accuracy, efficiency and memory consumption of the ACA BEM, MEA BEM and hybrid methods. It is indicated that the hybrid BEMs can reach the same level of accuracy as the ACA BEM and MEA BEM. The efficiency of each hybrid BEM is higher than that of the MEA BEM but lower than that of the ACA BEM. The memory consumptions of the hybrid BEMs are larger than that of the ACA BEM but less than that of the MEA BEM. The algorithm used to approximate the far-field submatrices corresponding to the cells and their nearest interactional cells determines the accuracy, efficiency and memory consumption of the hybrid BEMs. The proposed hybrid BEMs have both operation and storage logarithmic-linear complexity. They are feasible.