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Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this work, a new type of interpolation for the acoustic field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation has been found in the current work to be highly successful. Results are shown for a variety of classical scattering problems, and also for scattering from nonconvex obstacles. Notable results include a conclusion that, using this new formulation, only approximately 2.5 degrees of freedom per wavelength are required. Compared with the 8 to 10 degrees of freedom normally required for conventional boundary (and finite) elements, this shows the marked improvement in storage requirement. Moreover, the new formulation is shown to be extremely accurate. It is estimated that for 2D Helmholtz problems, and for a given computational resource, the frequency range allowed by this method is extended by a factor of three over conventional direct collocation Boundary Element Method. Recent successful developments of the current method for plane elastodynamics problems are also briefly outlined.

The present article studies what effect the shape of a rigid acoustic barrier has on the acoustic insertion loss provided by the barrier. The Boundary Element Method (BEM), formulated in the frequency domain, is used to evaluate the sound propagation around acoustic screens in the vicinity of a tall building. The acoustic screen is assumed to be non-absorbing, and the building is modeled as an infinite barrier. Signals in the time domain are obtained from the frequency domain computations by applying inverse Fourier transforms. In the examples provided, the height of the acoustic barrier remains constant, but different geometric shapes are modeled. The results obtained for a vertical barrier are used as a reference.

Numerical methods for computing the three-dimensional pressure field in a flat fluid channel bounded either by a rigid boundary, an elastic semi-infinite medium or by a layer of sediment, subjected to incoherent line sources are presented. After verification Greens functions are incorporated in a Boundary Element Method (BEM) code that simulates the pressure variation inside the fluid channel in the vicinity of a rigid or elastic inclusion, avoiding the discretization of the fluid and solid channel interfaces. After the verification of the solution, the models developed are then used to simulate the pressure variation within the fluid channel in the presence of infinitely long rigid and elastic inclusions of differing sizes, when the channel is struck by a spatially-sinusoidal harmonic pressure line load. The results are then compared with those obtained when the channel floor is assumed to be rigid. Time domain results are given by means of inverse Fourier transforms, to help understand how the mechanical properties of the channel floor may affect the variation of the pressure field within the channel.

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.

This paper presents a review of basic concepts of the boundary element method (BEM) for solving 3D half-space problems in a homogeneous medium and in frequency domain. The usual BEM for exterior problems can be extended easily for half-space problems only if the infinite plane is either rigid or soft, since the necessary tailored Green’s function is available. The difficulties arise when the infinite plane has finite impedance. Numerous expressions for the Green’s function have been found which need to be computed numerically. The practical implementation of some of these formulas shows that their application depends on the type of impedance of the plane. In this work, several formulas in frequency domain are discussed. Some of them have been implemented in a BEM formulation and results of their application in specific numerical examples are summarized. As a complement, two formulas of the Green’s function in time domain are presented. These formulas have been computed numerically and after the application of the Fourier Transformation compared with the frequency domain formulas and with a FEM calculation.

Recent years have seen a renewed interest in the theories of extended continuum mechanics. These allow for a finer and relatively simple modeling of physical phenomena occurring on the microscopic level. The Eringen’s micromorphic medium belongs to this class and allows accounting for the material microstructure. A subclass of this model was applied to model the mechanical behavior of cardiac tissue. With the aid of a specifically developed numerical tool, the validity of the approach is demonstrated using different myocardial infarct scenario.

Understanding the deformation of arterial walls under loading is essential for the definition of some new therapeutic protocols. This requires the modeling of the mechanical behavior of the artery wall. In this work, in order to account for the microstructure, each of the conventional three layers of the artery is assumed to behave like a dilatation elastic solid. The resulting compound is then submitted to various loads and the response analyzed in order to highlight the contribution of the microstructure. Finally, the impact of a localized zone of microstructure modification on the overall deformation is investigated.

The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential equations is an attractive numerical approach. Its accuracy deteriorates in the presence of Neumann-type boundary conditions which are practically inevitable in solid mechanics. The main appeal of the BEM can be maintained by a judicious coupling of the pure BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, seems versatile and effective. This is demonstrated by considering some linear and nonlinear elasticity problems including multi-physics and multi-field problems.

In this work, a multi-scaling homogenization process using boundary element formulation (BEM) for modeling a two-dimensional multi-phase microstructure containing irregular’s inclusions is presented. The BEM is very attractive for multiscale modeling tools for heterogeneous materials. In this approach, the iterative inhomogeneity discretization of the external boundary is disregarded, leading to a computational low cost. This approach was used for solving the elastic problem of a representative volume element (RVE) and the field theory medium. The main goal relies on finding the effective properties of micro-heterogeneous materials within a homogeneous and orthotropic matrix. Expressions for evaluating the effective properties under Plane Stress (PT) for orthotropic materials were also presented. Generally, the numerical models consider the graphite nodules as voids for GGG-40 and the roundness is close circular geometry. In this sense, a nodular cast iron GGG-40 microgram was obtained by X-ray computed tomography and Laser Confocal Microscope System, allowing the modeling of the true nodule shape. The numerical results showed good agreement with the experimental tests. The inclusions of graphite were considered as voids in the material matrix. Experimental stress–strain tests and micrographic analysis were used to determine the Young’s modulus, spatial distributions, as well as, nodule shape. The numerical in this work was compared with the obtained experimental results in this work. The comparison between the obtained experimental data with those available in the literature also showed good agreement.

The numerical stability of different formulas for the correction term of the half-space Green’s function is investigated. The formula with complex monopoles is taken as a reference. The expressions of Koh and Yook, tested in a previous publication [R. Piscoya and M. Ochmann, Acoustical Green’s function and boundary element techniques for 3D half-space problems, J. Comput. Acoust. (2017), https://doi.org/10.1142/S0218396X17300018], are rewritten to improve their range of application. The formulas of Sommerfeld and Thomasson are analyzed and its suitability for a BEM implementation is evaluated by comparing their accuracy against our reference. For the sake of completeness, the first and second derivatives of the formulas are explicitly written.

The problem is the scattering of a plane sound wave at a rough water-air interface. The purpose of this paper is to describe in detail the method and demonstrate its work with simple examples. The main advantage of this approach is that there are no limits on the relation between the shape of the surface and the incident wave, so we can consider large Rayleigh parameter, shading, multiple scattering. The solution of the Helmholtz equation in the form of an integral over the boundary is used only in the inner domain, in the outer domain the separation of variables is used to obtain a nonlocal integral boundary condition on the artificial boundary.

This paper describes an innovative computational model developed to solve two-dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier-Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three-step finite element method. The arbitrary Lagrangian-Eulerian (ALE) method is incorporated into the model, to solve the moving boundary problems. For illustration of the present numerical code, a vortex-induced cross-flow oscillations of a circular cylinder mounted on an elastic dashpot-spring system is considered. The phenomena of the beat, lock-in, and resonance are revealed in the Reynolds number range between 100 and 110, which are much narrower than the previous results by experimental and numerical studies.