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The efficient numerical solution of the exterior Helmholtz equation modeling the acoustic scattering by an obstacle is considered. The exterior problem is approximated by truncating the domain with a rectangular boundary and using either a perfectly matched layer or a second-order absorbing boundary condition to reduce reflections from the artificial boundary. The scattering problem is solved iteratively by using a domain embedding method with an efficient separable preconditioner. With this approach, it is possible to realize the GMRES iterations in a low-dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner. The accuracy and the efficiency of the proposed solution technique are studied with numerical experiments.

The aim of this paper is to study the time-harmonic scattering problem in a coupled fluid-porous medium system. We consider two different models for the treatment of porous materials: the Allard–Champoux equations and an approximate model based on a wall impedance condition. Both models are compared by computing analytically their respective solutions for unbounded planar obstacles, considering successively plane and spherical waves. A numerical method combining an optimal bounded PML and finite elements is also introduced to compute the solutions of both problems for more general axisymmetric geometries. This method is used to compare the solutions for a spherical absorber.

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 investigates the efficiency of the wave finite element (WFE) method to assess the vibroacoustic behavior of finite baffled axisymmetric elastic pipes interacting with internal and external acoustic fluids. The pipes, of either homogeneous or multi-layered cross-sections, are surrounded by an external fluid of infinite extent, which can be light or heavy. The Sommerfeld radiation condition is taken into account by considering a perfectly matched layer (PML) around the external fluid. The method involves the computation of waves traveling along an axisymmetric multi-physics waveguide that incorporates a pipe, internal and external fluids, as well as a PML. Numerical experiments are carried out which highlight the relevance of the WFE method in terms of accuracy and CPU time savings, in comparison with the conventional finite element analysis.

In ocean waveguides, the ocean bottom is usually approximated as a half-space. Thus, there exist no reflection waves at the half-space bottom and condition of radiation at infinity should be satisfied. In numerical solutions like parabolic equation methods, the depth domain has to be truncated, which can generate reflection waves from the truncated ocean bottom. To reduce the effect of reflection waves and to simulate an unbounded ocean bottom accurately, an artificial absorbing layer (ABL) was used. As was demonstrated, an ABL meets well the demand of accuracy in sound field calculation. However, both the sea-bottom layer and the artificial absorbing layer are needed to be set quite thick by using an ABL technique. Fortunately, a PML with several wavelengths can keep similar calculation accuracy with an ABL with dozens of wavelengths. In this paper, perfectly matched layer (PML) techniques for three parabolic equation (PE) models RAM, RAMS and a three-dimensional PE model in underwater acoustics are presented. A key technique of PML “complex coordinate stretching” is used to truncate unbounded domains and to simulate infinity radiation conditions instead of the ABL in those models. The numerical results illustrate that the PML technique is of higher efficiency than the ABL technique at truncating the infinity domain with minimal spurious reflections in PE models.

This paper proposes a finite-element (FE) and perfectly matched layer (PML)modeling of three-dimensional (3D) scattering of transient elastic waves in a cracked infinite plate with rectangular cross-section. The FE predictions are validated against 3D semi-analytical literature results. The effects of PML parameters on a root-mean-square error estimate are measured against the reference FE predictions computed using extended meshes. The proposed model is shown, through the numerical examples, to offer huge saving in real run-time at a slight degradation in accuracy. Practical applications indicate its potential in modeling elastic-wave-based nondestructive evaluation of engineering structures.

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

In this paper, we studied the finite volume formulations for solving the diffraction grating problem that is truncated by the perfectly matched layer (PML) technique. Based on a reliable the a-posteriori error estimate, an adaptive PML finite volume method is discussed for the numerical approximation of the diffraction grating problem. The PML parameters are obtained numerically by sharp a-posteriori error estimates of the PML finite volume method such as the thickness of the layer and the medium property. It is worth mentioning in the a-posteriori error estimates that we derive the error representation formula and use a $L^2$-orthogonality property of the residual similar to the Galerkin orthogonality used in the finite element method. Furthermore, the lower bound is established to demonstrate the efficiency of the a-posteriori error estimates. Numerical experiments are given to illustrate the accuracy and robustness of our adaptive algorithm.

For wave propagation problems in infinite-domains, truncation of the far-field by an artificial boundary is essential to define a bounded domain of interest; resultant difficulties are the radiation condition and generation of incident waves. Instead of the radiation condition, an absorbing boundary condition (ABC) is implemented in an inhomogeneous exterior domain, based on the perfectly matched layer (PML) technique. Complex coordinate stretching, a key PML concept, analytically continues a governing equation in the domain of interest into a PML equation as an anisotropic absorbing boundary in the exterior domain; a system of equivalent equations governs waves in the whole computational domain, and thus the PML is reflectionless at the artificial boundary, an interface between the PML and the domain of interest. For generation of incident waves, wave-maker modeling is proposed based on an idea of plain topography and wave-ray tracing. A source function along the interface is a curvilinear integral in a weak form for the governing equation. Finite element examples for wave propagation in one-dimension verify ability and efficiency of techniques with PML ABCs; besides, those for wave scattering by a circular cylinder on a slope show effectiveness of the wave-maker modeling.

For flow noise simulations, the nonreflecting boundary condition (NRBC) is significant to confine the computational domain to a small domain. Lattice Boltzmann method (LBM) has advantages for noise because of its low dissipation, but is limited to the uniform grid. In this paper, an absorbing boundary condition (ABC) based on perfectly matched layer (PML) technique is introduced to LBM. Then PML stability is analyzed and a new strategy is developed to achieve robustness. Invoking the decoupling time integration, the underlying equation for streaming is solved with the nodal discontinuous Galerkin method. Benchmark acoustic problems were used to demonstrate the PML absorption. Moreover, PML parameters, long time behavior and inhomogeneous pseudo mean flow are discussed. The methodology appears to work very well and would be hoped for practical flow noise computation.

The eigenfunctions of the modified Helmholtz operator have no orthogonality in a bounded domain with a perfectly matched layer (PML), which makes it difficult to calculate the coordinates under two different local bases when the marching algorithm is applied. In this paper, we derive the conjugate eigenfunctions of the operator and discuss the cross orthogonality between the eigenfunctions and their conjugate eigenfunctions. On the other hand, we derive a simple formula for calculating the coordinates under the local base. The numerical results indicate that this method is effective.

This paper proposes a new numerical framework to simulate ultrasound wave propagation in 3D viscoelastic heterogeneous media based on the elastodynamic wave equation including a 3D second-order time-domain perfectly matched layer formulation. A finite difference discretization of this formulation is presented, along with a stability analysis. The resulting model is capable of simulating 3D shear and longitudinal acoustic waves for arbitrary source geometries and excitations, together with arbitrary initial and boundary conditions. A simulation example is provided to show the application of our proposed method for tissue elastography imaging. Specifically, the propagation of shear waves from a localized lesion to the surrounding normal tissue is examined.