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This paper presents the boundary element method solutions of the Helmholtz integral equation for vibrating bodies near rigid planes. These solutions are performed using an in-house code generating one-half, one-quarter, and one-eighth of a free-space algorithm automatically. The code has the capability of examining near fields of acoustic sources in detail and particularly convenient for machines placed in close proximity to rigid planes. In the paper, three types of sources are handled and the acoustic effect of the presence of rigid planes is discussed. As a basic source, dilating sphere is the first source. The second one is radiating cube. The third is washing machine, as a real and common noise source disturbing the domestic comfort. The paper provides opinion about the directivity of sound pressure fields, forms their visual record in mind around vibrating bodies near reflecting surfaces; numerical vision about scattering effects of rigid walls around machinery; and also points out the possibility and feasibility of the solution of symmetric objects in half/quarter space instead of free space. [ABSTRACT FROM AUTHOR]

The paper presents a topology optimization methodology for 2D elastodynamic problems using the boundary element method (BEM). The topological derivative is derived based on the variation method and the adjoint variable method. The level set method is employed for the representation of the material domain and voids within a specified design domain. Thus, the boundaries can easily be generated, following the zero isocontour of the level set function. Numerical implementation is carried out to demonstrate the effectiveness of the proposed topology optimization methodology in wave isolation and waveguide problems. [ABSTRACT FROM AUTHOR]

To predict the behavior of reservoir fluids in porous media and their investigation at the macroscopic level, it is necessary to study in detail the hydrodynamic flows in porous media at the microscale level from the point of view of the individual pore spaces taking into account their structural features. This paper deals with the analysis of a periodic flow of a viscous incompressible fluid and dispersed systems in a flat channel of rectangular cross section with irregular side walls under a constant pressure drop. Using an efficient numerical approach based on the 3D Boundary Element Method accelerated by the Fast Multipole Method on heterogeneous computing architectures, the influence of irregularities of various size and shape present on microchannel walls on the hydrodynamic flows of the viscous fluid flow and the emulsion droplet dynamics in a capillary micromodel of the porous medium is studied. The results of the present paper can also be useful in the design of microfluidic devices. [ABSTRACT FROM AUTHOR]

Modeling and simulating a power distribution network (PDN) for printed circuit boards with irregular board shapes and multi‐layer stackup is computationally inefficient using full‐wave simulations. This paper presents a new concept of using deep learning for PDN impedance prediction. A boundary element method (BEM) is applied to efficiently calculate the impedance for arbitrary board shape and stackup. Then over one million boards with different shapes, stackup, integrated circuits (IC) location, and decap placement are randomly generated to train a deep neural network (DNN). The trained DNN can predict the impedance accurately for new board configurations that have not been used for training. The consumed time using the trained DNN is only 0.1 s, which is over 100 times faster than the BEM method and 10 000 times faster than full‐wave simulations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Ordnance Equipment Engineering is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Noise pollution is the most serious environmental pollution, which seriously affects people's normal life and physical and mental health, as well as normal production work. Therefore, noise control is necessary, but before noise control, the first thing to do is to identify the location of the noise source, and the noise control work is meaningless when the noise cannot be identified. Flat plate structures are a fundamental part of complex ship structures, and their vibration, noise, and their interrelationships when excited by the outside world are receiving increasing attention. The core of the research in this paper is the identification of the sound source of the vibrating plate. A method combining phase conjugation with interior boundary element method is developed for the identification of the pressure and normal velocity distribution of a vibrating plate. An interior problem is formed by enclosing the phase conjugation array plane and the plate surface. The pressures at the array elements are phase-conjugated as the specified pressure boundary condition. The impedance relationship between the surface pressure and the surface normal velocity of the plate is utilized as a specified impedance boundary condition. The interior boundary element method is applied to solve the interior problem. The identification of the surface pressure and normal velocity distribution is studied numerically. The numerical results show that with the array located in the near field the proposed method achieves subwavelength focusing to identify the surface pressure and normal velocity distribution and clearly shows the response shapes. [ABSTRACT FROM AUTHOR]

The peridynamics (PD), as a promising nonlocal continuum mechanics theory, shines in solving discontinuous problems. Up to now, various numericalmethods, such as the peridynamicmesh-free particle method (PD-MPM), peridynamic finite element method (PD-FEM), and peridynamic boundary element method (PD-BEM), have been proposed. PD-BEM, in particular, outperforms other methods by eliminating spurious boundary softening, efficiently handling infinite problems, and ensuring high computational accuracy. However, the existing PD-BEM is constructed exclusively for bond-based peridynamics (BBPD) with fixed Poisson's ratio, limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems. In this paper, we address these limitations by introducing the boundary element method (BEM) for ordinary state-based peridynamics (OSPD-BEM). Additionally, we present a crack propagationmodel embeddedwithin the framework of OSPD-BEM to simulate crack propagations. To validate the effectiveness of OSPD-BEM, we conduct four numerical examples: deformation under uniaxial loading, crack initiation in a double-notched specimen, wedge-splitting test, and threepoint bending test. The results demonstrate the accuracy and efficiency of OSPD-BEM, highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson's ratios. Moreover, OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM. [ABSTRACT FROM AUTHOR]

This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology. [ABSTRACT FROM AUTHOR]

The corrosion problem of the tank floor of the oil depot tank area becomes more and more serious with the extension of the operation time. At present, how to determine the potential distribution of the storage tank floor and how to judge the cathodic protection effect of the storage tank floor is the bottleneck of technological development. In this paper, by constructing a mathematical model of cathodic protection in the tank area, influence of deep well anode on potential distribution of tank bottom is calculated by boundary element method (BEM) with computer programming, to study the potential distribution of the tank floor under different anode parameters. The results show that the calculated results are in good agreement with the field measured results, which verifies the accuracy and reliability of the calculation. [ABSTRACT FROM AUTHOR]

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to propose a new boundary element method (BEM) modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The numerical solution of the heat conduction equation subjected to a non-local condition is described using a boundary element model. The total amount of heat energy contained inside the solid under consideration is specified by the non-local condition. The procedure of solving the heat equation will reveal an unknown control function that governs the temperature on a specific region of the solid's boundary. The initial stress BEM for structures with strain-softening damage is employed in a boundary element program with iterations in each load increment to develop a plasticity model with yield limit deterioration. To avoid the difficulties associated with the numerical calculation of singular integrals, the regularization technique is applicable to integral operators. To validate the physical correctness and efficiency of the suggested formulation, a numerical case is solved. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative approach to numerically model Structure–Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM–FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design. [ABSTRACT FROM AUTHOR]

The major theme of this research is to develop the numerical scheme for the computation of nonlinear problems by the implementation of the boundary element method dependent on Taylor's series. This paper deals with the problem of laminar flow in a semiporous channel in the presence of a transverse magnetic field and the homotopy analysis method (HAM) is employed along with the general boundary element method to compute an approximated solution of the system of nonlinear differential equation governing the problem concerned. A well-known and useful nonlinear differential equation of fluid mechanics F (3) (η) + 1 2 F (η) F (2) (η) = 0 with the boundary conditions F (0) = 0 = F (1) (0) , F 1 (∞) = 1 is referred as an example to show a glimpse into the basic idea of the method and technique used in this paper. It shows the capabilities and wide range of applications of HAM using Taylor series expansion of the derived integral equation. A comparison of HAM with the results calculated previously has been discussed. The solution obtained with HAM in comparison with the numeric solution shows remarkable accuracy. Root mean square formula is computed for the convergence analysis at various values. An increment in the number of elements depicting the convergent results as error is decreased. [ABSTRACT FROM AUTHOR]

The paper is devoted to the development of the displacement discontinuity method for plane problems of fracture mechanics in consideration of the curvature of crack lines. In this paper, some new representations of biharmonic functions are found. This is necessary to obtain the analytical solutions of problems for an elastic plane weakened by a crack in the form of a circular arc. A numerical method is proposed on the basis of these analytical solutions. The numerical values of the stress intensity factor are compared with its known analytical value. [ABSTRACT FROM AUTHOR]

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process. A Matlab code implementing this technique is attached at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of multiple isotropic/anisotropic inclusions (or inhomogeneities) in an unbounded isotropic matrix. In order to introduce the VIEM as an accurate and efficient numerical method for the three-dimensional elastostatic inclusion (or inhomogeneity) problem, multiple isotropic/orthotropic spherical inclusions (or inhomogeneities) in an unbounded isotropic matrix under uniform remote tensile loading are investigated. [ABSTRACT FROM AUTHOR]

This paper describes, for the first time, the application of an Elastodynamic Boundary Element Method (BEM) in Laplace Domain for the Structural Health Monitoring (SHM) of poly-crystalline materials. The study focuses on Ultrasonic Guided Wave (UGW) propagation and investigates the wave–material interactions at micro-scale. The study aims to investigate the interaction of UGWs with assessing micro-structural features such as grain size, morphology, degradation, and flaws. Numerical simulations of the most common micro-structural features demonstrate the accuracy and validity of the proposed method. Particular attention is paid to the study of porosity and its influence on material macro-properties. Different crystal morphologies such as cubic, rhombic, and truncated octahedral are considered. The detection of voids based on the changes in the amplitude and Time of Arrival (ToA) of the backscattered signal is investigated. The study also considers inter-granular cracks, which cause laceration, and examines flaw position/orientation, length, and distance from a specific reference. Furthermore, a framework is proposed for generating Probability of Detection (PoD) curves using numerical simulations. Experimental tests in pristine conditions are shown to be in good agreement with the numerical simulations in terms of ToA, signal amplitude, and wave velocity. The numerical simulations provide insights into wave propagation and wave–material interactions, including different types of defects at the micro-scale. Overall, the BEM and UGW methods are shown to be effective tools for better understanding micro-structural features and their influence on the macro-structural properties of poly-crystalline materials. [ABSTRACT FROM AUTHOR]

The primary aim of this paper is to obtain numerical solutions for the unsteady Helmholtz equation governing harmonic acoustic problems in anisotropic trigonometrically graded materials. To achieve this, the paper proposes a method that combines Laplace transform (LT) and boundary element method (BEM). Several examples of problems related to anisotropic trigonometrically graded media are presented to illustrate that the proposed method is accurate and straightforward to implement. [ABSTRACT FROM AUTHOR]

The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artificial boundary condition. The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields, such as sound waves or electromagnetic waves, provided that the considered domain is infinite or unbounded in all directions. However, the substantial wave motion is considered in water of finite depth, that is, the fluid domain is bounded vertically but unbounded horizontally. Thus, the DtN boundary condition is given on an artificial cylindrical surface, which divides the water domain into an interior and exterior region. The boundary integral equation is adopted to implement the present model. In the case of a floating cylinder, the results of hydrodynamic coefficients of a chamfer box are discussed. [ABSTRACT FROM AUTHOR]

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary conditions. Previous applications of the boundary element method to diffusion curves have relied on polygonal approximations, which either forfeit the high-order smoothness of Bézier curves, or, when the polygonal approximation is extremely detailed, result in large and costly systems of equations that must be solved. In this paper, we utilize the boundary integral equation method to accurately and efficiently solve the underlying partial differential equation. Given a desired resolution and viewport, we then interpolate this solution and use the boundary element method to render it. We couple this hybrid approach with the fast multipole method on a non-uniform quadtree for efficient computation. Furthermore, we introduce an adaptive strategy to enable truly scalable infinite-resolution diffusion curves. [ABSTRACT FROM AUTHOR]

Pile raft foundation (PRF) is a common foundation type for buildings and bridge piers which has been commonly subjected to eccentric vertical load in engineering applications. Dissimilar PRF is often adopted to reduce the excessive settlement and differential settlement of superstructures. The behavior of dissimilar PRF under eccentric vertical load is a significant issue and investigated with the boundary element method in this paper. In this method, the dissimilar pile–soil system is decomposed into extended soil elements and fictitious pile elements. The second kind of Fredholm integral governing equation of the axial force of fictitious piles is established based on the compatibility condition of axial strain between the extended soil and fictitious piles. An iterative procedure is adopted to analyze the average settlement w and rotation slope θ of raft stemming from the settlement compatibility condition of the top of each element and the equilibrium condition of the raft. Furthermore, the axial force and settlement of each element along its depth can be predicted. The corresponding results agree well with a reported case and the finite element method. The characteristics of 3 × 1 and 3 × 3 dissimilar PRFs under eccentric vertical load, including non-dimensional vertical stiffness N0/wEsd, differential settlement wd and the load sharing ratio of typical elements Ni/N0, are systematically investigated by considering different eccentricity e, length/diameter ratios of pile l/d and pile–soil stiffness ratio Ep/Es conditions. The N0/wEsd increases with l/d, while the load sharing ratios of the raft Nraft/N0 and wd decreases with l/d. The eccentricity e has a significant effect on wd and Ni/N0 and a neglect effect on N0/wEsd and Nraft/N0. The N0/wEsd, wd and Ni/N0 are significantly increased with Ep/Es. This research is expected to provide insights to the practitioners into the dissimilar PRF design under eccentric vertical load. [ABSTRACT FROM AUTHOR]

This paper presents a numerical model using the boundary element method for determining the hydrodynamic added mass and added damping of an elastic bridge pier with arbitrary cross-section. Combining the Euler–Bernoulli beam theory with the constant boundary element method, the modal superposition method is used to consider the deformable boundary conditions on the surface of elastic piers to couple the interaction between the elastic pier and water, and the equations for the hydrodynamic added mass and added damping of a general section pier considering the effect of pier-water coupling are derived. The accuracy of the developed model is verified by a benchmark experiment. The developed model is calculated for circular piers and compared with the added mass analytical formulation. The effects of oscillating frequency and structure geometry on the added mass and added damping are further investigated. Results demonstrate that the developed model can be used to solve the hydrodynamic added mass and added damping problems of the elastic bridge pier. Compared to the analytical formula, the developed method incorporates the consideration of added damping in the analysis of the pier-water coupling problem. Oscillating frequency and structure geometry have significant effects on added mass and added damping. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of magnetic field on two-dimensional flow of a viscous, incompressible fluid through composite porous channel using non-primitive boundary element method (BEM). We consider a rectangular channel consisting of two packings that are filled with fully saturated porous medium. It is assumed that both the porous regions are homogenous and isotropic with different permeabilities. Brinkman equation governs the fluid flow through porous media. We analyze the effect of Hartman number, stress-jump coefficient, Darcy number, thickness parameter, electrical conductivity ratio, and viscosity ratio on fluid mechanics. We present the effect of stress-jump coefficients on the interfacial velocity of the fluid against the thickness parameter and observe that the interfacial velocity increases with increasing stress-jump coefficients. We notice that for a fixed value of thickness parameter, the magnitude of vorticity (at lower and upper walls) increases with increasing Darcy number. Moreover, we observe that the magnitude of vorticity at the lower wall decreases and increases at the upper wall with increasing thickness parameter. We compute the Brinkman layer thickness near the interface of the composite porous channel in terms of several flow parameters and observe that the Brinkman layer thickness is strongly depend on the Hartman number, Darcy number, viscosity ratios, and stress-jump coefficient, respectively. [ABSTRACT FROM AUTHOR]

The modeling of the turbine blades in aero-parts presents difficulties in conventional domain solution techniques, especially when internal cooling air passages and a thermal barrier coating (TBC) are applied. This paper presents a very efficient 3D modeling of the anisotropic heat conduction in turbine blades with the boundary element method (BEM), where both the TBC and cooling air passages are considered. The BEM is very ideal for this modeling, since only boundary meshes are required for it; however, a serious problem of nearly singular integration will arise in modeling with coarse meshes. In this article, an efficient modeling and computational algorithm using the BEM is applied for the simulation of heat conduction in the turbine blades of aero-parts. The present work proposes a simplified BEM model to replace multiple thin coating layers on the top of the blade. In the end, the veracity of the implemented BEM code as well as its computational efficiency are illustrated with a few examples, showing that the settled temperature on the substrate can be reduced by 20% by employing a TBC. As compared to the analyses with ANSYS, the percentages of difference were within 2%, while the CPU time spent by the BEM algorithm was about 1/8 of that of ANSYS, not to mention the meshing efforts saved by adopting by a treatment of equivalent convection. [ABSTRACT FROM AUTHOR]

Copyright of Natural Gas Industry is the property of Natural Gas Industry Journal Agency and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed. [ABSTRACT FROM AUTHOR]

This paper presents the thermo-acoustic frequency response of an un-baffled rectangular panel subjected to an external excitation load. A boundary element method BEM has been employed taking into account the Kirchhoff-Helmholtz K-H integral equation for the acoustic pressure and with the fluid-plate interface boundary condition the acoustic pressure jump over the panel is calculated. The thermal effects are considered regarding in the form of a uniform increment of temperature of the panel and are analysed in order to prevent the buckling phenomena. The excitation force considered is in the form of a concentrated load at some point of the panel and the deformation modes correspond to the vacuum case. Applying a collocation method for the panel equation, a frequency transfer function is obtained that relates the deflexion of the panel with the applied load. The effect of several geometric parameters, different thermal loads and location of the load applied on the acoustic radiated power and the acoustic efficiency spectrum are evaluated. Furthermore, the influence of the excitation frequency on the sound directivity is evaluated. The verification of the method is proven with other works. [ABSTRACT FROM AUTHOR]

The Burton-Miller method is widely used to solve the problem of solution non-uniqueness in a conventional boundary element method (CBEM). Although this method is very robust, the hypersingular integral kernel contained in its normal derivative equation increases the computational complexity and reduces the computational accuracy. In this paper, a coupled double boundary Burton-Miller method with unique solutions at full wave numbers is proposed. The aforementioned process is done by replacing the normal integral equation of the Burton-Miller method with the virtual indirect boundary element method (VIBEM) integral equation of combined layer potential and using the equivalent relationship between their coefficient matrices. The proposed method inherits the high-precision advantages of VIBEM and avoids the hypersingular integrals of traditional Burton-Miller methods. In particular, no singular integral is present when the plane element is used for discretization. The numerical results of acoustic radiation and scattering show that the calculation accuracy of the coupled double boundary Burton-Miller method is higher than that of CBEM and the conventional Burton-Miller method. Moreover, the condition number of the coefficient matrix is much lower than that of VIBEM. Lastly, the computation time is less than that of the conventional Burton-Miller method. • Avoiding the calculation of hypersingular integrals in the Burton-Miller method. • Significantly improved the computational accuracy of the Burton-Miller method. • The non-uniqueness of the solution of the boundary integral equation is overcome. • The matrix condition number of the virtual boundary element method is reduced. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Semi-Analytical method for Barrier Option (SABO) applied to continuously monitored Arithmetic Asian Options with barrier. The effectiveness and utility of this approach, based on collocation Boundary Element Method (BEM), has already been tested for European style barrier options in other frameworks and in particular with reference to the similar but unusual Geometric Asian Options. European style Arithmetic Asian Options are more common among practitioners, but much more difficult to treat. Hence a deep investigation of the strategies applied to face the numerical challenges involved in their evaluation by SABO is here presented, together with several results that show the performance of the considered approach. [ABSTRACT FROM AUTHOR]

This paper explores the unsteady Helmholtz type equation with quadratically varying coefficients for anisotropic inhomogeneous media. The paper proposes using a combined Laplace transform and boundary element method to find numerical solutions to problems governed by the equation. The variable coefficients equation is transformed into a constant coefficients equation which is then written in a boundary integral equation involving a time-free fundamental solution. The boundary-only integral equation is used with a standard boundary element method to find the numerical solutions. The results are then transformed numerically using the Stehfest formula to get solutions in the time variable. The paper concludes that the combined Laplace transform and boundary element method is both easy to implement and accurate, as demonstrated by problems related to anisotropic quadratically graded media. [ABSTRACT FROM AUTHOR]

In d dimensions, accurately approximating an arbitrary function oscillating with frequency ≤ k requires ~kd degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber k and in d dimensions) suffers from the pollution effect if, as k→ ∞, the total number of degrees of freedom needed to maintain accuracy grows faster than this natural threshold (i.e., faster than kd for domain-based formulations, such as finite element methods, and kd-1 for boundary-based formulations, such as boundary element methods). It is well known that the h-version of the finite element method (FEM) (where accuracy is increased by decreasing the meshwidth h and keeping the polynomial degree p fixed) suffers from the pollution effect, and research over the last ~30 years has resulted in a near-complete rigorous understanding of how quickly the number of degrees of freedom must grow with k to maintain accuracy (and how this depends on both p and properties of the scatterer). In contrast to the h-FEM, at least empirically, the h-version of the boundary element method (BEM) does not suffer from the pollution effect (recall that in the boundary element method the scattering problem is reformulated as an integral equation on the boundary of the scatterer, with this integral equation then solved numerically using a finite element-type approximation space). However, the current best results in the literature on how quickly the number of degrees of freedom for the h-BEM must grow with k to maintain accuracy fall short of proving this. In this paper, we prove that the h-version of the Galerkin method applied to the standard second-kind boundary integral equations for solving the Helmholtz exterior Dirichlet problem does not suffer from the pollution effect when the obstacle is nontrapping (i.e., does not trap geometric-optic rays). While the proof of this result relies on information about the large-k behavior of Helmholtz solution operators, we show in an appendix how the result can be proved using only Fourier series and asymptotics of Hankel and Bessel functions when the obstacle is a 2-d ball. [ABSTRACT FROM AUTHOR]

Near-field acoustic holography (NAH) based on the boundary element method (BEM) is a powerful tool for noise source identification which is the premise of noise control. For large-scale structures, the measurement aperture should be large enough to ensure that the reconstruction results are accurate. However, the layout of field points often cannot meet the conditions necessary for reliable measurements. The patch NAH methods proposed in previous literature do not explore the influence of the initial and extrapolated aperture on the reconstruction of the vibration velocity. In this paper, the field distribution modes are redefined by the BEM and applied to extrapolation technology. First, the sound pressure of the field points on an expanded hologram is obtained by a data extrapolation method. The expanded data can then be used to reconstruct the vibration velocity of the structure and the sound pressure in the sound field via BEM-based NAH. A modified Tikhonov regularization is utilized in the inverse process. Different sound sources with simple or complex radiated sound fields are used for simulations to explore the influence of the initial and extrapolated aperture on the reconstruction. The application scope of the proposed extrapolation technology is identified and the conclusions are verified by experiments. [ABSTRACT FROM AUTHOR]

Many ultrasonic non-destructive evaluation measurement models use a composite technique in which processes such as transduction, beam propagation, scattering etc. are described separately using sub-models. The output response in these composite models is then obtained by combining the outputs of sub-models using analytical techniques. The Kirchhoff approximation (KA) has typically been a preferred approach for modeling the scattering of ultrasonic waves from defects because it is less resource-intensive than full-wave scattering (FWS) models. In this paper, we study the validity (accuracy) of the KA in modeling various benchmark measurements. We describe a composite model and apply it to simulate benchmark tests. We obtain two sets of results separately with the KA and the boundary element method (BEM), without changing any of the other sub-models used in the composite model. We compare model predictions with measurement data to study the validity of KA under different test scenarios as well as to identify the use-cases for FWS models such as the BEM. [ABSTRACT FROM AUTHOR]

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step—generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials. [ABSTRACT FROM AUTHOR]

Tolerance analysis including tolerance model representation and assembly deviation propagation, is a key approach for predicting and controlling the assembly accuracy of mechanical product. In the current researches, the Non-Gaussian skin model shapes (NSMS) is a valid approach to represent tolerance model of parts considering form defects. However, there is a lack of valid methods to analyze the deviation propagation of mechanical assembly involving parallel and serial connections due to without considering the effect of local surface deformations between mating surfaces (LSDMS) in assembly process, which may affect the assembly accuracy analysis. In addition, the calculation of relative positioning deviation between mating surfaces (RPDMS) of parallel connection has not been combined with practical assembly process closely, which may lead to the loss of accuracy. To address above problems, this paper proposes an assembly accuracy analysis approach of mechanical assembly involving parallel and serial connections considering form defects and LSDMS. Firstly, an integrated Jacobian-NSMS model is presented based on NSMS and Unified Jacobian-Torsor model, which combines the advantages of efficient deviation propagation analysis and high-fidelity representation of tolerance. Secondly, based on the registration method and the difference surface method for solving RPDMS of serial connections, the RPDMS of parallel connection is obtained by performing algebraic operations combining with practical assembly process, by which the assembly involving parallel and serial connections is transformed into a new serial assembly, then the assembly deviation for mechanical assembly involving parallel and serial connections considering form defects and LSDMS can be calculated with the integrated Jacobian-NSMS model. Finally, a case study is presented to verify the proposed method, the result shows that there is different effect on assembly deviation between considering and without considering form defects and LSDMS, which indicates that the form defects and LSDMS have non-ignorable effect on assembly accuracy analysis of mechanical assembly involving parallel and serial connections. In addition, the result shows there is different effect on assembly deviation between considering and without considering practical assembly process in parallel connection. It is expected that the proposed method can help improve the assembly accuracy of mechanical assembly involving parallel and serial connections. • Assembly accuracy analysis of product involving parallel connections is vital to ensure assembly quality. • Integrated Jacobian-NSMS model is developed considering spatial distribution characteristics of form deviations. • The relative positioning deviation of parallel connection is calculated according to practical assembly process. • An approach of assembly deviation propagation analysis for different parallel connections is developed. • Form deviations and local surface deformations have non-negligible influence on assembly accuracy involving parallel connections. [ABSTRACT FROM AUTHOR]

When modeling sound waves in fluids it can be important to include the viscous and thermal losses originating from the fluids' interaction with boundaries. In the audible frequency range, the thickness of the boundary layers is between a micrometer and a millimeter. As such the viscous and thermal losses are important when simulating the properties of small acoustical devices such as e.g. hearing aids or transducers. However, the inclusion of viscous and thermal losses is a computationally demanding task as it requires a fine discretization of the boundary layer in order to fully capture the complicated physical phenomena happening on the microscale. Recently, there has been developments to ease the computational demands using both the Finite Element Method and the Boundary Element Method, by approximating the losses using the Boundary Layer Impedance (BLI) boundary condition. In this paper, we extend previous developments for multi-frequency analysis using the Reduced Order Series Expansion Boundary Element Method to handle the BLI condition. This model follows a two-step procedure: Using a series expansion to decrease the assembly time of the BEM matrices and a projection to reduce the overall memory consumption of the model. Results from two acoustic interior problems show that the model decreases the total computational time by around 96% while using less than 15% of the memory. For both test setups the limiting factor of the accuracy was the reduction and not the series expansion. [ABSTRACT FROM AUTHOR]

The sensitivity and optical properties of silver nanoprisms (triangular plates with round‐truncated corners) are investigated in this paper. Results of boundary element method simulations are compared with experimental results and literature data. Based on electron microscopy images of the synthesized nanoprisms, a single‐particle model is set up for simulations with three running parameters: edge length, thickness, and roundness (defined as the radius of the circumscribed circle divided by the edge length). These geometric parameters can be optimized during chemical synthesis to create sensors with improved sensitivity. The effect of biomolecular layers is also investigated. As a novel approach to improve the agreement between the simulated and experimentally measured extinction spectra, the single‐particle model is extended to consider the variation of the prisms' parameters in the form of distributions. The resulting extinction cross‐section spectra correspond well with the experimental data. The calculated bulk refractive index sensitivity is 670 nm/RIU (RIU stands for refractive index unit) for the single particle model (length = 150 nm, thickness = 10 nm, and roundness = 0.1), while (690 ± 5) nm/RIU for the extended model. The presented model and obtained relations between sensitivity and geometry can be effectively used to design and optimize the fabrication technologies for silver nanoprism‐based sensing applications. [ABSTRACT FROM AUTHOR]