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In this paper, we study a plane-parallel flow of the homogeneous inviscid incompressible fluid. The close attention is paid to the free boundary deformation under the forces of self-gravitation and fluid rotation. The problem is studied numerically, i.e., we propose the numerical algorithm for the free boundary calculation. The algorithm is based on the boundary element method. Algorithm applications include calculation of thin cumulative jets. The second point of interest is numerical results validation. The computational accuracy is controlled through the conservation laws. In this paper, we provide the derivation of conservation laws of energy and angular momentum for the case of rotating flows. In addition, we analytically investigate dynamics of two-dimensional near-equilibrium shapes and check the consistency of the analytical and numerical results. [ABSTRACT FROM AUTHOR]

In this paper, with the consideration of thermal effects, eight equally important systems of constitutive laws generally used to describe anisotropic magneto-electro-elastic (MEE) materials are all considered. We provide simple mathematical relations to convert any one of the eight equation sets to the other seven sets. The equivalent reduced properties for two-dimensional analysis are obtained for eight possible different plane states of MEE solids. Complex variable Stroh formalism is used to derive the fundamental solution for two-dimensional thermo-MEE analysis. By using the identities of Stroh formalism, the complex form solution can be converted into real form. With the real form fundamental solution, the trouble induced by the multi-valued complex logarithmic function is circumvented and the extra line integral that appears in the thermal analysis of the boundary element method (BEM) can be eliminated. Thus, the temperature information inside the domain required by the extra line integral can be avoided, and a truly BEM for thermo-MEE analysis is achieved for the first time in the literature. The influence of heat source represented by the heat generation rate is also considered in our formulation. Verification of our solution is made by comparison with the analytical solution and the solution obtained by BEM using complex form solution with extra line integral as well as the solution by commercial finite element software ANSYS. [ABSTRACT FROM AUTHOR]

The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multipole boundary element method (FMBEM) based on the Burton–Miller formulation for 3-D acoustics is presented in this paper. In this adaptive FMBEM, the Burton–Miller formulation using a linear combination of the CBIE and hypersingular BIE (HBIE) is applied to overcome the non-uniqueness difficulties. The iterative solver generalized minimal residual (GMRES) and fast multipole method (FMM) are adopted to improve the overall computational efficiency. This adaptive FMBEM for acoustics is an extension of the adaptive FMBEM for 3-D potential problems developed by the authors recently. Several examples on large-scale acoustic radiation and scattering problems are presented in this paper which show that the developed adaptive FMBEM can be several times faster than the non-adaptive FMBEM while maintaining the accuracies of the BEM. [ABSTRACT FROM AUTHOR]

An adaptive fast multipole boundary element method (FMBEM) for general three-dimensional (3-D) potential problems is presented in this paper. This adaptive FMBEM uses an adaptive tree structure that can balance the multipole to local translations (M2L) and the direct evaluations of the near-field integrals, and thus can reduce the number of the more costly direct evaluations. Furthermore, the coefficients used in the preconditioner for the iterative solver (GMRES) are stored and used repeatedly in the direct evaluations of the near-field contributions. In this way, the computational efficiency of the adaptive FMBEM is improved significantly. The adaptive FMBEM can be applied to both the original FMBEM formulation and the new FMBEM with diagonal translations. Several numerical examples are presented to demonstrate the efficiency and accuracy of the adaptive FMBEM for studying large-scale 3-D potential problems. The adaptive FMBEM is found to be about 50% faster than the non-adaptive version of the new FMBEM in solving the model (with 558,000 elements) for porous materials studied in this paper. The computational efficiencies and accuracies of the FMBEM as compared with the finite element method (FEM) are also studied using a heat-sink model. It is found that the adaptive FMBEM is especially advantageous in modeling problems with complicated domains for which free meshes with much more finite elements would be needed with the FEM. [ABSTRACT FROM AUTHOR]

Thin components, such as baffles, extended inlet/outlet tubes, and internal connecting tubes, are commonly used in reactive mufflers for cancelation of sound at particular frequency peaks. To provide additional absorption effects at higher frequencies, porous sound absorbing materials may be used on the muffler interior wall surface or on any internal thin components. If the sound absorbing material is backed by a rigid surface, it is usually modeled by the local normal impedance approach. The local impedance modeling on the interior wall surface is straightforward and has been extensively used in the boundary element method, in which the boundary surface is just moved forward to the contact surface between the lining and air. On the other hand, the local impedance modeling on any internal thin components is relatively rare. This paper first presents a direct mixed-body boundary element formulation for a thin body covered by local impedance on either side or both sides of the thin body. The local impedance can be from the lining material itself, or from the lining material plus a protective perforated metal cover. Several test cases with experimental comparison are presented in this paper. [ABSTRACT FROM AUTHOR]

Predicting the load–settlement and load–transfer behaviors of rammed aggregate piers are important aspects of design. Use of advanced engineering models, however, can be complex involving uncertainty in selection of nonlinear constitutive model parameters for the aggregate and surrounding matrix soils and in selection of in situ stress fields. For purposes of simpler design calculations, this paper uses the closed-form approximate solution and the boundary-element method using both elastic (i.e., neglecting interface slip) and elastic–plastic soil–pier interface (i.e., considering interface slip) to predict load–settlement and load–transfer for rammed aggregate piers. Unlike previous studies that evaluate load–settlement and load–transfer for stiff, slender piles (e.g., concrete and steel piles) or fully penetrating granular piles, this paper focuses on floating rammed aggregate piers having slenderness ratios (L/D) of 3–10 and pier–soil stiffness ratios (Ep/Es) of 5–80. Predictions of load–settlement and load–transfer as a function of depth are compared to three full-scale instrumented load tests. Based on the calibrated models, equations for predicting load–settlement response and load–transfer as functions of Ep/Es, and L/D are presented with example calculations. [ABSTRACT FROM AUTHOR]

The paper deals with inverse thermoelasticity problems. A general, robust, and numerically efficient technique, for retrieving the multi-dimensional, highly varying distributions of boundary conditions is presented. In the class of considered inverse problems, both input data and sought-for quantities are usually specified at the domain boundary, only. As a sequence of forward sub-solutions underlies the inverse analysis, the numerical method of choice for solving the field problem is the boundary element method (BEM). The derived inverse technique is capable of retrieving boundary condition distributions in steady state and transient problems. The accuracy and stability of the algorithm are verified by considering problems involving constant, functionally graded, and temperature dependent material properties. Strain components and temperatures, subject to uncertainties, are used as input data. Presented numerical examples show that the method is capable of reconstructing mechanical and thermal loads with reasonable accuracy. [ABSTRACT FROM AUTHOR]

Three-dimensional (3-D) capacitance-extraction algorithms are important due to their high accuracy. However, the current 3-D algorithms are slow and thus their application is limited. In this paper, we present a novel method to significantly speed up capacitance-extraction algorithms based on boundary element methods (BEMs), under uniform and multiple dielectrics. The n × n coefficient matrix in the BEM is dense, even when approximated with the fast multipole method or hierarchical-refinement method, where n is the number of panels needed to discretize the conductor surfaces and dielectric interfaces. As a result, effective preconditioners are hard to obtain and iterative solvers converge slowly. In this paper, we introduce a linear transformation to convert the n × n dense coefficient matrix into a sparse matrix with O(n) nonzero entries, and then use incomplete factorization to produce a very effective preconditioner. For the k × k bus-crossing benchmark, our method requires at most four iterations, whereas previous best methods such as FastCap and HiCap require 10-20 iterations. As a result, our algorithm is up to 70 times faster than FastCap and up to 2 times faster than HiCap on these benchmarks. Additional experiments illustrate that our method consistently outperforms previous best methods by a large magnitude on complex industrial problems with multiple dielectrics. [ABSTRACT FROM AUTHOR]

This paper deals with three-dimensional electromagnetic scattering problems. The usual integral equations corresponding to electromagnetic scattering problems in general have the inconvenience of resonant solutions. Mautz and Harrington have derived an integral equation without such inconvenience. However, there are two arbitrary parameters contained in this integral equation. Further, when the integral equation is solved by numerical analysis based on the boundary element method, both expansion functions and weighting functions must be introduced. Although little flexibility exists in the selection of the expansion functions, two selection branches exist for the weighting functions. Hence, when the three-dimensional electromagnetic scattering problem is specifically analyzed numerically, selection of the parameters and the weight functions becomes important. Their selection should be carried out according to a reasonable evaluation standard. In the present paper, the condition number is used as the evaluation standard. It is shown which selection is the best among these choices. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(12): 61–68, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10149 [ABSTRACT FROM AUTHOR]

This paper presents a boundary element method for calculating the sound pressure level on and above a ground-board placed on an infinite ground plane with constant impedance. This method uses the Green's function for the Helmholtz equation in a half-space bounded by an infinite impedance plane and therefore avoids the complications which occur when modeling the ground as a finite impedance plane (which results in diffraction from the edges of the ground plane). Two formulations are presented: the first one models a finite thickness ground-board, whilst the second one models a zero-thickness ground-board with the upper surface coplanar with the ground plane. The method is validated against an equivalent finite element method simulation and example calculations are presented for typical ground-board designs used for outdoor noise measurements on different ground impedance planes and incidence angles. It is shown that the sound pressure level on the upper surface of a ground-board placed on a non-rigid ground can vary significantly and that this variation is dependant on the ground impedance, angle of incidence and frequency. These findings are consistent with previous investigations and highlight the fact that noise measurements made using ground-board mounted microphones on a non-rigid ground are dependant on the impedance of the surrounding ground surface. The method presented in this paper could be used to develop corrections to straightforwardly account for this effect. [ABSTRACT FROM AUTHOR]

This is the preface of a special issue dedicated to the memory of Francisco Javier Sayas who passed away on April 2, 2019. The articles reflect Sayas' main research interests in the numerical analysis of partial differential equations, containing contributions on the scattering and propagation of acoustic and electromagnetic waves, and the analysis of discontinuous Galerkin schemes, boundary element methods, and coupled schemes. We discuss the main contributions of Sayas and give an overview of the results covered by this special issue. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian 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.)

A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM. [ABSTRACT FROM AUTHOR]

This paper introduces a new system that utilizes the advantages of boundary element analysis in structural engineering applications. A standardized building information model (BIM) for automated structural analysis and design of reinforced concrete plates based on the boundary element method (BEM) is proposed. Based on the model view definition approach, BIM standards are presented for the preprocessing and postprocessing of BEM analysis. Furthermore, standards are proposed for automated structural design of structural slab and beam elements based on the BEM analysis results. For each of the BIM components, standards are provided for the object structure, data flow, and graphical user interface (GUI). The extensibility of the software and applicability for a wide range of research and practical applications are considered in all the proposed standards. The system created can act as the basis for structural analysis and design of building floor and foundation problems. Object-oriented programming is used to implement the standards in a prototype. The prototype was verified by application to the solution of practical structural engineering problems. The performance of the proposed system is evaluated in terms of the modeling and the processing time required to analyze typical structural engineering applications using the prototype. [ABSTRACT FROM AUTHOR]

This paper is devoted to a Robin coefficient identification problem for one-dimensional time-fractional diffusion equation. Based on the separation of variables, we transform the identification problem into a nonlinear Volterra integral equation of the first kind with the Robin coefficient and the Dirichlet data on a part of boundary as unknown functions. Then, we use a boundary element method to discrete the first kind integral equation and obtain a nonlinear system of algebraic equations. The conjugate gradient method is applied to solve a regularized optimization problem and finally, we obtain a suitable regularized approximation to the Robin coefficient. Three numerical examples are provided to show the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

In several electromagnetic applications, field quantities are confined in layers that are thin with respect to other geometrical dimensions. The numerical solution of these phenomena has led to the development of special formulations. Among these, the surface impedance boundary conditions (SIBCs) have been extensively investigated in the past decades, often coupling them to other techniques for the analysis of volumes, such as the finite-element or boundary element methods. In this paper, the SIBCs are presented by the light of finite formulation and extended to include the considered magnetic nonlinearity. [ABSTRACT FROM AUTHOR]

In this paper, the hybrid finite-element method (FEM) singular Dirichlet boundary condition iteration method, already developed for 2-D skin-effect problems, is extended to the 3-D solution of time-harmonic eddy current problems. The method is similar to the well-known FEM-boundary-element method (BEM), but it assumes a Dirichlet boundary condition on the truncation boundary instead of a Neumann one. Shorter solving times are obtained with respect to FEM-BEM. [ABSTRACT FROM AUTHOR]

This paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains. Design/methodology/approach – A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach. Findings – Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems. Originality/value – An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis. [ABSTRACT FROM AUTHOR]

The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high-frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high-frequency solution asymptotics. In this paper, we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction phase functions combined with mesh refinement. We develop our methodology in the context of scattering by a class of sound-soft non-convex polygons, presenting a rigorous numerical analysis (supported by numerical results) which proves the effectiveness of our HNA approximation space at high frequencies. Our analysis is based on a study of certain approximation properties of the Fresnel integral and related functions, which govern the shadow boundary behaviour. [ABSTRACT FROM AUTHOR]

Dual techniques have been used in many engineering papers to deal with singularity and ill-conditioning of the boundary element method (BEM). In the first part of the two-part article, our efforts were focused on studying the theoretical aspects of this problem, including the analysis of errors and the study of stability. We provided the theoretical analysis for Laplace equation in elliptic domains with elliptic holes. To bypass the degenerate scales of Dirichlet problems, the second and the first kinds of the null field methods (NFM) are used for the exterior and the interior boundaries, simultaneously. This approach is called the dual null field method (DNFM). This paper is the second part of the study. Numerical results for degenerate models of an elliptic domain with one elliptic hole at $a + b = 2$ are carried out to verify the theoretical analysis obtained. The collocation Trefftz method (CTM) is also designed for comparisons. Both the DNFM and the CTM can provide excellent numerical performances. The convergence rates are the same but the stability of CTM is excellent and can achieve the constant condition numbers, Cond = $O(1)$.

Accurate evaluation of domain integrals is crucial for the overall accuracy of the boundary element method (BEM), particularly when dealing with dynamic problems and those involving body forces. The radial integration method (RIM) is a well-established and effective technique for computing domain integrals in boundary element analysis. When calculating domain integrals in transient problems, the integrand of time-dependent kernels tends to near-singularity and may oscillate rapidly as the time step decreases. To overcome this issue, an efficient non-linear coordinate transformation, combined with an element subdivision technique, is presented in this paper to enhance the computational accuracy of the domain integrals. Significant improvement in the computational accuracy of domain integrals, particularly with small time steps, can be achieved. Several representative examples are presented and discussed to demonstrate the accuracy and efficiency of the present method. [ABSTRACT FROM AUTHOR]

The use of boundary elements in two-dimensional acoustic analysis is presented in this study, along with a detailed explanation of how to derive the final discrete equations from the fundamental fluctuation equations. In order to overcome the fictitious eigenfrequency problem that might arise during the examination of the external sound field, this work employs the Burton-Miller approach. Additionally, this work uses the Taylor expansion to extract the frequency-dependent component from the BEM function, which speeds up the computation and removes the frequency dependency of the system coefficient matrix. The effect of the radiated acoustic field generated by underwater structures' on thin-walled structures such as submarines and ships is inspected in this work. Numerical examples verify the accuracy of the proposed method and the efficiency improvement. [ABSTRACT FROM AUTHOR]

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method. [ABSTRACT FROM AUTHOR]

An efficient boundary element method (BEM) formulation for three-dimensional elastoplasticity is presented in this paper. The BEM formulation for nonlinear problems requires discretization of the surface as well as part of the volume. In this paper nine-noded quadrilateral elements are used for modelling the surface and 27-noded brick elements for the volume. Particular attention is paid to the accurate evaluation of the Cauchy principal value volume integrals appearing in the interior stress calculations. An explicit initial strain formulation is used to satisfy the non-linearity. The accuracy of the proposed method is demonstrated by solving a number of benchmark problems. [ABSTRACT FROM AUTHOR]

By using Cauchy’s integral formula of analytical complex function and the third-order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi-infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method. [ABSTRACT FROM AUTHOR]

This paper diseusses the general principle of finding the cut-off frequencies in two-dielectric layered waveguides by using the boundary element method, based on the fundamental solution of a two dimensional Helmholtz equation. In terms of the formulae given in the paper, some numerical results are obtained for two commonly used configurations. The fimal results show that the method is of an appreciable precision. [ABSTRACT FROM AUTHOR]

The unsteady problems of anisotropic quadratically graded materials are discussed in this paper. Numerical solutions to a diffusion-convection equation of quadratically varying coefficients are sought by using a combined Laplace transform and boundary element method. First, the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation can consequently be written in a pure boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. Some examples are considered to verify the analysis and also to show the accuracy, efficiency and consistency of the numerical procedure. The combined Laplace transform and boundary element method is easy to implement for solving unsteady diffusion-convection problems of anisotropic quadratically graded media. [ABSTRACT FROM AUTHOR]

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplacetransformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation. [ABSTRACT FROM AUTHOR]

"How long is the coast of Britain?" was the question stated by Mandelbrot. Using smaller and smaller rulers the coast length limits to infinity. If this logic is applied to the fractal heat sink geometry, infinite cooling capacity should be obtained using fractals with mathematically infinite surface area. The aim of this article is to check this idea using Richardson extrapolation of numerical simulation results varying the fractal element length from one to zero. As expected, the extrapolated cooling capacity has a noninfinite limit. The presented fractal heat sink geometry is non-competitive to the straight fins. [ABSTRACT FROM AUTHOR]

This paper proposes a mechanics-based method for calculating the elastic-plastic contact behaviors in tolerance analysis. Specifically, form deviations of geometric features are modeled based on the concept of Skin Model Shapes (SMS). Elastic-plastic contact behaviors are calculated by an improved Boundary Element Method (BEM). The calculation accuracy and efficiency are compared with the Finite Element Method (FEM). The simulation results indicate that the proposed method has good calculation accuracy and significantly improves the calculation efficiency at the same time, which provides a feasible method to consider the effects of elastic-plastic contact behaviors in tolerance analysis. [ABSTRACT FROM AUTHOR]

In this paper, we study boundary element method with high order impedance bound- ary conditions (HOIBC) to solve Maxwell's equations. The unknowns are electric and magnetic currents J and M: We propose several formulations and study the existence and uniqueness of the solution. Then, we discretize these formulations with a finite element method based on Lagrange elements. We give numerical tests of the HOIBC solution. [ABSTRACT FROM AUTHOR]

Love waves have great potential in geological inspection and ultrasonic nondestructive testing for near-surface underground characteristics. A thorough and effective utilization of the Love wave requires a better understanding of its scattering phenomenon. The paper studies the problem of Love wave scattering by cavity-like flaws on the interface between the upper layer and the lower half-plane. For the forward analysis, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns, which can effectively eliminate fictitious reflections introduced by model truncation. For inverse analysis, we propose a quantitative reconstruction procedure for the flaw shape using reflection coefficients of the first-order Love wave. By theoretical deduction, it can be proved that the cavity's geometric shape is approximately expressed as an inverse spatial Fourier transform of far-field reflection coefficients in the wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and high consistency is shown between the reconstructed flaw images and the geometric characteristics of the actual flaws. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an efficient topology optimization procedure for exterior acoustic‐structure interaction problems, in which the coupled systems are formulated by the boundary element method (BEM) and the finite element method (FEM). So far, the topology optimization based on the coupled FEM‐BEM still faces several issues needed to be addressed, especially the efficient design sensitivity analysis for the coupled systems. In this work, we contribute to these issues in two main aspects. Firstly, the adjoint variable method (AVM) formulations are derived for sensitivity analysis of arbitrary objective function, and the feedback coupling between the structural and acoustic domains are taken into consideration in the sensitivity analysis. Secondly, in addition to the application of fast multipole method (FMM) in the acoustic BEM response analysis, the FMM is now updated to adapt to the arising different multiplications in the AVM equations. These accelerations save considerable computing time and memory. Numerical tests show that the developed approach permits its application to large‐scale problems. Finally, some basic observations for the optimized designs are drawn from the numerical investigations. [ABSTRACT FROM AUTHOR]

• Hypersingular heat flux interface integral equation is derived. • Interface fluxes are calculated for multi-medium heat transfer analysis using IIBEM. • IIBEM is a promising BEM for solving complicated practical engineering problems. In this paper, based on a direct method for evaluating hypersingular integrals, a heat flux interface integral equation is presented to calculate the hypersingular interface heat fluxes in multi-medium heat transfer analysis by using the interface integral boundary element method (IIBEM). The recently proposed IIBEM has a significant advantage of a single integral equation method for solving multi-medium problems, which makes up for the lack of boundary integral equations to solve multi-medium problems. Compared with conventional multi-domain boundary element method (MDBEM), the IIBEM is more efficient in input data preparation, program coding and computational time. However, a big issue encountered is the determination of interface heat fluxes in multi-medium heat transfer analysis through using IIBEM, since the derived flux interface integral equation involves hypersingular integrals on the interface, and no additional information can be utilized to recover the heat fluxes by using the in-direct "traction-recovery" methods. In this paper, based on a new efficient direct method for numerical evaluation of high order singular curved boundary integrals, the hypersingularities in flux interface integral equation are precisely evaluated, and based on the successful implementation of flux hypersingular integral equation, the interface heat fluxes are firstly calculated in the multi-medium heat transfer analysis by using IIBEM. Several two- and three-dimensional numerical examples are given to validate the correctness of the presented method. [ABSTRACT FROM AUTHOR]

Abstract This paper presented a new transformation technique from multi-domain integrals into equivalent boundary integrals, by utilizing this technique, an efficient meshless interface integral boundary element method (meshless IIBEM) is proposed for solving heat conduction in multi-non-homogeneous media with multiple heat sources. Firstly, the interface integral equation for multi-medium heat conduction is derived, considering the varying properties of thermal conductivities. Compared with conventional multi-domain boundary element method (MDBEM), the presented interface integral equation method is more efficient in data preparing, program coding and computational efficiency. However, a big issue is encountered to develop a meshless IIBEM without internal cells for solving heat conduction in multi-non-homogeneous media, since the commonly used transformation technique from single domain integrals into equivalent boundary ones cannot be directly employed to transform the multi-domain integral appeared in the interface integral equation presented in this paper. A new multi-domain transformation technique is presented in this paper by improving the conventional robust radial integration method (RIM) through using a combination approach with a powerful domain decomposition technique. Using this combination approach, the multi-domain integrals are transformed into a series outer boundary and interface integrals, which can be evaluated precisely through the discretization and integration over the outer boundary and interface elements. A high-precision single integral equation method characterized as meshless IIBEM is developed to solve heat conduction in multi-non-homogeneous media with or without multiple heat sources. Numerical examples are given to verify the correctness of the newly proposed method. [ABSTRACT FROM AUTHOR]

Highlights • This paper highlights the development of a BEM model for the frictional hysteresis behavior at the adhesive contact of two surfaces. • The start of gross sliding regime is controlled by the contact repulsive force and not the external normal force. • Adhesion increases the contact repulsive force and consequently, the static friction force. • Both adhesion and roughness increase the pre-sliding distance, exclusively. • The combined effect of adhesion and roughness on the pre-sliding distance is not cumulative but symbiotic. Abstract Friction hysteresis results from an oscillating friction force at a contact interface. At nano-scale, this phenomenon is affected by the roughness of the contact interface and adhesion. In nanotribology, therefore, it is highly desirable to understand and predict this behavior to estimate the energy loss and possible wear. This paper presents a boundary element model (BEM) for the adhesive friction hysteresis contact at the interface of two bodies of arbitrary geometry. In the model, adhesion is represented by means of a Dugdale approximation of the total work of adhesion at local areas with a very small gap between the two surfaces. The amplitude of the oscillating tangential displacement is very small compared to the contact area which means that the interface does not experience gross-sliding between the two surfaces (the contact remains in the pre-sliding state). Hence, the frictional contact is divided into sticking and slipping regions, defined based on the local values for shear stress and normal pressure, and the rate of relative displacement. The model is first verified by comparing the numerical and analytical (Mindlin theory) solutions for the contact of a smooth ball and a flat of identical materials under a fixed normal force and an oscillating friction force. Then, the problem is solved at the smooth interface between a rigid ball and an elastic flat for various values of the work of adhesion. It is shown that as the work of adhesion increases, both static friction force and pre-sliding displacement increase due to the increase in the contact repulsive force. In addition, the rough interface between a glass ball against a silicon wafer and a DLC (Diamond-Like Carbon) coating is considered. Since adhesion depends on the interface roughness, the corresponding contact repulsive force is different for these interfaces. For the smoother interface, a larger contact repulsive force and consequently, a larger static friction force and pre-sliding displacement are obtained. [ABSTRACT FROM AUTHOR]

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace's equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller's equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised. [ABSTRACT FROM AUTHOR]

In this paper we develop a new class of semidiscrete Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to the asymptotic behavior of the solution through a certain direct sum of appropriate function spaces weighted by the oscillations in the incident field of radiation. Specifically, the function spaces in the illuminated/shadow regions and the shadow boundaries are simply algebraic polynomials, whereas those in the transition regions are generated utilizing novel, yet simple, frequency-dependent changes of variables perfectly matched with the boundary layers of the amplitude in these regions. We rigorously verify for compact, smooth and strictly convex obstacles that, with increasing wavenumber k, these methods require, for any ε > 0, only an |$\mathscr{O}\left (k^{\varepsilon } \right)$| increase in the number of degrees of freedom (DoF) to maintain any given accuracy independent on frequency. These theoretical results are confirmed by numerical tests that show that, for sufficiently large DoF, the error tends to decrease with increasing wavenumber k. [ABSTRACT FROM AUTHOR]

Based on the wave radiation and diffraction theory, this paper investigates a new type breakwater with upper arc-shaped plate by using the boundary element method (BEM). By comparing with other three designs of plate type breakwater (lower arc-shaped plate, single horizontal plate and double horizontal plate), this new type breakwater has been proved more effective. The wave exiting force, transmission and reflection coefficients are analyzed and discussed. In order to reveal the wave elimination mechanism of this type of breakwater, the velocity field around the breakwater is obtained. It is shown that: (1) The sway exciting force is minimal. (2) When the ratio of the submergence and wave amplitude is 0.05, the wave elimination effect will increase by 50% compared with other three types of breakwater. (3) The obvious backflow is found above the plate in the velocity field analysis. [ABSTRACT FROM AUTHOR]

This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon (including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics (wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency (η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady‐state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results. [ABSTRACT FROM AUTHOR]

The present paper is dedicated to numerical solving of three dimensional boundary-value problems in poroviscoelastic formulation. The poroviscoelastic formulation is treated as a combination of Biot's theory of poroelasticity and elastic-viscoelastic correspondence principle. Kelvin-Voigt model and Standard linear solid model are employed in order to describe viscoelastic media properties. Boundary element method and boundary integral equation method are applied to obtain Laplace domain solution of boundary-value problem. Modified Durbin's algorithm of numerical inversion of Laplace transform is used to perform solutions in time domain. Research is also dedicated to development of numerical modelling technique based on Boundary Element Method (BEM) in Laplace domain for solution of three dimensional transient poroviscoelastic problems. A problem of the three-dimensional poroviscoelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading at another is considered. Viscosity parameter influence on dynamic responses of displacements and tractions is studied. [ABSTRACT FROM AUTHOR]