Assuming linear theory, the phenomenon of scattering of waves by a circular arc shaped barrier with nonuniform porosity is studied. The water region is considered to be of infinite or finite depth. Based on a judicious application of Green’s integral theorem, the corresponding boundary value problem is reduced to a hypersingular integral equation of second kind. The boundary element method and the collocation method are adopted to solve the hypersingular integral equation, and we ensure a good matching of the solutions obtained by the two methods. The reflection coefficient and energy dissipation are evaluated by using the solution of the integral equation which is then studied graphically. Different choices of distributions of pores on the barrier are considered, and we observe that the nonuniform porosity of the barrier has significant effect on the reflected wave and the energy dissipation.

The boundary element method for the eddy current problem (BEM-ECP) was proposed in a number of papers and is applicable to important tasks such as the problem of inductive heating and transmission of electromagnetic energy. BEM-ECP requires the construction of a system of linear algebraic equations in which the matrix is inherently dense and is constructed out of element matrices. For the process of the element matrix computation, two cases are normally considered: far-field interaction and near-field interaction, because the construction of element matrices requires integration of a singular function. In this article, we suggest a transform that allows computing the matrix components of the near-singular interaction part while implementing only the single and double layer potentials. The previously suggested modified double layer potential (MDLP) can be integrated by means of this transform, which simplifies the program implementation of BEM-ECP significantly. Solving model problems, we analyse the drawbacks of the previously suggested approach. This analysis includes the proof of the MDLP singularity that makes the integration of this potential a rather difficult task without the help of our transform. The previously suggested approach does not work well with surfaces that are not smooth. Our approach does consider such cases, which is its main advantage. We demonstrate this on the model problems with known analytical solutions.

In engineering applications, it is pretty often to have domain heat source involved inside. This article proposes an approach using the boundary element method to study thermal stresses in 3D anisotropic solids when internal domain heat source is involved. As has been well noticed, thermal effect will give rise to a volume integral, where its direct evaluation will need domain discretization. This shall definitely destroy the most distinctive notion of the boundary element method that only boundary discretization is required. The present work presents an analytical transformation of the volume integral in the boundary integral equation due to the presence of internal volume heat source. For simplicity, distribution of the heat source is modeled by a quadratic function. When needed, the formulations can be further extended to treat higher-ordered volume heat sources. Indeed, the present work has completely restored the boundary discretization feature of the boundary element method for treating 3D anisotropic thermoelasticity involving volume heat source.

In engineering, it is quite often to have applications of the heat transfer of conduction having domain heat generation present inside. The paper aims to present boundary element formulations for analyzing the three-dimensional heat-conduction in dissimilarly bonded anisotropic media involving quadratic volume heat sources. In this paper, the additional volume integral present in the boundary integral equation is analytically transformed to the boundary surface for the volume heat sources modeled by quadratic functions. The technique of domain-mapping is employed to treat the three-dimensional anisotropic heat conduction in multiply adjoined media with proper interfacial conditions provided. For showing our successful implementation, a few example cases are analyzed with verification of independent analyses by the finite element method.

In engineering industries, composite laminates have been widely applied for various applications. This work presents an efficient analysis of the interlaminar stresses in three-dimensional thin layered anisotropic composites by the boundary element method (BEM). Due to the nearly singular integrals in the boundary integral equation, the conventional BEM approach cannot be applied to analyze the composite layers that are very thin. The present work employs the self-regularization scheme to analyze the interlaminar stresses in thin anisotropic composites. In the end, a few benchmark examples are presented to show the applicability of the present approach.

This research targets investigation of the internal elastic field near the boundaries of 3D anisotropic bodies by the boundary element method (BEM). This analysis appears to be most important, especially for the interest in the internal solutions near corners or crack tips, where structural failure is most likely to occur. Although the BEM is very efficient for analyzing the problem, nearly singular integration will arise when the internal point of interest stays near the boundary. The present work is to show how the self-regularized boundary integral equation (BIE) can be applied to the interior analysis for 3D generally anisotropic bodies. So far, to the authors' best knowledge, no implementation work has been reported in the literature for successfully treating the near boundary solutions in 3D generally anisotropic solids. In the end, a few benchmark examples are presented to demonstrate the veracity of the present approach for the interior BEM analysis of 3D anisotropic elasticity.

This paper is to present the treatment of internal thermoelastic stress analysis in 3D anisotropic bodies by the boundary element method (BEM). Fundamentally, thermal effects will give rise to an additional volume integral in the boundary integral equation (BIE). By applying the fundamental solutions represented by Fourier series, the volume integral has been analytically transformed to the boundary. For the present work, spatial differentiations of the integral equation are performed to give displacement gradients at internal points of interest. This differentiated integral equation is further implemented to perform thermoelastic stress analysis inside 3D anisotropic bodies. This analysis is particularly important in engineering applications when thermoelastic stresses concentrations are present inside the bodies. The present work is the first BEM implementation for this study by the transformed BIE. In the end, two benchmark examples are tested to demonstrate the applicability of the present BEM treatment.

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.

This paper presents a regularization scheme for the nearly singular integrals used for 3D elastostatic boundary element analysis. For the regularization process, the local projection coordinates of the source point are first located via an iteration procedure. For planar elements, the boundary integrals are analytically integrated by parts to smooth the drastic fluctuations of their integrands so that the regularized forms can be numerically integrated by any conventional schemes in an usual manner. The validity of the formulations is numerically tested using the Gauss Quadrature scheme. The test shows the accuracy is satisfactory for the distance ratio (distance: Element characteristic length) falling below micro-scale. To further demonstrate our successful implementation, a numerical example is studied with verifications compared with ANSYS analysis.

The present paper shows the applicability of the Dual Boundary Element Method to analyze plastic, visco-plastic and creep behavior in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate are analyzed. Special attention is taken when the discretization of the domain is done. In Fact, for the plasticity and viscoplasticity cases only the region susceptible to yielding was discretized, whereas, the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study this kind of non-linear problems. Results from the present formulation are compared to those of the well-established Finite Element Technique, and they are in good agreement. Important fracture mechanic parameters such as KI, KII, J- and C- integrals are also included. In general, the results, for the plastic, visco-plastic and creep cases, show that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased.

This paper presents a dynamic formulation of the boundary element method for stress and failure criterion analyses of anisotropic thin plates. The elastostatic fundamental solutions are used in the formulations and inertia terms are treated as body forces. The radial integration method (RIM) is used to obtain a boundary element formulationithout any domain integral for general anisotropic plate problems. In the RIM, the augmented thin plate spline is used as the approximation function. A formulation for transient analysis is implemented. The time integration is carried out using the Houbolt method. Integral equations for the second derivatives of deflection are developed and all derivatives of fundamental solutions are computed analytically. Only the boundary is discretized in the formulation. Numerical results show good agreement with results available in literature as well as finite element results.

This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically well-conditioned integral equation (noted GCSIE) proposed in [30] is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasi-optimal for Lipschitz polyhedron, the second being a CFIE-like formulation [14]. In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.

The reduced basis method is a model reduction technique yielding substantial savings ofcomputational time when a solution to a parametrized equation has to be computed for manyvalues of the parameter. Certification of the approximation is possible by means of ana posteriori error bound. Under appropriate assumptions, this errorbound is computed with an algorithm of complexity independent of the size of the fullproblem. In practice, the evaluation of the error bound can become very sensitive toround-off errors. We propose herein an explanation of this fact. A first remedy has beenproposed in [F. Casenave, Accurate a posteriori error evaluation in thereduced basis method. C. R. Math. Acad. Sci. Paris 350(2012) 539–542.]. Herein, we improve this remedy by proposing a new approximationof the error bound using the empirical interpolation method (EIM). This method achieveshigher levels of accuracy and requires potentially less precomputations than the usualformula. A version of the EIM stabilized with respect to round-off errors is also derived.The method is illustrated on a simple one-dimensional diffusion problem and athree-dimensional acoustic scattering problem solved by a boundary element method.

Nous étudions l’effet d’une couche mince rugueuse périodique déposée sur une structuresemi-infinie, dans le contexte Helmholtz bi-dimensionnel. Formellement, nous obtenons desconditions de transmission équivalentes à l’ordre 1, par des techniques de typehomogénéisation. Suivent alors la résolution du problème du milieu effectif éclairé parune onde plane, et le calcul de la fonction de Green effective ; le tout par analyse deFourier. Dans un deuxième temps, nous considérons le problème de diffraction par un objetpénétrable enfoui dans la structure recouverte par la couche rugueuse. Nous le résolvonspar la méthode des éléments finis de frontière, dans le milieu effectif. Des résultatsnumériques sont présentés. Enfin, le modèle effectif est validé dans le cas d’une coucheplate, et l’approximation de Born est utilisée pour tester le code des équationsintégrales.

In the conventional boundary element analysis, near-singularities are present in the associated boundary integral equation for problems involving ultra-thin media. For this case, any conventional numerical schemes will fail to yield proper values for the integrals. In this paper, the boundary integrals of the boundary element method for 3D potential problems are fully regularized by the technique of integration by parts under the local coordinate system. The fully regularized integrands are expressed as very explicit formulations that can be easily programmed into a computer code. Numerical tests carried out for a typical case have verified the accuracy of the approach for any orders of small distance between the source and the element under integration.

Since matrix compression has paved the way for discretizing the boundary integralequation formulations of electromagnetics scattering on very fine meshes, preconditionersfor the resulting linear systems have become key to efficient simulations. Operatorpreconditioning based on Calderón identities has proved to be a powerful device fordevising preconditioners. However, this is not possible for the usual first-kind boundaryformulations for electromagnetic scattering at general penetrable composite obstacles. Wepropose a new first-kind boundary integral equation formulation following the reasoningemployed in [X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zürich (2011)] foracoustic scattering. We call it multi-trace formulation, because itsunknowns are two pairs of traces on interfaces in the interior of the scatterer. We give acomprehensive analysis culminating in a proof of coercivity, and uniqueness and existenceof solution. We establish a Calderón identity for the multi-trace formulation, which formsthe foundation for operator preconditioning in the case of conforming Galerkin boundaryelement discretization.

When fluid passes a cavitator in the supercavitating flow, a supercavity forms behind the cavitator. Variation of the cavitator attack angle can influence theshape of the formed supercavity behind the cavitator. Consequently, it will affect the stability of supercavity behind the supercavitating cavitator with after body. In this study, a direct boundary element method (DBEM) is being formulated and numerically solved for3D unbounded potential flowspassing supercavitating bodies of revolution at different attack angles. In the analysis of potential flows passing supercavitating bodies at non-zero attack angles, a cavity closure model must be employed in order to close the mathematical formulationand guarantee the solution uniqueness. In the present study, we employ modified Riabouchinsky closure model. Since the location of the cavity surface is unknown at prior, an iterative scheme is used and for the first stage, an arbitrary cavity surface is assumed. The flow field is then solved and by an iterative process, the location of the cavity surface is corrected. Upon convergence, the exact boundary conditions are satisfied on the body-cavity boundary. A powerful CFD codeis developed to solve the 3D supercavitating flows behind all types of axisymmetric cavitators (such as disk, cone, etc) at zero and non-zero attack angles. The predictions of the CFD code are compared with those generated by verified existing data. The predictions of the code for supercavitating cones and disks seem to be excellent. Using the obtained data from CFD code, we investigate the supercavity shapesand corresponding stability at different attack angles with a fixed cavitation number.

The simple expansion chamber muffler is a base control device whose use is to attenuate sound power, and has been known for a long time. Some of the most compelling research has focused on the mufflers with a straight inlet and outlet. To date, a muffler with a right angle inlet has never been studied. Therefore, the purpose of this work is to analyze the simple expansion chamber muffler with a right angle inlet. The numerical results show a comparable agreement between the experiment and other numerical approaches. A discussion is also presented in this work on the muffler with a different radius to that of the inlet/outlet pipe, a different inlet part, etc. The result clearly shows that the attenuation of the muffler with a right angle inlet is better than that with a straight inlet at particular frequencies. In addition, the mufflers do not have any absorbent linings attached to the inside of them, unlike the right angle-inlets which do. However, the propagation of sound in the muffler with a right angle inlet can lead its sound power to be attenuated about 10 ∼ 40dB at those particular frequencies.

Due to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou [3] are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.