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For the simulation of acoustic-structure interaction problems, the coupled field equations must be solved. The structure is commonly discretized using finite elements, whereas for the acoustic field the boundary element method (BEM) is favorable. A mortar BEM-FEM coupling algorithm is developed that allows the combination of non-conforming meshes. The high flexibility for the choice of discretizations offers a high efficiency, since specialized shape functions and adaptive mesh refinement can be used in the subdomains. The mortar coupling algorithm yields a saddle point problem that is solved using a preconditioned inexact Uzawa algorithm. The iterative solver enables the use of the fast multipole BEM and thus coupled simulations on large boundary element models. [ABSTRACT FROM AUTHOR]

In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper deals with the rectangular tensile sheet with symmetric double edge notch cracks. Such a crack problem is called an edge notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method), two edge notch models are analyzed in detail. By changing the geometrical forms and parameters of the edge notch, and by comparing the stress intensity factors (SIFs) of the edge notch crack problem with those of the double edge cracked plate tension specimen (DECT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the edge notch on the SIFs of the DECT specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the DECT specimen So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the DECT specimen. [ABSTRACT FROM AUTHOR]

A new extended integral equation is introduced for three-dimensional electromagnetic scattering problems, and a method is proposed for analyzing this extended integral equation numerically by means of a new boundary element method in which vector shape functions are used. In the conventional boundary integral equation, there is no unique solution to the electromagnetic wave at the angular frequency coinciding with the one characteristic to the system. Several methods are proposed for alleviating this problem; however, each has its own problem. This paper proposes an extended integral equation in which the observation points are allocated on a closed surface in- side the scatterer adjacent to the scatterer surface. Not only does the extended integral equation proposed in this paper a frequencies, hut also it overcomes various deficiencies of the conventional integral equation method. in this paper, the extended integral equation for a three-dimensional perfectly conducting scatterer is derived first and its uniqueness of the solution is proven. Further, for practical examples, this extended integral equation is solved numerically by means of the new boundary element method using vector shape functions. The uniqueness and accuracy of the solution are studied numerically. [ABSTRACT FROM AUTHOR]

A new numerical method is proposed for the analysis of the electromagnetic scattering problem by an inhomogeneous scatterer. Although the finite-element method and the boundary-element method have a high degree of generality, several difficulties occur i they are applied to the electromagnetic scattering problem. First, in the case of the finite-element method, treatment of inhomogeneous regions is easy, but that of an open region is difficult. Hence, the finite-element method is not suited for the scattering problems in which open regions such as the exterior of the scattering body need to be treated. On the other hand, in the case of the boundary-element method, treatment of the open region is easy but that of inhomogeneous regions is difficult. In this paper, a new combination of the finite-element and boundary-element methods is proposed in which the advantages of both are incorporated. The new combined method proposed in this paper solves several difficulties of the conventional combination method by means of the boundary-element method using the extended integral equation for which observation points are placed on the closed loop inside the scatterer. Numerical computations are carried out for a number of examples so that it is proven that the present method can be applied to scatterers with arbitrary shapes and arbitrary permiltivity distributions. Further, it is shown that in addition to the far field, the near field can be found. [ABSTRACT FROM AUTHOR]

The paper deals with the concept of magnetic current loop as a source model for finite thin-wire antennas. The formulation is based on the Pocklington integro-differential equation with reduced kernel, which is handled by means of various numerical techniques, mostly using the Galerkin-Bubnov variant of Indirect Boundary Element Method. Extensive numerical experiments were carried out on various dipole and monopole antennas using different sources (delta gap, magnetic frill, and magnetic current loop), and results for input admittance are compared with measured data. The magnetic current loop source ensures accurate solution for input admittance. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem. A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The solution of the frictionless contact/detachment problem was performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a study of primal and dual Steklov‐Poincaré approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of the solution is possible by postprocessing Ritz elements. Assessments are provided on a 3D mechanical problem. [ABSTRACT FROM AUTHOR]

This paper describes a large-scale magnetic field analysis by means of the hybrid finite element-boundary element (FE-BE) method. The hybrid FE-BE method is well-suited for solving open electromagnetic field problems that comprise movement, nonlinear media, and eddy current. In general, however, large memory and computational costs are required due to the dense blocks in the system matrix generated by the BE part of the hybrid formulation. In order to overcome the above difficulties, we introduce the fast multipole method (FMM) to the hybrid FE-BE formulation developed by ourselves. Furthermore, we propose a novel preconditioning technique suitable for the hybrid FE-BE method with the FMM. Some numerical results that demonstrate the effectiveness of the proposed approach are also presented. ©2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(1): 73–80, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20508 [ABSTRACT FROM AUTHOR]

In this paper, the integral equations (guided-mode extracted integral equations) of a near field optics CAD proposed earlier are extended for a two-dimensional near field optics circuit using an aperture probe coated with metal. As a specific example, an aperture-probe manipulator with a two-dimensional configuration is chosen. In particular, a derivation of the boundary integral equation is described in detail for the incident TM mode, in which a simple extension of the previous results is not possible. The validity and effectiveness of the proposed integral equations are demonstrated by simulation using the boundary element method. It is shown that an attractive force directed toward the aperture is exerted on an infinitesimal dielectric cylinder placed near the aperture. The characteristics of the aperture probe coated with metal are compared in detail with those of the uncoated probe reported earlier. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(9): 32–41, 2000 [ABSTRACT FROM AUTHOR]

The article presents a paper, which formulates a general problem of electromagnetic wave analysis to a boundary element problem. The case of perfect conductors is also discussed. The boundary element method is applied to the analysis of cylindrical and rectangular shaped cavities. Results obtained by the said method are compared with those by the analytical method. The most typical boundary conditions for perfect conductor are expressed as Hn - Et1 - Et2 - 0. It is very useful that in the proposed method the boundary conditions can be expressed in terms of these quantities when using the finite element boundary element hybrid method.

The problem of scattering of TE and TM waves by a grating made of finitely many cylinders is analyzed by means of the boundary element method. The number of unknowns for the matrix equation obtained by discretizing the integral equation for the surface current increases in proportion to the number of cylinders. The total number of components of the coefficient matrix often exceeds the capacity of the computer. In such cases, it is not possible to use the direct solution based on the inverse matrix. Hence, an iterative method is used. In this paper, the conjugate gradient method is used as such an iterative method. In recognition of the fact that the coefficient matrix of the matrix equation is a block Toeplitz matrix, it is extended to a block circulant matrix to which the fast Fourier transform (FFT) is applied for reduction of the computer capacitance requirement and the computation time. As a numerical example, the current distributions induced on a grating made of about 30 circular cylinders are computed. It is shown that the edge effect is particularly large if an anomaly occurs. [ABSTRACT FROM AUTHOR]

The boundary element method,introduced originally as a numerical technique for solution of potential problems and structural engineering problems, has been applied to numerous electromagnetic problems, most of which are in the area of boundary value problems. However, little has been reported on the applications to eigenvalue problems such as analysis of the propagation characteristics of a transmission line. In this paper, the boundary element method is applied for the eigenmode analysis of a dielectric waveguide to demonstrate the usefulness of the method for eigenvalue problems. From the numerical analysis nonphysical (spurious) solutions similar to the case of finite element method are found to appear. Since the appearance of such spurious solutions significantly damages the usefulness of the method, it is important to develop a procedure to eliminate them. Spurious solutions are studied to determine their cause, and an improved boundary element method is proposed that does not admit them. [ABSTRACT FROM AUTHOR]

In this paper, the interaction between two immiscible fluids with a finite mobility ratio is investigated numerically within a Hele-Shaw cell. Fingering instabilities initiated at the interface between a low-viscosity fluid and a high-viscosity fluid are analysed at varying capillary numbers and mobility ratios using a finite mobility ratio model. The present work is motivated by the possible development of interfacial instabilities that can occur in porous media during the process of C O2 sequestration but does not pretend to analyse this complex problem. Instead, we present a detailed study of the analogous problem occurring in a Hele-Shaw cell, giving indications of possible plume patterns that can develop during the C O2 injection. The numerical scheme utilises a boundary element method in which the normal velocity at the interface of the two fluids is directly computed through the evaluation of a hypersingular integral. The boundary integral equation is solved using a Neumann convergent series with cubic B-Spline boundary discretisation, exhibiting sixth-order spatial convergence. The convergent series allows the long-term nonlinear dynamics of growing viscous fingers to be explored accurately and efficiently. Simulations in low-mobility ratio regimes reveal large differences in fingering patterns compared with those predicted by previous high-mobility ratio models. Most significantly, classical finger shielding between competing fingers is inhibited. Secondary fingers can possess significant velocity, allowing greater interaction with primary fingers compared with high-mobility ratio flows. Eventually, this interaction can lead to base thinning and the breaking of fingers into separate bubbles. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The paper presents closed-form solutions for stress and displacement influence functions for stress discontinuity (SD) and displacement discontinuity (DD) elements, for a two-dimensional plane-strain elastic, transversely anisotropic medium. The solutions for SD elements are based on Kelvin's problem and for DD elements on the concept of dipoles. Stress and displacement influence functions are derived for the following elements: constant SD, linear SD, constant DD, linear DD, square root DD, parabolic DD, constant DD surface, and linear DD surface elements. The formulations are incorporated into FROCK, a hybridized boundary element method code, and are validated by providing comparisons between the results from FROCK and the finite element code ABAQUS. A limited parametric analysis shows the effects of slight anisotropy on the stress field around the tip of a crack and of the orientation of the crack with respect to the axes of elastic symmetry. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY We discuss explicit coupling schemes for fluid-structure interaction problems where the added mass effect is important. In this paper, we show the close relation between coupling schemes by using Nitsche's method and a Robin-Robin type coupling. In the latter case, the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators. Recalling the explicit method proposed in Comput. Methods Appl. Mech. Engrg. 198(5-8):766-784, 2009, we make the observation that this scheme is stable under a hyperbolic type CFL condition, but that optimal accuracy imposes a parabolic type CFL conditions because of the splitting error. Two strategies to enhance the accuracy of the coupling scheme under the hyperbolic CFL-condition are suggested, one using extrapolation and defect-correction and one using a penalty-free non-symmetric Nitsche method. Finally, we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper investigates the two-dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady-state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi-region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to calculate and develop equations for crack-surface displacements for two-symmetric cracks emanating from a circular hole in an infinite plate for use in strip-yield crack-closure models. In particular, the displacements were determined under two loading conditions: (1) remote applied stress and (2) uniform stress applied to a segment of the crack surface (partially loaded crack). The displacements were calculated by an integral-equation method based on accurate stress-intensity factor equations for concentrated forces applied to the crack surfaces and those for remote applied stress or for a partially loaded crack surface. A boundary-element code was also used to calculate crack-surface displacements for some selected cases. Comparisons made with crack-surface displacement equations previously developed for the same crack configuration and loading showed significant differences near the location where the crack intersected the hole surface. However, the previous equations were fairly accurate near the crack-tip location. Herein an improved crack-surface displacement equation was developed for the case of remote applied stress. For the partially loaded crack case, only numerical comparisons were made between the previous equations and numerical integration. A rapid algorithm, based on the integral-equation method, was developed to calculate these displacements. Because cracks emanating from a hole are quite common in the aerospace industry, accurate displacement solutions are crucial for improving life-prediction methods based on the strip-yield crack-closure models. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional numerical procedure based on the boundary integral equations to model acoustic waves of finite-amplitude. The analysis is performed in the frequency domain. By applying the perturbation technique up to the second-order term, the governing differential equations are written as a system of two Helmholtz equations, one is homogeneous and the other one is inhomogeneous. Both are transformed into integral equations, which can be numerically solved without domain discretization by the use of the dual reciprocity boundary element method (DRBEM). To the authors' knowledge, this is the first application of DRBEM to nonlinear acoustics. The numerical procedure can be applied to predict the propagation of finite but of moderate amplitude acoustic waves in domains of any geometry. The final formulation is validated by comparison with an analytical solution derived by the authors. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a numerical prediction model of mixed-mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed-mode loading and a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present optimal preconditioned iterative methods to solve indefinite linear systems of equations arising from symmetric coupling of finite elements and boundary elements. This is a block-diagonal preconditioner together with a conjugate residual method and a preconditioned inner-outer iteration. We prove the efficiency of these methods by showing that the number of iterations to preserve a given accuracy is bounded independent of the number of unknowns. Numerical examples underline the efficiency of these methods. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the scattering of in-plane compressional (P) and shear (SV) waves by boomerang, three-, four-, five-, and six-pointed star shaped inclusions using a boundary element method. Special case when the shape of the four-pointed star becomes square is also considered. Numerical examples are given for some star shapes of the inclusion, and the scattering cross sections are plotted as a function of frequency. The response simplifies for the limited cases of a hole and a rigid inclusion, but with quite different behavior for each. [ABSTRACT FROM AUTHOR]

This paper presents a novel radiation boundary condition (RBC) with the spectral integral method (SIM) to truncate the computational domain in the finite-element method (FEM). Because of the spectral accuracy of the SIM, the sampling density on the radiation boundary requires less than four points per wavelength to achieve a high accuracy (1%). As a result, the introduction of the SIM as an RBC actually can decrease the total number of unknowns in the system equation. Numerical results illustrate the usefulness of this novel RBC for both homogeneous and inhomogeneous objects. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1995–2002, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22608 [ABSTRACT FROM AUTHOR]

An embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi-brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete. [ABSTRACT FROM AUTHOR]

This paper presents a meshing algorithm for domains with internal boundaries. It is an extension of the gridding algorithm presented by Persson and Strang. The resulting triangulation matches all boundaries, and the triangles are all nearly equilateral. Equilateral triangles are beneficial for a finite volume discretization, as fluid flow between elements of very different size is only possible at small timesteps. The mesh generator is compared with the well regarded Triangle programme, where both element quality and simulation performance are checked. It is shown that our mesh generator consistently delivers better meshes. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There exists a set U in the plane, such that elements of U correspond to minimal stable solutions of a two-parameter elliptic system. For points on the boundary ϒ of U, there exist weak solutions to the elliptic system. The paper studies the properties of the curve ϒ. 2000 Mathematics Subject Classification 35J55, 35B05, 35K50, 35K55. [ABSTRACT FROM PUBLISHER]

This paper presents a new symmetric formulation for structural acoustics in the frequency domain. Usually, the structural domain is discretized with the Finite-Element Method (FEM), whereas the Boundary Element Method (BEM) is used for the treatment of the infinite acoustic domain. Coupling formulations generally suffer from the dense and unsymmetric equation system of the BEM. To circumvent this drawback, the acoustic domain is discretized here with the Hybrid Stress Boundary Element Method (HSBEM), which is based on a variational principle. The discretized formulation consists of a symmetric stiffness-type equation based on a dynamic flexibility matrix in frequency domain. The HSBEM is thus easily coupled with other symmetric discretization methods, combining the advantages of a boundary formulation and a symmetric approach. An issue of the method is the evaluation of the flexibility matrix. This contribution extends former publications of the authors by a detailed analysis of the implementation of this matrix, leading to a new clustering scheme for an efficient treatment, based on the special structure of the integral kernel. Moreover, the treatment of hyper-singular integral kernels without integration, based on orthogonality properties for interior and exterior domains is outlined. Examples show the consistency of this approach. Finally, a coupled formulation for structural acoustics employing the HSBEM for the structure and the acoustic domain is introduced. Several numerical tests elucidate the applicability of the method and the proposed improvements. [ABSTRACT FROM AUTHOR]

There are two versions of the Proper Iteration Lemma. The stronger (but less well-known) version can be used to give simpler proofs of iteration theorems (e.g., [7, Lemma 24] versus [9, Theorem IX.4.7]). In this paper we give another demonstration of the fecundity of the stronger version by giving a short proof of Shelah's theorem on the preservation of the ωω-bounding property. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a mixed method for the characterization of ridged circular waveguide discontinuities. The method is based on integral equations in combination with a scalar Green's function and a boundary element method for the calculation an arbitrary ridged circular waveguide's mode spectrum. The modes computed by this technique are used as trial function bases for the characterization of arbitrary ridged circular waveguide discontinuities. An improved variational multimodal formulation is used for the characterization of the step discontinuity. Coupling coefficients are evaluated by post processing of the matrices already used in the modes' determination, and the overall scattering matrix is obtained by cascading the impedance matrix of such a discontinuity. In order to validate this method, screws used in filter design and spectrum polarizer are modeled and the numerical results are verified by excellent agreement with published data. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 478–482, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10643 [ABSTRACT FROM AUTHOR]

This paper presents a full wave method for the determination of the mathematical model of a 3D waveguide structure in the form of the pole expansion in the s-plane of its generalized admittance matrix. The method is based on a boundary integral-resonant mode expansion approach. By the introduction of appropriate state-variables, the method leads to the pole expansion by solving a linear generalized eigenvalue problem, like in the well-known techniques used up to now in frequency/time domain modelling based on finite difference or finite element methods. With respect to these methods we have the advantage of a significant reduction in both memory allocation and computing time. Two examples show the accuracy of the results and the efficiency of the method. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The authors earlier proposed a revolving permanent-magnet type wheel called the “magnet wheel,” which has the functions of both induction repulsive magnetic levitation and thrust. In this paper, the relationship between magnetic poles and lift force or thrust characteristics is examined to investigate the performance. Five types of magnet wheels are discussed in an experimental study and four more types are used in a theoretical study with three-dimensional numerical analysis. The following parameters are considered: magnetomotive force (mmf) of a permanent magnet; thickness of the magnet in the magnetizing direction; total volume of magnets; fundamental factor; distortion factor of the space mmf distribution of poles; pole pitch; diameter of magnet wheel; mechanical clearance; and thickness and resistivity of conducting plate. The results show the following: 1. The lift force per unit of magnet volume is approximately proportional to the fundamental factor of the space mmf distribution of the poles. A low degree space harmonic mmf is effective in increasing lift force. 2. The driving power per unit of lift force is almost entirely independent of the configuration of the primary member, including pole arrangement and position relative to the secondary conducting plate, respectively, and depends only on the resistance of the conducting plate. 3. In both the “partial-overlap type” and “tilt type” magnet wheels, many poles with sufficiently large pole pitch are useful. In the tilt type the use of a small tilt angle is desirable. © 1999 Scripta Technica, Electr Eng Jpn, 128(4): 111–120, 1999 [ABSTRACT FROM AUTHOR]

This paper presents an approach for the modelling of gas flows in thin gaps within two parallel plates. Starting from the derivation of a diffusion limit for a linear kinetic equation, we propose a first step of how to model nonlinear situations with the help of parameter lists obtained from numerical results. [ABSTRACT FROM AUTHOR]

The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction. [ABSTRACT FROM AUTHOR]

This paper treats a united-form solution for a point force applied at the interior of an infinite transversely isotropic solid. Several heuristic functions are adopted to obtain the expressions of the solution based on the general solution. To exclude some indeterminate attributes, the expressions are rewritten. In the final expressions, unlike previous publications where the solutions are expressed in different forms, or when some individual constants have different definitions depending on the conditions satisfied by the elastic constants, we provide united solutions which are suitable for all stable transversely isotropic materials and isotropic materials. Thus accurate numerical evaluation of the boundary element method can be performed directly without the need to resolve the singularity algebraically. Some numerical examples with BEM are also presented in this paper. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the direct boundary element method (DBEM) of analysis, much of the numerical computation involves line integrations along a boundary. The integration is usually performed by quadrature, and in recent previous papers by the author1,2 it has been shown that integration can in general be carried out analytically, with the results of the integration presented as algebraic functions, and programmed accordingly. These results have, to this time, been presented for straight boundaries, with application to thin-plate bending analysis only. For an arbitrary shaped curved element, the derivation of closed-form expressions for boundary integrations is not possible. A semi-analytical-numerical procedure, based on representing the boundary as piecewise straight is developed in this paper. In this procedure, the boundary shape is considered independent of the approximation of the boundary variables, and in the sense that each ‘quadratic’ boundary element is considered geometrically to be made up of several piecewise cubic functions, the formulation might be termed ‘super-parametric’ Generally, a curved boundary does not necessarily imply a need for higher-order approximation of boundary variables, but does necessitate that the more complicated shape be accurately modelled. The integration procedure presented in this paper can be applied in other two-dimensional problems. [ABSTRACT FROM AUTHOR]

The asymmetry of the stiffness matrix in the boundary element method makes the coupling of the boundary and finite element methods difficult. In the paper, the author presents a new boundary element method model in which the stiffness matrix in the model is close to symmetry. After symmetrization, the stiffness matrix can be used as an ordinary finite element type element stiffness matrix to be assembled in the total stiffness matrix. Compared with the directly symmetrized model,1.2 the model in the paper has higher accuracy. [ABSTRACT FROM AUTHOR]

Simulations of excavations of tunnels can be performed by means of a coupling strategy using the boundary-element-method (BEM) and the finite-element-method (FEM). The BEM is employed for the discretization of the far-field of the tunnel, whereas the FEM is used for the interior of the tunnel and its vicinity. This strategy is based on the assumption that the influence of material non-linearities in the far-field can be neglected. The coefficient matrices of the resulting systems of linear, algebraic equations consist of a symmetric, banded, sparse part resulting from the FE subdomain and an unsymmetric, fully populated part obtained from the BE subdomain. Substantial reductions of the CPU time and the disk space required for the solution of the systems of linear, algebraic equations can be achieved by employing iterative solvers with preconditioning and using the computer hardware intelligently. In this paper, two strategies based on such solvers are proposed and explained in detail. The convergence behaviour of the implemented iterative solvers with regards to pure BE calculations is studied by means os solving selected numerical examples. The advantages of the two proposed methods relative to the original, direct solution strategy are demonstrated on the basis of coupled simulations. Additionally, some comments concerning the use of iterative solvers on a vector computer are given. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to answer some questions posed by Doob [2] in 1965 concerning the boundary cluster sets of harmonic and superharmonic functions on the half-space D given by D = Rn−1 × (0, + ∞), where n ≥ 2. Let f: D → [−∞, +∞] and let Z ∈ δD. Following Doob, we write BZ (respectively CZ) for the non-tangential (respectively minimal fine) cluster set of f at Z. Thus l ∈ BZ if and only if there is a sequence (Xm) of points in D which approaches Z non-tangentially and satisfies f(Xm) → l. Also, l ∈ CZ if and only if there is a subset E of D which is not minimally thin at Z with respect to D, and which satisfies f(X) → l as X → Z along E. (We refer to the book by Doob [3, 1.XII] for an account of the minimal fine topology. In particular, the latter equivalence may be found in [3, 1.XII.16].) If f is superharmonic on D, then (see [2, §6]) both sets BZ and CZ are subintervals of [−∞, +∞]. Let λ denote (n − 1)-dimensional measure on δD. The following results are due to Doob [2, Theorem 6.1 and p. 123]. 1991 Mathematics Subject Classification 31B25. [ABSTRACT FROM AUTHOR]

Electromagnetic field analysis has a very important role in the design and performance analysis of electric machinery and apparatus. The analysis baa been conducted using many methods such as the difference equation method, the finite element method and the boundary element method. Currently, it is possible to take into account the effects of the nonlinearity of material characteristics and eddy current in analyzing the electromagnetic field of multimedium space with open boundary. The remarkable progress in computing speed and memory capacity of recent large-scale computers takes it possible to analyze not only the two-dimensional field but also the three-dimensional field.

With a view to evaluating the human exposure to ion current generated under a dc power transmission line, the exposure was evaluated by means of a numerical method (1) a new ion current analysis method was developed which can be applied to bodies with complex shapes such as biological bodies. (2) The method is based on the boundary element method, (3) the space charge terms were processed under an assumption of a lumped source of ion current, and (4) comparing the theoretical and experimental data, the error was evaluated. The method was then applied to biological bodies. It was found that the electric field on the surface of the biological body in the ion current field becomes larger than the one obtained in the Laplace field without ion current. This result indicates the importance of the analysis of the ion current field. Further, the variation of the electric field concentration accompanied by changes in the posture of the human body were clarified. The variation of the surface electric field when a body is charged by the ion current was clarified, as well. Hence, this paper provides useful information on the determination of the safety standard and on evaluation of the biological effects of ion current field. [ABSTRACT FROM AUTHOR]

In principle, the finite element method is an analysis method in which an inhomogeneous waveguide with a closed boundary and a complex geometry. By contrast, the boundary element method is suited for the analysis of an open-region problem. In this paper, as a method for analyzing the propagation characteristics of the guided modes in an open waveguide, the finite element method is applied to the electromagnetic field of the interior region while the boundary element method is applied to the field outside the waveguide. The fields of the two regions are then connected at the boundary. By means of the present method, it is possible to analyze without spurious solutions the guided modes in an open waveguide with a cladding made of a different material and an inhomogeneous interior region with a complex geometry. Also, the coefficient matrix of the matrix equation to be solved becomes square. As practical examples, the dispersion characteristics of the rectangular dielectric waveguides and channel waveguides are analyzed so that the validity of the method is verified. [ABSTRACT FROM AUTHOR]

Differential equation methods often are used for the analysis of the waves scattered by a dielectric grating. It is known that accurate numerical solutions can be obtained if the number of expansion terms of the spatial harmonics is increased. However, when the differential equation method is applied to a dielectric grating with an extremely large permittivity, the convergence speed of the solution becomes excessively slow in the TM wave analysis. Because of the increase of the computation time and the memory capacity, an analysis based on the differential equation method becomes difficult in practice. In this paper, it is shown that a boundary element method using Green's function satisfying the periodic condition is effective for the analysis. By introduction of pseudo-periodic Green's function, the definition region for the integral equation is limited to the grating surface. In comparison to the boundary element method using the Hankel function, the number of linear equations is reduced. By means of numerical examples, it is shown that the convergence speed of the solution by the present method is faster and the computation time is significantly shorter than the solution by the differential equation method even in the TM wave analysis of a dielectric grating with a large loss. [ABSTRACT FROM AUTHOR]

Although actual optical integrated circuits have three-dimensional (3-D) structures, almost all the existing theoretical studies integrated circuits replace them by the corresponding 2-D structures via the effective-index method. This 2-D structures often become asymmetric discontinuities in a symmetric dielectric slab waveguide. A method has already been proposed which makes it possible to analyze discontinuities in an open dielectric waveguide by continuing the finite-element and boundary-element methods. The applicability of this new method was restricted to symmetric discontinuities. In this paper, by considering the anti-symmetric modes of the waveguide, the combined method of finite and boundary elements is extended to asymmetric discontinuities. The present method is applied to a transverse displacement and the convergence of the solution is examined numerically. Also, for a transverse displacement and a waveguide bend, the scattering characteristics including the radiation patterns are calculated. The computed results are compared with those obtained by other methods and the validity and effectiveness of the method herein are compared. [ABSTRACT FROM AUTHOR]

The boundary element method has drawn wide attention as a novel numerical method of the boundary integration equation, and it has already been applied to the electromagnetic initial value problems. In this paper, we apply the boundary element method to the electromagnetic wave eigenvalue problems and establish a numerical method which is applicable to analyze the guided modes of waveguides with arbitrary structure. Then as an application example of the present method, we make numerical calculation of the elliptical core optical fiber, which is the typical polarization holding optical fiber, and clarify the cutoff frequencies of the first- and second- order higher modes of the fiber. Also, the propagation constant and the geometrical anisotropy of the fundamental mode of the fiber are obtained. Again, the maximum anisotropy of the elliptical core fiber is shown to be obtained for the normalized frequency of 1.85 and ellipse factor of the core equal to 0.8. From these results we conclude that the boundary element method has high accuracy of calculation, is easy to apply, and has highly stable solution. [ABSTRACT FROM AUTHOR]

The paper proposes an iterative procedure, called current iteration, for the finite element solution of two-dimensional steady-state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre-existing finite clement code for bounded problems. An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2-D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques. [ABSTRACT FROM AUTHOR]

This paper describes the application of the boundary element method to solving two-dimensional steady slow viscous flow problems (creeping flow) in thermal silicon oxidation. The proposed method used the velocity-pressure formulation. The use of the incompressibility condition as a boundary condition and the application of the second Green's identity to transform the domain integral into a boundary integral result in a system of three boundary integral equations for velocity components and pressure. Solution of this system to be an ill-posed problem because of the presence of boundary conditions of the first kind. Two methods of regularization are employed. The numerical results for trench oxidation process are presented. [ABSTRACT FROM AUTHOR]

This study investigates regularization techniques for the boundary knot method (BKM). We consider three regularization methods and two approaches for the determination of the regularization parameter. Our numerical experiments show that Tikhonov regularization in conjunction with generalized cross-validation approach outperforms the other regularization techniques in the BKM solution of Helmholtz and modified Helmholtz problems. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]