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## Integral Equations (integral + equation)
Kinds of Integral Equations
Terms modified by Integral Equations
## Selected Abstracts## Analysis of fluid-structure interaction in low pressure MEMS by Integral Equations PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Attilio FrangiArticle first published online: 25 FEB 200The evaluation of gas dissipation occurring in inertial polysilicon MEMS is addressed focusing the attention on the free,molecule flow. In this regime, which is very often of interest for industrial applications, collisions between molecules can be neglected and the momentum transfer to the moving shuttle can be easily computed. Since the surfaces of silicon MEMS are generally very rough, a complete diffusion model is adopted to describe the wall,molecule interaction. A Boundary Integral Equation approach is proposed and it is shown that the introduction of the key assumption of small perturbations is crucial in the development of a robust and fast numerical tool. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## On a compounding assets model with positive jumps APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2008Yinghui DongAbstract In this paper, a compounding assets model with positive jumps is proposed. Integral equations and integro-differential equations for the survival probability and the ruin probability for the proposed model are derived. By using a probability method, an exact expression in the form of series for the ruin probability is obtained. Some closed-form expressions for the survival probability are deduced by solving certain integro-differential equations. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Demographic analysis of continuous-time life-history models ECOLOGY LETTERS, Issue 1 2008André M. De RoosAbstract I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as a continuous development through time. The method is generally applicable to analyse population growth and performance for a wide range of individual life-history models, including cases in which the population consists of different types of individuals or in which the environment is fluctuating periodically. It complements comparable methods developed for discrete-time dynamics modelled with matrix or integral projection models. The basic idea behind the method is to use Lotka's integral equation for the population growth rate and compute the integral occurring in that equation by integrating an ordinary differential equation, analogous to recently derived methods to compute steady-states of physiologically structured population models. I illustrate application of the method using a number of published life-history models. [source] ## Iterative generalized cross-validation for fusing heteroscedastic data of inverse ill-posed problems GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2009Peiliang XuSUMMARY The method of generalized cross-validation (GCV) has been widely used to determine the regularization parameter, because the criterion minimizes the average predicted residuals of measured data and depends solely on data. The data-driven advantage is valid only if the variance,covariance matrix of the data can be represented as the product of a given positive definite matrix and a scalar unknown noise variance. In practice, important geophysical inverse ill-posed problems have often been solved by combining different types of data. The stochastic model of measurements in this case contains a number of different unknown variance components. Although the weighting factors, or equivalently the variance components, have been shown to significantly affect joint inversion results of geophysical ill-posed problems, they have been either assumed to be known or empirically chosen. No solid statistical foundation is available yet to correctly determine the weighting factors of different types of data in joint geophysical inversion. We extend the GCV method to accommodate both the regularization parameter and the variance components. The extended version of GCV essentially consists of two steps, one to estimate the variance components by fixing the regularization parameter and the other to determine the regularization parameter by using the GCV method and by fixing the variance components. We simulate two examples: a purely mathematical integral equation of the first kind modified from the first example of Phillips (1962) and a typical geophysical example of downward continuation to recover the gravity anomalies on the surface of the Earth from satellite measurements. Based on the two simulated examples, we extensively compare the iterative GCV method with existing methods, which have shown that the method works well to correctly recover the unknown variance components and determine the regularization parameter. In other words, our method lets data speak for themselves, decide the correct weighting factors of different types of geophysical data, and determine the regularization parameter. In addition, we derive an unbiased estimator of the noise variance by correcting the biases of the regularized residuals. A simplified formula to save the time of computation is also given. The two new estimators of the noise variance are compared with six existing methods through numerical simulations. The simulation results have shown that the two new estimators perform as well as Wahba's estimator for highly ill-posed problems and outperform any existing methods for moderately ill-posed problems. [source] ## A semi-spectral modelling of landslide tsunamis GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2008Nazmi PostaciogluSUMMARY A new, semi-spectral technique based on integral equations is introduced for the landslide tsunami problem. The technique does not use the shallow water approximation and resolves the dispersive surface wavefield generated by sliding material over a bathymetric profile. The wave scattering due to the bathymetric profile on which the slide occurs is calculated solving an integral equation. On the free surface, the linearized kinematic and dynamic boundary conditions are imposed. Method of images is adopted to solve for a source-sink distribution on the bathymetry to simulate the motion of the landslide and to satisfy the kinematic condition on the sea bottom. An asymptotic relation for the far field is also derived. The application to a landslide tsunami generation scenario in the Sea of Marmara reveals that a thickness H submarine mass failure on the southern rim of the Ç,narc,k Basin would create a wave peak of around 0.5 H on the ,1000 m deep Ç,narc,k Basin. [source] ## The hydroelectric problem of porous rocks: inversion of the position of the water table from self-potential data GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004A. RevilSUMMARY The self-potential (SP) method is a fast and cheap reconnaissance tool sensitive to ground water flow in unconfined aquifers. A model based on the use of Green's functions for the coupled hydroelectric problem yields an integral equation relating the SP field to the distribution of the piezometric head describing the phreatic surface and to the electrical resistivity contrast through this phreatic surface. We apply this model to SP data measured on the south flank of the Piton de la Fournaise volcano, a large shield volcano located on Réunion island, Indian ocean. The phreatic surface, inverted with the help of the Simplex algorithm from the SP data, agrees well with the available information in this area [one borehole and electromagnetic (EM) data]. This interpretation scheme, which we call electrography, has many applications to the crucial problem of water supply in volcanic areas where drilling is expensive. [source] ## On strike-slip faulting in layered media GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2002Maurizio BonafedeSummary We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress). [source] ## A study of ground-structure interaction in dynamic plate load testing INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2002Bojan B. GuzinaAbstract A mathematical treatment is presented for the forced vertical vibration of a padded annular footing on a layered viscoelastic half-space. On assuming a depth-independent stress distribution for the interfacial buffer, the set of triple integral equations stemming from the problem is reduced to a Fredholm integral equation of the second kind. The solution method, which is tailored to capture the stress concentrations beneath footing edges, is highlighted. To cater to small-scale geophysical applications, the model is used to investigate the near-field effects of ground-loading system interaction in dynamic geotechnical and pavement testing. Numerical results indicate that the uniform-pressure assumption for the contact load between the composite disc and the ground which is customary in dynamic plate load testing may lead to significant errors in the diagnosis of subsurface soil and pavement conditions. Beyond its direct application to non-intrusive site characterization, the proposed solution can be used in the seismic analysis of a variety of structures involving annular foundation geometries. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Self-similar solution of a plane-strain fracture driven by a power-law fluid INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2002J. I. AdachiAbstract This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n,0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Frictional contact of laminated elastic half-spaces allowing interface cavities. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2001Part 1: Analytical treatmentAbstract The paper deals with the plane problem on frictional contact of stratified elastic half-spaces provided discontinuity of their direct touch. Imperfectness of contact of the bodies is assumed to be caused by surface unevenness of their surface layers. The problem is formulated within the framework of the homogenized model with microlocal parameters. Using the method of complex potentials in combination with the method of interface gaps the problem is reduced to a singular integral equation on the function of interface gap height. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## A relation between the logarithmic capacity and the condition number of the BEM-matrices INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007W. DijkstraAbstract We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Electrostatic BEM for MEMS with thin beams INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2005Zhongping BaoAbstract Micro-electro-mechanical (MEM) and nano-electro-mechanical (NEM) systems sometimes use beam- or plate-shaped conductors that can be very thin,with h/L,,,(10,2,10,3) (in terms of the thickness h and length L of a beam or the side of a square pate). Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently,especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such objects. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with logarithmically singular kernels, results in a powerful technique for the BEM analysis of such problems with thin beams. This new approach, in fact, works best for very thin beams. This thin beam BEM is derived and discussed in this work. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Vector Hankel transform analysis of a tunable circular microstrip patch INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005T. FortakiAbstract In this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very efficient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning effect on the resonant frequency and half-power bandwidth are also presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-DebainAbstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A numerical solution for the equation of the lifting surface in ground effects INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2002r DragoAbstract Using the Gauss-type quadrature formulas one discretizes the 2d integral equation of the lifting surface in ground effects. Numerical calculations of the aerodynamical coefficients are performed for the elliptical and rectangular wings. Copyright 2002 John Wiley & Sons, Ltd. [source] ## An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001E. E. TheotokoglouAbstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Local discretization error bounds using interval boundary element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009B. F. ZalewskiAbstract In this paper, a method to account for the point-wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen,Loève expansions INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2008K. J. CraigAbstract For the accurate prediction of the collapse behaviour of thin cylindrical shells, it is accepted that geometrical and other imperfections in material properties and loading have to be accounted for in the simulation. There are different methods of incorporating imperfections, depending on the availability of accurate imperfection data. The current paper uses a spectral decomposition of geometrical uncertainty (Karhunen,Loève expansions). To specify the covariance of the required random field, two methods are used. First, available experimentally measured imperfection fields are used as input for a principal component analysis based on pattern recognition literature, thereby reducing the cost of the eigenanalysis. Second, the covariance function is specified analytically and the resulting Friedholm integral equation of the second kind is solved using a wavelet-Galerkin approach. Experimentally determined correlation lengths are used as input for the analytical covariance functions. The above procedure enables the generation of imperfection fields for applications where the geometry is slightly modified from the original measured geometry. For example, 100 shells are perturbed with the resulting random fields obtained from both methods, and the results in the form of temporal normal forces during buckling, as simulated using LS-DYNA®, as well as the statistics of a Monte Carlo analysis of the 100 shells in each case are presented. Although numerically determined mean values of the limit load of the current and another numerical study differ from the experimental results due to the omission of imperfections other than geometrical, the coefficients of variation are shown to be in close agreement. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Fully hierarchical divergence-conforming basis functions on tetrahedral cells, with applications INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Matthys M. BothaAbstract A new set of hierarchical, divergence-conforming, vector basis functions on curvilinear tetrahedrons is presented. The basis can model both mixed- and full-order polynomial spaces to arbitrary order, as defined by Raviart and Thomas, and Nédélec. Solenoidal- and non-solenoidal components are separately represented on the element, except in the case of the mixed first-order space, for which a decomposition procedure on the global, mesh-wide level is presented. Therefore, the hierarchical aspect of the basis can be made to extend down to zero polynomial order. The basis can be used to model divergence-conforming quantities, such as electromagnetic flux- and current density, fluid velocity, etc., within numerical methods such as the finite element method (FEM) or integral equation-based methods. The basis is ideally suited to p -adaptive analysis. The paper concludes with two example applications. The first is the FEM-based solution of the linearized acoustic vector wave equation, where it is shown how the decomposition into solenoidal components and their complements can be used to stabilize the method at low frequencies. The second is the solution of the electric field, volume integral equation for electromagnetic scattering analysis, where the benefits of the decomposition are again demonstrated. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Full-wave analysis of single cylindrical striplines and microstriplines with multilayer dielectrics INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Farid BouttoutAbstract In this paper, the spectral-domain method is used to calculate the propagation characteristics of cylindrical microstrip transmission lines. The problem is formulated using an electric field integral equation and the spectral-domain Green's function. The solutions of the field components are obtained in matrix forms, which facilitate the calculations of the Green's function and the power flowing over the lines. The Green's functions are obtained in terms of transition matrices over the dielectric layers. The obtained integral equation is solved by moment method using four kinds of basis functions. The convergence of the method is proven. Based on the power,current definition, a stationary expression for the characteristic impedance has been derived analytically. Numerical results of the effective dielectric constant and the characteristic impedance for various line parameters are calculated and analysed. The computed data are found to be in good agreement with results obtained using other methods. The formulation is then applied to covered microstripline, microstripline and stripline with air gaps, for which data are not found in the literature to date. The presented method is used to guide design of microstrip coil for magnetic resonance imaging. This method is also suitable for investigation of multiconductor strip lines. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Meshless analysis of potential problems in three dimensions with the hybrid boundary node method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004Jianming ZhangAbstract Combining a modified functional with the moving least-squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary-only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ,boundary layer effect' in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## A Galerkin boundary integral method for multiple circular elastic inclusions INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001S. G. MogilevskayaAbstract The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss,Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Instationary aeroelastic computation of yacht sails INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2001Heinrich SchoopAbstract Effective schemes exist to calculate aerodynamic forces for thin bodies and structural dynamics of flexible membranes. The fluid dynamic of thin wings in a irrotational flow leads to the lifting surface theory. Neglecting the inertia of the membrane the structural dynamics are solved by the non-linear (FEM). But the interaction of flexible membranes and an irrotational flow causes problems due to the different nature of the mathematical equations. On the one hand, there is a partial differential equation for the structural dynamics and on the other hand, there is a singular integral equation for the aerodynamics. The numerical discretization scheme has to fit these different types of equation. Our work introduces a new interaction scheme to couple the singular integral equation of the lifting surface theory with the non-linear FEM of the membrane static. The fundamental examinations, showed by Schoop et al. (International Journal for Numerical Methods in Engineering 1998; 41: 217,219), are applied to realistic sail geometries and the aerodynamics is extended to instationary flow conditions. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity BEM INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001Yoshihiro OchiaiAbstract If the initial temperature is assumed to be constant, a domain integral is not needed to solve unsteady heat conduction problems without heat generation using the boundary element method (BEM).However, with heat generation or a non-uniform initial temperature distribution, the domain integral is necessary. This paper demonstrates that two-dimensional problems of unsteady heat conduction with heat generation and a non-uniform initial temperature distribution can be solved approximately without the domain integral by the triple-reciprocity boundary element method. In this method, heat generation and the initial temperature distribution are interpolated using the boundary integral equation. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## On the spectrum of the electric field integral equation and the convergence of the moment method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Karl F. WarnickAbstract Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low-order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Self-propulsion of oscillating wings in incompressible flow INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2008A. CarabineanuAbstract In this paper, we show that the oscillatory motion of an airfoil (wing) in an ideal fluid can determine the apparition of thrust. In the framework of the linearized perturbation theory, the pressure jump over the oscillating wing is the solution of a two-dimensional hypersingular integral equation. Using appropriate quadrature formulas, we discretize the oscillatory lifting surface integral equation in order to obtain the jump of the pressure across the surface. Integrating numerically, we obtain the drag coefficient. For some oscillatory motions, if the frequency of the oscillations surpasses a certain value, the drag coefficient becomes negative, i.e. there appears a propulsive force. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Steady/unsteady aerodynamic analysis of wings at subsonic, sonic and supersonic Mach numbers using a 3D panel method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Jeonghyun ChoAbstract This paper treats the kernel function of an integral equation that relates a known or prescribed upwash distribution to an unknown lift distribution for a finite wing. The pressure kernel functions of the singular integral equation are summarized for all speed range in the Laplace transform domain. The sonic kernel function has been reduced to a form, which can be conveniently evaluated as a finite limit from both the subsonic and supersonic sides when the Mach number tends to one. Several examples are solved including rectangular wings, swept wings, a supersonic transport wing and a harmonically oscillating wing. Present results are given with other numerical data, showing continuous results through the unit Mach number. Computed results are in good agreement with other numerical results. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A numerical method to solve the m -terms of a submerged body with forward speed INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002W.-Y. DuanAbstract To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m -terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m -terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Flexible GMRES-FFT method for fast matrix solution: application to 3D dielectric bodies electromagnetic scattering INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2004R. S. ChenAbstract In this paper, the electromagnetic wave scattering is analysed by the efficient Krylov subspace iterative fast Fourier transform (FFT) technique in terms of the electric field integral equation (EFIE) for a dielectric body of general shape, inhomogeneity, and anisotropy. However, when the permittivity of the scatter becomes large, the convergence rate of Krylov subspace iterative methods slow down. Therefore, the inner,outer flexible generalized minimum residual method (FGMRES) is used to accelerate the iteration. As a result, nearly 10 times convergence improvement is achieved for high permittivity cases. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Efficient analysis of wireless communication antennas using an accurate [Z] matrix interpolation technique INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 4 2010Yikai ChenAbstract An accurate impedance matrix interpolation technique based on the surface integral equation (SIE) is presented for the analysis of wireless communication antennas over wide frequency bands. The first-order derivative of the impedance matrix at the internal frequency is considered in the cubic polynomial-based interpolation scheme, thus the novel impedance matrix interpolation scheme will provide high accuracy and high efficiency over a frequency band. To demonstrate the efficiency and accuracy of the proposed method, numerical results for planar inverted F antennas (PIFA) and a wideband E-shaped patch antenna are presented. Good agreement among the interpolation results, exact MoM solutions, finite element method (FEM) solutions, and measured data is observed over the bandwidth. Besides, dimensions of the feeding probe are also studied to investigate their effect on the input impedance and radiation patterns. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010. [source] |