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This paper considers the inverse problem of determining the time‐dependent coefficient in the time‐fractional diffusion‐wave equation. In this case, an initial boundary value problem was set for the fractional diffusion‐wave equation, and an additional condition was given for the inverse problem of determining the coefficient from this equation. First of all, it was considered the initial boundary value problem. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag‐Leffler function and the generalized singular Gronwall inequality, we get a priori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved. The stability estimate is also obtained. [ABSTRACT FROM AUTHOR]

In this research, two systems of nonlinear Volterra integral equation and Volterra integro‐differential equation were considered. New results in sense of Ulam stabilities in relation to these two systems were proved on a finite interval. The proof of the results on the Ulam stabilities of that classes of the equations are based on the nonlinear alternative related to Banach's contraction principle. The outcomes of this research give new contribution to the theory of Ulam stabilities. [ABSTRACT FROM AUTHOR]

In this paper, the inverse problem of determining the time‐dependent reaction–diffusion coefficient in the Cauchy problem for the time‐fractional diffusion equation with the Hilfer operator by a single observation at the point x=0$$ x=0 $$ of the diffusion process is studied. To represent the solution of the direct problem, the fundamental solution of this equation is constructed and properties of this solution are investigated. The fundamental solution contains Fox's H$$ H $$‐functions widely used in fractional calculus. The fundamental solution for the fractional diffusion operator with the Hilfer derivative is also obtained in terms of the Yang Y$$ Y $$‐function, and it is shown that they coincide. Using estimates of the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown coefficient, which will be used in investigation of inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation, the contracted mapping principle is applied. The local existence and global uniqueness results and the conditional stability estimate of solution are proven. [ABSTRACT FROM AUTHOR]

Taking into account a wavelet transform associated with the quadratic‐phase Fourier transform, we obtain several types of uncertainty principles, as well as identify conditions that guarantee the unique solution for a class of integral equations (related with the previous mentioned transforms). Namely, we obtain a Heisenberg–Pauli–Weyl‐type uncertainty principle, a logarithmic‐type uncertainty principle, a local‐type uncertainty principle, an entropy‐based uncertainty principle, a Nazarov‐type uncertainty principle, an Amrein–Berthier–Benedicks‐type uncertainty principle, a Donoho–Stark‐type uncertainty principle, a Hardy‐type uncertainty principle, and a Beurling‐type uncertainty principle for such quadratic‐phase wavelet transform. For this, it is crucial to consider a convolution and its consequences in establishing an explicit relation with the quadratic‐phase Fourier transform. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with an integral system u(x)=Wβ,γup−1v(x),u>0inRn,v(x)=Iαup(x),v>0inRn,$$ \left\{\begin{array}{l}u(x)={W}_{\beta, \gamma}\left({u}^{p-1}v\right)(x),u>0\kern0.5em \mathrm{in}\kern0.5em {R}^n,\\ {}v(x)={I}_{\alpha}\left({u}^p\right)(x),v>0\kern0.5em \mathrm{in}\kern0.5em {R}^n,\end{array}\right. $$where p≥1,0<α,βγ1$$ p\ge 1,0<\alpha, \beta \gamma 1 $$. Base on the integrability of positive solutions, we obtain some Liouville theorems and the decay rates of positive solutions at infinity. In addition, we use the properties of the contraction map and the shrinking map to prove that u$$ u $$ is Lipschitz continuous. In particular, the Serrin type condition is established, which plays an important role to classify the positive solutions. [ABSTRACT FROM AUTHOR]

In this work, we investigate a generalization of the Tricomi problem for a loaded mixed‐type equation with the Riemann–Liouville fractional differential operator. By using the method of integral equations, a unique solvability of the formulated problem given in piecewise non‐parallel characteristics is proven. [ABSTRACT FROM AUTHOR]

In this paper, the full‐wave volume‐surface integral equation (VSIE), the modified surface integration (MSI) method, and the ray‐tracing process are combined to efficiently analyze the electromagnetic performance of receiving antennas enclosed by radome with variable thickness. The mutual interactions between the antenna and the radome are considered by coupling the VSIE and MSI in a nested iterative manner, in which the VSIE is applied to model the complex antenna with composite conductor‐dielectric structure, while the MSI method is used to deal with the large‐size dielectric radome. To improve modeling accuracy of the MSI method for multilayered radome with variable thickness, the ray‐tracing technique is incorporated to calculate the angles of incidence and refraction at each interface and the local thickness of the dielectric wall for each sampling ray and then the local transmission matrix. Numerical results illustrate the accuracy and effectiveness of the proposed method. Plain Language Summary: To effectively study the electromagnetic performance of receiving antennas ensconced by radomes with varying thickness, the full‐wave volume‐surface integral equation, the modified surface integration (MSI) technique, and the ray‐tracing procedure are combined. Key Points: The entire radome‐enclosed antenna system is divided into the antenna region modeled by method of moment and radome region modeled by modified surface integrationThe mutual interactions between the antenna and the radome are calculated up to the second‐orderThe electromagnetic field transmission through the variable‐thickness radome is computed by the ray tracing process and the ABCD Matrix method [ABSTRACT FROM AUTHOR]

It is well known that any classical Lotka–Volterra (LV) operator (associated with quadratic stochastic operator) defined on the simplex is a homeomorphism. On the other hand, more general LV systems have important applications in the time evolution of conflicting species in biology. It is natural to study the bijectivity of such kind of LV operators. There is an example of a LV operator which is not injective. In this paper, we introduce a class of LV operators that are bijective. As an application of our result, the existence and uniqueness of solution of a class of Hammerstein integral equations is proved. [ABSTRACT FROM AUTHOR]

In this paper, the pricing problem of callable–puttable convertible bonds written on a single underlying asset is studied with an integral equation (IE) approach. The complication of the pricing exercise results from the tangled presence of callability, puttability, as well as conversion, which have led to possible coexistence of two moving boundaries at the same time, depending on the call price, the put price, and the conversion ratio. If a callable–puttable convertible bond needs to be priced at a time sufficiently far away from the expiry, only the moving boundary associated with the puttability needs to be dealt with. When the pricing time is closer to expiry beyond a critical point, it is then possible to have two distinct cases. While the two moving boundaries associated with conversion and puttability coexist in one case, they may both disappear in another case; callability remains to be the only issue that needs to be dealt with. Furthermore, there exists another critical value, beyond which a callable–puttable convertible bond can be treated as its vanilla counterpart. Mathematically, various different scenarios demand different systems of IEs to be formulated and solved numerically. [ABSTRACT FROM AUTHOR]

Images obtained by airborne along‐track interferometric synthetic aperture radar (AT‐INSAR), provide tools to obtain ocean surface properties, such as the radial velocities of sea surface elevations. The estimation of these radial velocities from AT‐INSAR images is the interest of this work. We assume the Velocity Bunching Model relating the complex AT‐INSAR image at a point in the image plane, with the radial velocity of a scatterer point in the sea surface. The relation is by means of a nonlinear integral operator. Consequently, the estimation of radial velocities amounts to the solution of nonlinear and oscillatory integral equations. Our proposal is to solve the latter by Newton's methods on Hilbert function spaces, the so‐called optimize then discretize approach. The effectiveness is illustrated by means of numerical simulations evaluating the reconstruction of the radial velocities and the AT‐INSAR image. We show that this continuous version is accurate, and faster than the classical discretize then optimize version. A physical comparison is also carried out with the interferometric velocities. Key Points: The scalar field of radial velocities of a simulated ocean surface is constructed from a noisy along‐track interferometric synthetic aperture radar (AT‐INSAR) image of that surfaceThe nonlinear integral equation that relates radial velocities to AT‐INSAR intensities is solved by Newton's methods on function spacesRobustness is illustrated by recovering fields of radial velocities for different R/V ratios and other radar parameters [ABSTRACT FROM AUTHOR]

We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack. This formulation can be related to geological faults in elastic media or to irrotational incompressible flows in a half space minus an inner wall. The direct problem is well posed in an appropriate functional space. We study the related inverse problem where the jump across the crack is unknown, and more importantly, the geometry and the location of the crack are unknown. The data for the inverse problem are of Dirichlet type over a portion of the top boundary. We prove that this inverse problem is uniquely solvable under some assumptions on the geometry of the crack. The highlight of this paper is showing a stability result for this inverse problem. Assuming that the crack is planar, we show that reconstructing the plane containing the crack is Lipschitz stable despite the fact that the forcing term for the underlying PDE is unknown. This uniform stability result holds under the assumption that the forcing term is bounded above and the Dirichlet data are bounded below away from zero in appropriate norms. [ABSTRACT FROM AUTHOR]

In this paper, we consider two‐dimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation, the contracted mapping principle is applied. The local existence and global uniqueness results are proven. Also, the stability estimate is obtained. [ABSTRACT FROM AUTHOR]

In this research, we study a weakly singular Volterra integro differential equation with Caputo‐type fractional derivative. First, we derive a sufficient condition for the existence and uniqueness of the solution of this problem based on the maximum norm. It is observed that the condition depends on the domain of definition of the problem. Thereafter, we show that this condition will be independent of the domain of definition based on an equivalent weighted maximum norm. In addition, we have also provided a procedure to extend the existence and uniqueness of the solution in its domain of definition by partitioning it. We also derive a sufficient condition under which the model problem will provide an analytic solution. Next, we introduce an operator‐based parameterized method to generate an approximate solution of this problem. Convergence analysis of this approach is established here. Next, we have optimized this solution based on least square method. For this, residual minimization is used to obtain the optimal values of the auxiliary parameter. In addition, we have also provided an error bound based on this technique. Several numerical examples are produced to clarify the effective behavior of the convergence of the present method. Comparison of the standard method and optimized method based on residual minimization signify the better accuracy of modified one. In addition, we also consider an equivalent form of weakly singular integro differential equation of Heat transfer problem to show the high effectiveness of the present approach. [ABSTRACT FROM AUTHOR]

We begin with a treatment of the Caputo time‐fractional diffusion equation, by using the Laplace transform, to obtain a Volterra integro‐differential equation. We derive and utilize a numerical scheme that is derived in parallel to the L1‐method for the time variable and a standard fourth‐order approximation in the spatial variable. The main method derived in this article has a rate of convergence of O(kα + h4) for u(x, t) ∈ Cα([0, T]; C6(Ω)), 0 < α < 1, which improves previous regularity assumptions that require C2[0, T] regularity in the time variable. We also present a novel alternative method for a first‐order approximation in time, under a regularity assumption of u(x, t) ∈ C1([0, T]; C6(Ω)), while exhibiting order of convergence slightly more than O(k) in time. This allows for a much wider class of functions to be analyzed which was previously not possible under the L1‐method. We present numerical examples demonstrating these results and discuss future improvements and implications by using these techniques. [ABSTRACT FROM AUTHOR]

An analytical model is introduced to analyse moving Griffith crack in a monoclinic crystalline layer of finite width and infinite extent with moving parallel punch pressure acting at the bounding surface of the layer because of the propagation of plane waves under mechanical point loading. Formulation of the model includes coupled singular integral equations with Cauchy‐type singularities. The expression of stress intensity factor (SIF) at the tip of moving crack having constant point loading is established in the closed‐form by employing Hilbert transformation. Further, expression of SIF is deduced for some particular cases of the crystalline layer, that is, without punch pressure and anisotropy. For the sake of validation, the obtained results are matched with pre‐established and standard results. Numerical computations and graphical demonstrations have been carried out for crystalline materials with monoclinic symmetry like lithium niobate and lithium tantalate and for isotropic material as well to unravel the effect of punch pressure, crack length, distinct positions of acting point load and the velocity of crack on SIF. Further, influence of anisotropy has been traced out remarkably through comparative study that is one of the pinnacles of the present study. [ABSTRACT FROM AUTHOR]

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier‐type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener‐Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier‐type series are used to produce the solution formula of such equations, and a Shannon‐type sampling formula is also obtained. [ABSTRACT FROM AUTHOR]

This note reconsiders the marginal density of a threshold moving average process and proposes a simple yet effective numerical algorithm to implement that by solving an associated integral equation. This algorithm can also be applied to calculate stationary probability density or distribution functions of a few other types of nonlinear stationary stochastic processes numerically. [ABSTRACT FROM AUTHOR]

In this paper, we study an analog of the Gellerstedt problem for the third‐order loaded equation with boundary conditions on nonparallel characteristics in the hyperbolic domain of the equation. [ABSTRACT FROM AUTHOR]

Abstract: A butterfly‐based hierarchical LU factorization scheme for solving the PMCHWT equations for analyzing scattering from homogenous dielectric objects is presented. The proposed solver judiciously re‐orders the discretized integral operator and butterfly‐compresses blocks in the operator and its LU factors. The observed memory and CPU complexities scale as O(N log2N) and O(N1.5 log N), respectively. The proposed solver is applied to the analyses of scattering several large‐scale dielectric objects. [ABSTRACT FROM AUTHOR]

Abstract: In this article, an integral equation satisfied by the second moment function M2(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M2(t), when the first interarrival time has an exponential distribution. [ABSTRACT FROM AUTHOR]

This study is concerned with the dwell‐time stability for impulsive systems under periodic or aperiodic impulses. A Lyapunov‐like functional approach is established to study the stability for impulsive systems. The Lyapunov‐like functional is time‐varying and decreasing but is not imposed definite positive nor continuous. A specific Lyapunov‐like functional is constructed by introducing the integral of state together with the cross‐terms of the integral and impulsive states. A tight bounding is obtained for the derivative of this functional with the help of the improved Jensen inequality reported recently and the integral equation of the impulsive system. On the basis of the Lyapunov‐like functional approach, new dwell‐time‐dependent stability results with ranged dwell‐time, maximal dwell‐time and minimal dwell‐time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

An accurate expression for the exchange-correlation free energy f xc of homogeneous electron fluids at finite temperatures is presented on the basis of Singwi-Tosi-Land-Sjölander ( STLS) approximation. In addition to the derivation for the paramagnetic state, that for the ferromagnetic state is carried out afresh in which a correction in the strong Coulomb coupling regime is incorporated into the construction of the analytic expression as a function of the coupling constant and Fermi degeneracy. The fitting formula for f xc is then extended over any degree of spin polarization with the aid of available interpolation scheme. The proposed equation of state, called the iSTLS formula, shows reasonable agreement with the existing quantum Monte Carlo evaluations at finite temperatures in the paramagnetic state, thus giving a consensus for the thermodynamic functions between many-body theories and computer simulations. On the other hand, the current status for the agreement between various evaluations of f xc is relatively unsatisfactory in the ferromagnetic state, suggesting the necessity for further investigations. [ABSTRACT FROM AUTHOR]

We use a modification of Krasnoselskii's fixed point theorem introduced by Burton to show the periodicity and non-negativity of solutions for the nonlinear neutral differential equation with variable delay [ABSTRACT FROM AUTHOR]

In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated. [ABSTRACT FROM AUTHOR]

In the context of time harmonic wave scattering by piecewise homogeneous penetrable objects, we present a new variant of the multitrace boundary integral formulation, that differs from the local multitrace approach of (Jerez-Hanckes and Hiptmair, 2012) [13] by the presence of regularization terms involving boundary integral operators and localized at junctions i.e. points where at least three subdomains abut. We prove well-posedness and quasioptimal convergence of conforming Galerkin discretizations for this new formulation, and present numerical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2043-2062, 2015 [ABSTRACT FROM AUTHOR]

The Legendre pseudospectral method is developed for the numerical solution of nonlinear Duffing equation involving both integral and non-integral forcing terms. By using differentiation matrix, the problem is reduced to the solution of a system of algebraic equations. The method is general, easy to implement, and yields very accurate results. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed computational procedure. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality. [ABSTRACT FROM AUTHOR]

SUMMARY A parallelized multilevel fast multipole algorithm (MLFMA) is presented for simulating electromagnetic scattering from complex targets with anisotropic impedance surfaces. By employing both surface electric and magnetic currents as unknowns and weakly enforcing the anisotropic impedance boundary condition, a combined integral equation is formulated to generate a set of well-conditioned linear systems to be solved by MLFMA. To further improve the iterative convergence of the linear systems, a parallel sparse approximate inverse preconditioner is constructed from the near-field interaction of the system matrix. The MLFMA is parallelized to enable computation on a large number of processors for large-scale problems. Several numerical examples are presented to validate the algorithm and demonstrate its accuracy, scalability, and capability in handling large complex objects with anisotropic impedance surfaces. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Let k( ⋅ , ⋅ ) be a continuous kernel defined on Ω × Ω, Ω compact subset of [ABSTRACT FROM AUTHOR]

ABSTRACT Helmholtz decomposition (HD) is a vector analysis fundamental tool and plays an important role in electromagnetics (EM) and microwave engineering. Instead of applying HD to the EM solving process, this article proposes an integral equation based rigorous HD process to extract and analyze the known EM field. It provides much clearer insight into field coupling and radiation mechanism that is valuable to electromagnetic interference (EMI) and electromagnetic compatibility (EMC) analysis. Compared to the loop-tree based decomposition that is a quasi-HD, the proposed method is rigorous and frequency-independent. The algorithm verification and its application to coupling and resonating problems are presented. This method can provide a novel angle for the EM field analysis used in EMI/EMC, antennas, signal integrity, and relevant areas. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1838-1843, 2014 [ABSTRACT FROM AUTHOR]

Unlike synchronous processing, asynchronous processing is more efficient in biomedical and sensing networks applications as it is free from aliasing constraints and quantization error in the amplitude, it allows continuous–time processing and more importantly data is only acquired in significant parts of the signal. We consider signal decomposers based on the asynchronous sigma delta modulator (ASDM), a non‐linear feedback system that maps the signal amplitude into the zero‐crossings of a binary output signal. The input, the zero‐crossings and the ASDM parameters are related by an integral equation making the signal reconstruction difficult to implement. Modifying the model for the ASDM, we obtain a recursive equation that permits to obtain the non‐uniform samples from the zero‐time crossing values. Latticing the joint time‐frequency space into defined frequency bands, and time windows depending on the scale parameter different decompositions are possible. We present two cascade low‐ and high‐frequency decomposers, and a bank‐of‐filters parallel decomposer. This last decomposer using the modified ASDM behaves like a asynchronous analog to digital converter, and using an interpolator based on Prolate Spheroidal Wave functions allows reconstruction of the original signal. The asynchronous approaches proposed here are well suited for processing signals sparse in time, and for low‐power applications. [ABSTRACT FROM AUTHOR]

Empirical time-oxide layer thickness data of dry thermal oxidation of silicon were converted numerically into instantaneous growth rates by Tikhonov regularization. These growth rates are independent of any assumed kinetics of oxidation or functional form of the original data and can, therefore, be used in model testing of this important industrial process. A number of numerical issues in the Tikhonov regularization computation, for example, the expected monotonic decrease in growth rate with time and the large time span of some of the datasets, are addressed. Numerical results indicate that kinetic data presented in the form of growth rate-oxide layer thickness plots are more sensitive than the traditional time-oxide thickness plots for use in model testing and for parameter determination. The advantages of this new approach are demonstrated by three case studies covering the complete oxide thickness spectrum of interest to the microelectronic industry. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1810-1820, 2014 [ABSTRACT FROM AUTHOR]

Conventional control charts are often designed to optimize out-of-control average run length (ARL), while constraining in-control ARL to a desired value. The widely employed grid search approach in statistical process control (SPC) is time-consuming with unsatisfactory accuracy. Although the simulation-based ARL gradient estimators proposed by Fu and Hu [Manag Sci 45 (1999), 395-413] can alleviate this issue, it still requires a large number of simulation runs to significantly reduce the variance of gradient estimators. This article proposes a novel ARL gradient estimation approach based on integral equation for efficient analysis and design of control charts. Although this article compares with the results of Fu and Hu [Manag Sci 45 (1999), 395-413] based on the exponentially weighted moving average (EWMA) control chart, the proposed approach has wide applicability as it can generally fit into any control chart with Markovian property under any distributions. It is shown that the proposed method is able to provide a fast, accurate, and easy-to-implement algorithm for the design and analysis of EWMA charts, as compared to the simulation-based gradient estimation method. Moreover, the proposed gradient estimation method facilitates the computation of high-order derivatives that are valuable in sensitivity analysis. The code is written in Matlab, which is available on request. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 223-237, 2014 [ABSTRACT FROM AUTHOR]

SUMMARY This paper aims to develop a fast multigrid (MG) solver for a Fredholm integral equation of the first kind, arising from the 2D elastic frictional contact problem. After discretization on a rectangular contact area, the integral equation gives rise to a linear system with the coefficient matrix being dense, symmetric positive definite and Toeplitz. A so-called fast Fourier transform (FFT) smoother is proposed. This is based on a preconditioner M that approximates the inverse of the original coefficient matrix, and that is determined using the FFT technique. The iterates are then updated by Richardson iteration: adding the current residuals preconditioned with the Toeplitz preconditioner M. The FFT smoother significantly reduces most components of the error but enlarges several smooth components. This causes divergence of the MG method. Two approaches are studied to remedy this feature: subdomain deflation (SD) and row sum modification (RSM). MG with the FFT + RSM smoother appears to be more efficient than using the FFT + SD smoother. Moreover, the FFT + RSM smoother can be applied as an efficient iterative solver itself. The two methods related to RSM also show rapid convergence in a test with a wavy surface, where the Toeplitz structure is lost. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, 3D steady-state fluid flow in a porous medium with a large number of intersecting fractures is derived numerically by using collocation method. Fluid flow in the matrix and fractures is described by Darcy's law and Poiseuille's law, respectively. The recent theoretical development presented a general potential solution to model the steady-state flow in fractured porous media under a far-field condition. This solution is a hypersingular integral equation with pressure field in the fracture surfaces as the main unknown. The numerical procedure can resolve the problem for any form of fractures and also takes into account the interactions and the intersection between fractures. Once the pressure field and then the flux field in fractures have been determined, the pressure field in the porous matrix is computed completely. The basic problem of a single fracture is investigated, and a semi-analytical solution is presented. Using the solution obtained for a single fracture, Mori-Tanaka and self-consistent schemes are employed for upscaling the effective permeability of 3D fractured porous media. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT An improved scheme of integral equation-based overlapped domain decomposition method combined with an efficient direct solver based on hierarchical LU (H-LU) decomposition is proposed for the three-dimensional (3D) scattering problems. In this scheme, the H-LU direct method is utilized to solve the self-impedance matrix equation in each extended subdomain; simultaneously, the multilevel fast multipole algorithm is applied to complete the matrix vector product operation of mutual-impedance matrix between different subdomains. In the H-LU operation, a recompressed adaptive cross approximation technique is used to generate the low-rank approximations of the far-field matrices. After integrating all the techniques, the proposed scheme is very efficient especially for 3D electromagnetic scattering problems with multiple incident fields such as the computation of the monostatic radar cross section. Some examples are provided to demonstrate its accuracy and efficiency. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2027-2033, 2013 [ABSTRACT FROM AUTHOR]

ABSTRACT Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three-dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre-corrected fast Fourier transform (pFFT)-accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre-conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts. [ABSTRACT FROM AUTHOR]

We analyze electromagnetic scattering of transverse magnetic polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative index dielectric material. Such scattering problems are important for the modelization of, for example, light propagation in nano-optical components and metamaterials. The periodic scattering problem can be reformulated as a strongly singular volume integral equation, a technique that attracts continuous interest in the engineering community but has rarely received rigorous theoretic treatment. In this paper, we prove new (generalized) Gårding inequalities in weighted and unweighted Sobolev spaces for the strongly singular integral equation. These inequalities also hold for materials for which the real part of the material parameter takes negative values inside the diffraction grating, independently of the value of the imaginary part. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Y−ϕ(Z) ΙW]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function. [ABSTRACT FROM AUTHOR]

The article details a study on a procedure for computing partial derivatives of experimental data, published in wileyonlinelibrary.com on April 5, 2010. In order to obtain control over noise amplification, Tikhonov regularization, a specialized technique for handling ill-posed inverse problems, was used. Four practical examples that describe the implementation of the computation are presented. The study concludes that the method based on Tikhonov regulation produces reliable results when used to obtain partial derivatives of experimental data.

We present a fast approximate method for three-dimensional low frequency controlled source electro-magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea-bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation. [ABSTRACT FROM AUTHOR]

In this article, we consider two discrete-time risk models, in which dependent structures of the payments and the interest force are considered. Two autoregressive moving-average (ARMA) models are introduced to model the premiums and rates of interest, and the claims are assumed to be independent. Generalized Lundberg inequalities for the ruin probabilities are derived by using renewal recursive technique, which extend some known results. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the integral equation fast Fourier transform (IE-FFT) is implemented to solve the 3D full and partial coating scatterers. The real boundary condition is approximated by impedance boundary condition. The IE-FFT is utilized to accelerate the matrix-vector multiplication in the conjugate gradient (CG) iterative solver. And the Mesh Neighbor preconditioner is used to improve the iterative convergence of the CG solver. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 241–244, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24846 [ABSTRACT FROM AUTHOR]

Integral equation (IE) formulations solved by the Method of Moments (MoM) have been used successfully to address a vast variety of electromagnetic problems. Printed circuits embedded partially or totally in laterally bounded multilayered media such as microwave filters or planar antennas and their associated distribution networks are most efficiently treated by this technique. In the case that the structure as well as the excitation hold some symmetry requirements, simplifications may be applied on the problem leading to a considerable improvement in the reduction of computational time and the usage of resources. In this article, we have developed formulations providing theoretical background for applying different types of symmetry conditions in the framework of the MoM-based IE technique applied to printed circuits embedded in shielded multilayered media fed by coaxial lines. Additionally, a comprehensive convergence study has been performed to analyze the effect of mesh resolution and different aspect-ratios of the rectangular shield on the convergence rate of modal series representing the elements of the MoM matrix. Benefits of applying symmetry simplifications have been pointed out as well. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 221–226, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24868 [ABSTRACT FROM AUTHOR]

The “conventional” finite element-boundary integral (FE-BI) method suffers from two major drawbacks, one is the huge computer resources required by the dense BI submatrix; the other is the slow convergence rate of the resulting linear system of equations. In this article, both the drawbacks are investigated. First, the integral equation fast Fourier transform (IE-FFT) algorithm with a Gaussian interpolation scheme is employed to deal with the BI part. Second, an effective and simple preconditioner is developed for solving the matrix equation obtained from FE-BI method. Numerical results show that the proposed preconditioner can dramatically speed up the convergence of the FE-BI system, whatever the combined field integral equation (CFIE), the electric field integral equation (EFIE), and the magnetic field integral equation (MFIE) are employed on the truncation boundary. Some examples are given to demonstrate the accuracy and efficiency of the method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2065–2071, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24538 [ABSTRACT FROM AUTHOR]

In this article, a compound field integral equation approach has been applied to analyze the problem of quasi-waveguide structures, that is, structures consisting of a main waveguide with a constant cross section that may bear an arbitrary number of printed circuits backed by dielectric substrates. A detailed mathematical procedure is described to retrieve modal scattering parameters conventionally defined in planar multilayered structures excited by wave ports. In the case that the structure as well as the excitation holds symmetry requirements, simplifications may be applied to considerably improve the usage of computational resources. Formulations providing the theoretical background for applying symmetry conditions have also been developed in the context of this work. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2181–2186, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24575 [ABSTRACT FROM AUTHOR]

This article presents two practical applications of the Sources Reconstruction Method for antenna diagnostics and antenna manufacturing errors detection. The goal is to show the SRM capabilities to determine defective elements in antenna arrays as well as to detect irregularities in the surface of reflector antennas from the analysis of the aperture fields. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1664–1668, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24416 [ABSTRACT FROM AUTHOR]

The traditional thin dielectric sheet approximation (TDS) method models the electromagnetic scattering by thin dielectric sheet using surface integral equation. In this approximation, only the tangential current within the dielectric sheet is considered, and the vertical component is ignored. This article proposes a method that uses the volume integral equation solution to predict the vertical volume current and hence to improve the overall solution accuracy. The formulation is based on the hybrid surface (SIE) and volume integration equation (VIE) in which, the thin dielectric is modeled with SIE, and the thin layers are modeled by VIE. It is shown that the inclusion of the vertical current component does not increase memory and solution time. Numerical examples will be provided to demonstrate the effectiveness of this approach. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1978–1982, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23518 [ABSTRACT FROM AUTHOR]

Multiscalets in the multiwavelet family are used as the basis and testing functions in Galerkin's method. Since the multiscalets are orthogonal to their translations under the Sobolev inner product, the resulting Galerkin's method behaves like a collocation method but possesses the ability of derivative tracking for unknown functions in solving integral equations. The former makes the method simple in implementation and the latter allows to use coarse meshes in discretization. These robust features have been demonstrated in solving two-dimensional (2D) electromagnetic (EM) problems, but have not been exploited in three-dimensional (3D) scenarios. For 3D problems, the unknown functions in the integral equations are dependent on two coordinate variables. In order to preserve the use of coarse meshes for 3D cases, we realize the omnidirectional derivative tracking by tracking the directional derivatives along two orthogonal directions, or equivalently tracking the gradient. This process yields a nonsquare matrix equation and we use the least-squares method (LSM) to solve it. Numerical examples show that the multiscalet-based Galerkin's method is also robust in solving for 3D EM integral equations with a minor cost increase from LSM. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The solution of an integral equation using the method of moments leads to a system of linear equations. The resulting system of equations can be solved by direct and iterative methods. This paper introduces an iterative method utilizing Brezinski's θ algorithm. The algorithm has previously been used in accelerating the convergence of a scalar sequence. With the aid of two integral equations, it is shown that the algorithm is able to accelerate the convergence of a vector sequence resulting in the solution vector. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 589–592, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23155 [ABSTRACT FROM AUTHOR]