stability and convergence of the difference methods for the space time fractional advection diffusion equation abstract in this paper we consider a space time fractional advection dispersion equation stfade on a finite domain the stfade is obtained from the standard advection dispersion equation by replacing the first order time derivative by the caputo fractional derivative of order 0 1 and the first order and second order space derivatives by the riemman liouville fractional derivatives of order 0 1 and of order 1 2 respectively for the space fractional derivatives d x u x t and d x u x t we adopted the grunwald formula and the shift grunwald formula respectively we propose an implicit difference method idm and an explicit difference method edm to solve this equation stability and convergence of these methods are discussed using mathematical induction we prove that the idm is unconditionally stable and convergent but the edm is conditionally stable and convergent numerical results are in good agreement with theoretical analysis

loop star decomposition of basis functions in the discretization of the efie a general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder the proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions the completeness of the loop star basis is discussed employing the presented scheme the issue of the irrotational property of the nonsolenoidal functions is addressed

calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

an all frequency weakly singular surface integral equation for electromagnetism in dielectric media reformulation and well posedness analysis abstract we develop and analyze a surface integral equation sie whose solution pertains to numerical simulations of propagating time harmonic electromagnetic waves in three dimensional dielectric media the formulae to evaluate the far field pattern and propagation of the electric and magnetic fields in the interior and exterior of a dielectric body through surface integrals require the solution of a 2 2 system of weakly singular sies for the two unknown electric and magnetic fields at the interface surface of the dielectric body the sie is governed by an operator that is of the classical identity plus compact form the tangential surface currents and normal surface charges of the dielectric model can be easily computed from the surface electric and magnetic fields a novel feature of that second kind sie is that when augmented with two stabilization scalar equations the corresponding reformulation does not suffer from spurious resonances or low frequency breakdown we analyze this novel feature of the sie in both the sobolev and continuous function space settings without any tangential constraints by proving the uniqueness of the stabilized solution of the sie for all positive incident wave frequencies and physically appropriate real complex dielectric media constants using numerical examples we also demonstrate that without our stabilization constraints the 2 2 second kind sie suffers from some spurious resonances and incorporating the two additional scalar equations removes these spurious resonances at the zero frequency limit the two stabilization scalar equations are automatically satisfied and the 2 2 formulation nicely decouples to a well posed system at the zero frequency limit our analysis to establish the equivalence of the classical dielectric model governed by the maxwell equations and the all frequency sie based representation provides a natural decomposition of the surface unknowns into their tangential currents and normal charges the salient features of the representation and well posedness analysis provide a tool to develop a new class of efficient and high order algorithms with numerical analysis for simulation of the three dimensional dielectric media model from low to high frequencies

improving conditioning of electromagnetic surface integral equations using normalized field quantities when the surface integral equation method is applied to study electromagnetic scattering by dielectric or composite metallic and dielectric objects the unknowns i e the electric and magnetic surface current densities and the elements of the system matrix are often of the very different scales as a consequence the system matrix may have a high singular value condition number an efficient method is presented to balance the unknowns and the integral equations and the elements of the system matrix too the method is based on the use of normalized field quantities and unknowns and carefully chosen scaling factors in the case of dielectric and composite objects the condition numbers of the sie matrices can be reduced with several orders of magnitudes by the developed method in the case of high contrast objects or if the frequency is very low the developed method leads also to a clear improvement on the convergence of iterative solutions

comparison of integral equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm we consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations we compare various formulations when the objects are discretized with rao wilton glisson functions and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm mlfma for large problems we show that a combined field formulation namely the electric and magnetic current combined field integral equation jmcfie requires fewer iterations than other formulations within the context of mlfma in addition to its efficiency jmcfie is also more accurate than the normal formulations and becomes preferable especially when the problems cannot be solved easily with the tangential formulations

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

broadband muller mlfma for electromagnetic scattering by dielectric objects the multilevel fast multipole algorithm mlfma is very efficient for solving large scale electromagnetic scattering problems however at low frequencies or when the discretization is small compared with the wavelength both the mlfma and the underlying integral equation formulation typically suffer from a subwavelength breakdown for the electromagnetic scattering from a homogeneous dielectric object we obtain a stable and well conditioned surface integral formulation using a variant of the classical muumlller formulation and linear basis functions to overcome the subwavelength breakdown of the mlfma we use both propagating and evanescent plane waves to represent the fields the implementation is based on a combination of the spectral representation of the green s function and rokhlin s translation formula we also present a new interpolation scheme for the evanescent part which significantly improves the error controllability of the mlfma implementation several numerical results verify both the error controllability and scalability of the proposed algorithm

surface integral equation method of moments with multiregion basis functions applied to plasmonics a surface integral equation method of moments sie mom approach is presented for the solution of multiple homogeneous penetrable bodies the problem is formulated using multiregion mr piecewise vector basis functions defined uniformly on the boundary surfaces interfaces and line junctions the mr bases are oriented functions implicitly satisfying the boundary conditions their use greatly simplifies the formulation and thereby the implementation for the solution of arbitrary complex composite problems having multiple junctions moreover the generation of the mr functions involves a negligible overhead at the setup numerical examples are presented to demonstrate the accuracy and versatility of sie mom with mr basis functions in plasmonics where this approach remains much unexplored

an efficient surface integral equation solution to em scattering by chiral objects above a lossy half space in this paper an extension of the electric magnetic current combined field integral equation jmcfie is presented for the efficient analysis of em scattering by an arbitrary shaped homogenous chiral object located above a lossy half space this formulation can lead to a well tested equation system using the method of moments mom solution with the vector triangular basis functions and galerkin s method the multilevel fast multipole algorithm mlfma is then employed to reduce the memory requirement and computational complexity of the mom solution the inner outer flexible generalized minimal residual fgmres method is used to further speed up the convergence the accuracy and efficiency are confirmed with a couple of numerical examples

n dimensional fractional fokker planck equation and its solutions for anomalous radial two phase flow in porous media in this paper we present a time fractional fokker planck equation ffpe for radial two phase flow of liquid and gas in porous media the ffpe of order a is solved for both two and three dimensional flow patterns using the laplace transform method the general solutions of the ffpe for both two and three dimensional flows are given as a convolution integral of the input and a kernel in the laplace domain special solutions for a large value and a periodic boundary condition are also given in the time domain when the inverse laplace transform can be found analytically the ffpe for two phase flow in porous media presented in this paper is the first report of its kind

a surface integral equation formulation for low frequency scattering from a composite object a surface integral equation formulation is derived for low frequency scattering from a composite object this formulation allows those algorithms for finding the loop tree basis on simple surfaces to be applied to the complicated interfaces of a composite object by including the residue term in the k operator the present formulation induces the interface boundary conditions automatically and the resultant matrix equation can be solved directly without using the o n sup 2 number of unknowns reduction scheme numerical results validate that the algorithm is stable even at extremely low frequencies and for closely spaced structures

identification of non linear systems using multi scale ridges and skeletons of the wavelet transform abstract a new procedure of non linear system identification is presented the procedure employs the slowly varying time dependent amplitude and phase functions of the impulse response of the system these instantaneous characteristics are obtained from the ridges and skeletons of the wavelet transform the ridge extraction procedure uses the modulus of the transform and involves a combinatorial optimization algorithm based on simulated annealing the method is illustrated using two simple simulated examples it is shown that the procedure can be used for multi degree of freedom systems due to the frequency localization property of the continuous grossman morlet wavelets

damage size estimation by the continuous wavelet ridge analysis of dispersive bending waves in a beam the damage assessment in a structure consists of the estimation of its location and extent the objective of this work is to assess the damage size using the ratio of the incident wave toward and the reflected wave from the damage since waves to be analyzed are of the bending type the measured signals are highly dispersive it is almost impossible to estimate the magnitude ratio alone in the time domain so we propose to use the continuous wavelet transform of the measured signal and perform the ridge analysis in order to extract accurately the magnitudes of the incident and the reflected waves for a range of frequencies of interest from the measured wave signal wave experiments are conduced in a slender cylindrical beam and the magnetostrictive sensors are used to capture the bending waves in the beam to correlate the magnitude ratio with the damage size we employ the timoshenko beam theory several experiments are conducted to check the effectiveness of the proposed wavelet based method

weighted average finite difference methods for fractional diffusion equations a class of finite difference methods for solving fractional diffusion equations is considered these methods are an extension of the weighted average methods for ordinary non fractional diffusion equations their accuracy is of order x 2 and t except for the fractional version of the crank nicholson method where the accuracy with respect to the timestep is of order t 2 if a second order approximation to the fractional time derivative is used their stability is analyzed by means of a recently proposed procedure akin to the standard von neumann stability analysis a simple and accurate stability criterion valid for different discretization schemes of the fractional derivative arbitrary weight factor and arbitrary order of the fractional derivative is found and checked numerically some examples are provided in which the new methods numerical solutions are obtained and compared against exact solutions

electromagnetic modeling of high magnetic contrast media using calderon preconditioning in this contribution we present a calderon preconditioner for a novel single source equation to efficiently model electromagnetic scattering problems involving high magnetic contrasts through analysis of the spectral properties of the system matrix after discretization it is shown that this formulation does not break down when high permeabilities are present which was an unresolved problem of the calderon preconditioned poggio miller chan harrington wu tsai method the adopted discretization scheme which involves rao wilton glisson and buffa christiansen basis functions allows for an easy integration in existing commercial method of moments software the efficiency and accuracy of the presented method is corroborated by numerical examples c 2018 elsevier ltd all rights reserved

stable discretization of combined source integral equation for scattering by dielectric objects a stable discretization scheme is presented for the combined source integral equation csie of electromagnetic scattering from three dimensional arbitrarily shaped homogeneous dielectric objects the discretization scheme uses both the primary rao wilton glisson rwg and the dual buffa christiansen bc functions and avoids numerical problems that would appear if the equations were discretized with the rwg functions only

ridges reconstruction based on inverse wavelet transform ridges always carry important physical information in practice ridge reconstruction based on inverse wavelet transform is studied in this article it is emphasized that the points within the neighbor area have to be added in the reconstruction to avoid energy lost however no discussion has been proposed about how to choose the neighbor area up to now although it is the key to achieve good performance a formula is given in this article to calculate the width of the neighbor area which varies with scale and the signal itself some examples are given in this article to show the performance of the proposed method which manifests that the method works very well for signals with multiple components as long as there is no cross section between them it also works well when the signal to noise ratio is not very low

fractional wave equation with a frictional memory kernel of mittag leffler type abstract in this paper we give an analytical treatment of a fractional wave equation with caputo time fractional derivative and frictional memory kernel of mittag leffler type this problem generalizes a recently solved problem 62 of a wave equation for a vibrating string in presence of a fractional friction with power law memory kernel such equations can be used in the context of modeling processes in complex and viscoelastic media

spectral analysis of fractional kinetic equations with random data we present a spectral representation of the mean square solution of the fractional kinetic equation also known as fractional diffusion equation with random initial condition gaussian and non gaussian limiting distributions of the renormalized solution of the fractional in time and in space kinetic equation are described in terms of multiple stochastic integral representations

nested equivalent source approximation for the modeling of penetrable bodies a multiregion nested equivalent source approximation nesa is presented for the fast analysis of electromagnetic scattering by piecewise homogeneous media nesa was introduced for the analysis of metallic problems at low and moderate frequencies and later extended to the fully dynamic case with the introduction of a directional scheme in this communication we modify the wideband scheme for the analysis of arbitrary penetrable media the asymptotic computational costs of the algorithm are compatible with the state of the art factorizations namely linear and quasi linear o n and o n log n for moderate and high frequency problems respectively numerical examples validate the accuracy and favorable computational cost of nesa when applied to penetrable bodies

numerical characterization of divergence conforming constrained basis functions for surface integral equations this paper presents an algebraic method of generating arbitrary order basis functions suitable for use in moment methods the basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions leading to a matrix representation of the constraint condition the desired bases are then found through use of the singular value decomposition divergence conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations appropriate constraints for enforcing normal continuity at cell boundaries are discussed a variety of problems are analyzed using the constrained bases and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order

two high order numerical algorithms for solving the multi term time fractional diffusion wave equations in this paper we apply a high order difference scheme and galerkin spectral technique for the numerical solution of multi term time fractional partial differential equations the proposed methods are based on a finite difference scheme in time the time fractional derivatives which have been described in caputo s sense are approximated by a scheme of order o 3 1 2 and the space derivative is discretized with a fourth order compact finite difference procedure and galerkin spectral method we prove the unconditional stability of the compact procedure by coefficient matrix property the l convergence of the compact finite difference method has been proved by the energy method also we obtain an error estimate for galerkin spectral method numerical results are provided to verify the accuracy and efficiency of the proposed schemes

a second order accurate numerical method for the two dimensional fractional diffusion equation spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow finance and others in this paper we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation this numerical method combines the alternating directions implicit adi approach with a crank nicolson discretization and a richardson extrapolation to obtain an unconditionally stable second order accurate finite difference method the stability and the consistency of the method are established numerical solutions for an example super diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

a comparative study of surface integral equations for accurate and efficient analysis of plasmonic structures surface integral equations which are commonly used in electromagnetic simulations have recently been applied to various plasmonic problems while there is still no complete agreement on which formulations provide accurate and efficient solutions in this paper we present the strong material dependences of the conventional formulations revealing their contradictory performances for different problems we further explain the numerical problems in the constructed matrix equations shedding light on the design of alternative formulations that can be more accurate efficient and stable than the existing ones based on our observations in the limit cases we present a new formulation namely a modified combined tangential formulation mctf which provides stable solutions of plasmonic problems in wide ranges of negative permittivity values the favorable properties of mctf in comparison to other formulations are demonstrated not only on canonical problems but also on realistic cases involving nanowires

divergence conforming constrained basis functions for hexahedral volume elements this communication presents an algebraic method for constructing arbitrary order divergence conforming basis functions on hexahedral volume elements the appropriate constraints within and on the boundaries of elements are provided in particular the handling of faces where quantities are discontinuous is discussed the resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

least squares finite element solution of a fractional order two point boundary value problem in this paper a theoretical framework for the least squares finite element approximation of a fractional order differential equation is presented mapping properties for fractional dimensional operators on suitable fractional dimensional spaces are established using these properties existence and uniqueness of the least squares approximation is proven optimal error estimates are proven for piecewise linear trial elements numerical results are included which confirm the theoretical results

numerical techniques for the variable order time fractional diffusion equation abstract in this paper we consider the variable order time fractional diffusion equation we adopt the coimbra variable order vo time fractional operator which defines a consistent method for vo differentiation of physical variables the coimbra variable order fractional operator also can be viewed as a caputo type definition although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature here an approximate scheme is first proposed the stability convergence and solvability of this numerical scheme are discussed via the technique of fourier analysis numerical examples are provided to show that the numerical method is computationally efficient

identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform we consider the free response of a nonlinear vibrating system using the ridges and skeletons of the continuous wavelet transform we identify weak nonlinearities on damping and stiffness and estimate their physical parameters the crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform the method is applied to simulated single degree of freedom systems and multi degree of freedom systems with nonlinearities on damping and stiffness experimental validation of the nonlinear identification and parameter estimation method is presented the experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor

combined field integral equation formulation for inhomogeneous two and three dimensional bodies the junction problem a combined field integral equation cfie formulation is presented for two and three dimensional bodies having discrete dielectric and conducting regions a three dimensional case is restricted to bodies of revolution bors the two dimensional case is analogous to the bor case when the fourier mode number is zero the method of moments mm is used to solve the cfie in terms of two integral operators it is shown that the cfie formulation yields accurate answers for scattering problems where the scatterer may be internally resonant the cfie results were validated using mie series results and measured data the junction problem associated with the cfie based formulation is explicated and several geometries with multiple junctions are used to validate the general cfie formulation a number of configurations are tested where the penetrable region consisted of a free space coating extensive numerical studies have shown that such limiting cases are sensitive indicators of the stability of mm solutions and allow direct comparison of different configurations

fractional extensions of the temperature field problems in oil strata we consider fractional extensions of the incomplete lumped formulation and the lumped formulation of the temperature field problems in oil strata laplace transform is used to solve the corresponding heat equations with an additional term representing the internal heat sources efros theorem a generalized form of the laplace convolution is used to obtain the analytic solutions special cases are mentioned

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

dynamic testing of nonlinear vibrating structures using nonlinear normal modes modal testing and analysis is well established for linear systems the objective of this paper is to progress toward a practical experimental modal analysis ema methodology of nonlinear mechanical structures in this context nonlinear normal modes nnms offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena yet they have a clear and simple conceptual relation to the classical linear normal modes lnms a nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single nnm during the experiments with the help of time frequency analysis the energy dependence of nnm modal curves and their frequencies of oscillation are then extracted from the time series the proposed methodology is demonstrated using two numerical benchmarks a two degree of freedom system and a planar cantilever beam with a cubic spring at its free end

null field preconditioner with selected far field contribution for 3 d full wave efie in this paper a stable and effective preconditioner for the method of moments based electric field integral equation matrix based on the null field method is presented to expedite the convergence of krylov subspace based fast iterative solution the preconditioner is computed from all near field blocks and selected far field blocks in accordance with the null field procedure the final form of the preconditioner is block diagonal and therefore generates no additional fill ins in its inverse and is also amenable to parallelization a complexity analysis is presented to show the near linear cost of preconditioner construction and usage in terms of computation time and memory the numerical experiments with a sequential implementation demonstrate on an average 1 5 3 times speed up in the iterative solution time over threshold dependent incomplete lu based preconditioners

efficient surface integral equation using hierarchical vector bases for complex em scattering problems a set of hierarchical divergence conforming vector basis functions based on curved triangular patches is presented for method of moment mom solutions of surface integral equations in this paper the higher order method of combined field integral equation cfie solves perfect electric conductor electromagnetic scattering problems the higher order electric magnetic current combined field integral equation jmcfie formulations solves dielectric objects and their combination is able to efficiently analyzes the scattering of hybrid pec dielectric objects the expressions of the divergence conforming hierarchical basis functions up to order 3 5 are reported in this paper the multilevel fast multipole algorithm mlfma is then employed to reduce the memory requirements and computational complexity numerical experiments indicate that the proposed hierarchical vector basis functions can provide well conditioned linear system for iterative solution

homotopy perturbation method to time fractional diffusion equation with a moving boundary condition homotopy perturbation method is successfully extended to solve time fractional diffusion equation with a moving boundary condition and an approximate solution is obtained the comparison with the exact solution shows that the approximate solution is sufficiently accurate for practical application in most cases

on a low frequency and refinement stable pmchwt integral equation leveraging the quasi helmholtz projectors classical poggio miller chan harrington wu tsai pmchwt formulations for modeling radiation and scattering from penetrable objects suffer from ill conditioning when the frequency is low or when the mesh density is high the most effective techniques to solve these problems unfortunately either require the explicit detection of the so called global loops of the structure or suffer from numerical cancellation at extremely low frequency in this contribution a novel regularization method for the pmchwt equation is proposed which is based on the quasi helmholtz projectors this method not only solves both the low frequency and the dense mesh ill conditioning problems of the pmchwt but it is immune from low frequency numerical cancellations and it does not require the detection of global loops this is obtained by projecting the range space of the pmchwt operator onto a dual basis by rescaling the resulting quasi helmholtz components by replicating the strategy in the dual space and finally by combining the primal and the dual equations in a calderon like fashion implementation related treatments and details alternate the theoretical developments in order to maximize impact and practical applicability of the approach finally numerical results corroborate the theory and show the effectiveness of the new schemes in real case scenarios

novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts we present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three dimensional dielectric objects with arbitrarily low contrasts conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low i e when the electromagnetic material parameters of the scatterer and the host medium are close to each other we propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right hand side of the equations using fictitious incident fields then only the radiating currents are solved to calculate the scattered fields accurately this technique can easily be applied to the existing implementations of conventional formulations it requires negligible extra computational cost and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm we show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low contrast objects

continuous wavelet transform for modal identification using free decay response abstract this paper deals with the use of the continuous wavelet transform for system identification purposes the wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform a complete procedure for modal identification from free responses based on the continuous wavelet transform is presented two difficulties during the implementation of this technique are highlighted the edge effect and the choice of the time frequency localization of the wavelet transform some upper and lower bounds for the mother wavelet s parameters are given in order to improve the numerical computation three complex valued mother wavelets are studied and the full procedure is applied to a damped discrete system the correct choice of the mother wavelet s parameters leads to an accurate identification of the modal parameters

finite element method for the space and time fractional fokker planck equation we develop the finite element method for the numerical resolution of the space and time fractional fokker planck equation which is an effective tool for describing a process with both traps and flights the time fractional derivative of the equation is used to characterize the traps and the flights are depicted by the space fractional derivative the stability and error estimates are rigorously established and we prove that the convergent order is o k 2 alpha h mu where k is the time step size and h the space step size numerical computations are presented which demonstrate the effectiveness of the method and confirm the theoretical claims

uniform surface integral equation formulation for mixed impedance boundary conditions a numerical approach based on the surface integral equation sie method is developed for the analysis of time harmonic electromagnetic scattering by impenetrable objects equipped with mixed impedance boundary conditions mibcs mibc is an axially anisotropic generalization of the conventional isotropic leontovich impedance boundary condition the developed sie formulation utilizes surface helmholtz decomposition the self dual formulation of yan and jin and loop and star rwg functions a combined field formulation is applied to avoid internal resonances

a single boundary implicit and fft accelerated time domain finite element boundary integral solver a novel time domain finite element boundary integral fe bi solver for analyzing broadband scattering and radiation from free standing electromagnetically large and perfect electrically conducting platforms supporting inhomogeneous and geometrically intricate structures is presented the solver has three distinctive features that render it especially attractive for broadband analysis of installed antennas i the fe and bi solver components are hybridized using a single surface interface ii the hybrid equations are solved by an implicit time marching scheme accelerated by an outer jacobi iterative solver that leverages inner direct fe and iterative bi solvers iii the bi solver component is accelerated by a distributed memory parallel implementation of the time domain adaptive integral method based on the message passing interface the accuracy late time stability and performance of the proposed time domain fe bi solver are demonstrated via its application to various scattering and radiation problems moreover the solver is used to characterize conformally mounted antennas on several platforms including an aircraft

stabilization of integral equation formulations for the accurate solution of scattering problems involving low contrast dielectric objects the solution of scattering problems involving low contrast dielectric objects with three dimensional arbitrary shapes is considered using the traditional forms of the surface integral equations scattered fields cannot be calculated accurately if the contrast of the object is low therefore we consider the stabilization of the formulations by extracting the nonradiating parts of the equivalent currents we also investigate various types of stable formulations and show that accuracy can be improved systematically by eliminating the identity terms from the integral equation kernels traditional and stable formulations are compared not only for small scatterers but also for relatively large problems solved by employing the multilevel fast multipole algorithm stable and accurate solutions of dielectric contrasts as low as 10 4 are demonstrated on problems involving more than 250000 unknowns

some boundary value problems of temperature fields in oil strata we consider two boundary value problems related to the temperature fields in oil strata laplace and a generalized hankel transform are used to obtain the desired solutions efro s theorem which is a modified form of the convolution theorem for the laplace transform is generalized using confluent hypergeometric function particular cases of our results established here are in agreement with some known results given in the literature

exponentially converging nystrom methods in oblique diffraction of arbitrarily polarized waves by bianisotropic chiral cylinders with arbitrary smooth cross section we study oblique diffraction of arbitrarily polarized plane waves by a uniform homogeneous bianisotropic cylinder with arbitrarily shaped smooth boundary following a boundary integral equations formulation we develop a 4 4 system of combined field integral equations and another 4 4 system of muller type fredholm integral equations both these systems having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns are of the second kind and uniquely solvable efficient discretization via simple and rapidly converging nystrom algorithms enables one to obtain highly accurate results even for electrically large objects the proposed solution technique a fully accounts for the singular nature of the kernels b yields simple closed form expressions for all matrix elements and c appears to converge exponentially versus matrix size the analogous diffraction problem for an arbitrarily shaped smooth chiral cylinder may be treated as a simple special case of the present analysis

an eigencurrent approach to the analysis of electrically large 3 d structures using linear embedding via green s operators we present an extension of the linear embedding via green s operators lego procedure for efficiently dealing with 3 d electromagnetic composite structures in lego s notion we enclose the objects forming a structure within arbitrarily shaped domains bricks which by invoking the equivalence principle we characterize through scattering operators in the 2 d instance we then combined the bricks numerically in a cascade of successive embedding steps to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects in the 3 d case however this process becomes quite soon impracticable in that the resulting scattering matrices are too big to be stored and handled on most computers to circumvent this hurdle we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure which can be written analytically in terms of scattering operators of the bricks and transfer operators among them we then solve this equation by the method of moments combined with the eigencurrent expansion method which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures

a higher order multilevel fast multipole algorithm for scattering from mixed conducting dielectric bodies a higher order multilevel fast multipole algorithm mlfma is presented for computing electromagnetic scattering from three dimensional bodies comprising both conducting and dielectric objects the problem is formulated using the poggio miller chang harrington wu tsai 1973 1977 approach for multiple homogeneous dielectric objects and the combined field approach for conducting objects the resultant integral equations are discretized by the method of moments mom in which the conducting and dielectric surfaces interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling an implicit matrix filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions the resultant numerical system is then solved by mlfma which is tailored to accommodate the material properties of dielectric scatterers and the solution is accelerated using an incomplete lu decomposition preconditioner numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems

a multiple grid adaptive integral method for multi region problems a multiple grid extension of the adaptive integral method aim is presented for fast analysis of scattering from piecewise homogeneous structures the proposed scheme accelerates the iterative method of moments solution of the pertinent surface integral equations by employing multiple auxiliary cartesian grids if the structure of interest is composed of k homogeneous regions it introduces k different auxiliary grids it uses the k th auxiliary grid first to determine near zones for the basis functions and then to execute aim projection propagation interpolation and near zone pre correction stages in the k th region thus the aim stages are executed a total of k times using different grids and different groups of basis functions the proposed multiple grid aim scheme requires a total of o n nz near k n k clogn k c operations per iteration where n nz near denotes the total number of near zone interactions in all regions and n k c denotes the number of nodes of the k th cartesian grid numerical results validate the method s accuracy and reduced complexity for large scale canonical structures with large numbers of regions up to 106 degrees of freedom and 103 regions moreover an investigation of hf band wave propagation in a loblolly pine forest model demonstrates the method s generality and practical applicability multiple grid aim accelerated simulations with various tree models show that higher fidelity models for the trunk material and branch geometry are needed for accurate calculation of horizontally polarized field propagation while lower fidelity models can be satisfactory for analyzing vertically polarized field propagation

finite difference methods for fractional dispersion equations abstract in this paper the fractional weighted average finite difference method for space fractional advection dispersion equation is proposed which is based on shifted grunwald formula this method is unconditionally stable consistent and convergent a numerical example is given and the numerical results verify the theoretical conclusions

incomplete lu preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems we consider the preconditioned iterative solution of large dense linear systems where the coefficient matrix is a complex valued matrix arising from discretizing the integral equation of electromagnetic scattering for some scattering structures this matrix can be poorly conditioned the main purpose of this study is to evaluate the efficiency of a class of incomplete lu ilu factorization preconditioners for solving this type of matrices we solve the electromagnetic wave equations using the bicg method with an ilu preconditioner in the context of a multilevel fast multipole algorithm mlfma the novelty of this work is that the ilu preconditioner as constructed using the near part block diagonal submatrices generated from the mlfma experimental results show that the ilu preconditioner reduces the number of bicg iterations substantially compared to the block diagonal preconditioner the preconditioned iteration scheme also maintains the computational complexity of the mlfma and consequently reduces the total cpu time

generalized differential transform method application to differential equations of fractional order abstract in this paper we propose a new generalization of the one dimensional differential transform method that will extend the application of the method to differential equations of fractional order the new generalization is based on generalized taylor s formula and caputo fractional derivative several illustrative examples are given to demonstrate the effectiveness of the obtained results the new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives

application of combined field integral equation for electromagnetic scattering by dielectric and composite objects combined field integral equation cfie is applied for computing electromagnetic scattering by arbitrarily shaped three dimensional dielectric and composite objects the objectives of this paper are as follows first to present a cfie formulation which can be used in the analysis of piecewise dielectric and composite metallic and dielectric objects with junctions second to show that properly choosing the coupling coefficients of the equations the conditioning of the discretized matrix equation can be essentially improved and rapidly converging iterative solutions can be obtained even without preconditioning

synthetic functions analysis of large aperture coupled antennas the application is described the synthetic function expansion sfx approach to large arrays of aperture coupled antennas the problem is formulated in terms of coupled magnetic field continuity integral equations mfcie and electric field integral equations efie and discretized via the method of moments mom the sfx is a domain decomposition technique on each block of the broken down structure functions are generated with domain over the entire block these ldquosynthetic functionsrdquo sf are obtained from the solution of the electromagnetic problem for the isolated block upon specification of appropriate sources on the block bounding box and from a further singular value decomposition svd based procedure to select the relevant terms the complete problem is solved using the sfs as basis functions for the mom this results in a strong reduction of the mom matrix size applications are presented to configurations of open and cavity backed radiators

mixed inner outer iteration technique based surface integral equations for fast solving em scattering from penetrable objects in this paper a mixed inner outer iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures the most important novelty of the proposed technique is combining the tangential poggio miller chang harrington wu tsai as outer iteration and the electric magnetic current combined field integral equation as inner iteration respectively in this case the new method offers the guarantee of high accuracy with faster convergence especially for electrically dielectric structures in large scale furthermore it presents an excellent compatibility with sparse approximate inverse preconditioning numerical results are given to demonstrate the accuracy efficiency and compatibility of the proposed method

new solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation a physical mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order in this paper an anomalous subdiffusion equation asub de is considered a new implicit numerical method inm and two solution techniques for improving the order of convergence of the inm for solving the asub de are proposed the stability and convergence of the inm are investigated by the energy method some numerical examples are given the numerical results demonstrate the effectiveness of theoretical analysis these methods and supporting theoretical results can also be applied to other fractional integro differential equations and higher dimensional problems

accelerated computation of the free space green s function gradient of infinite phased arrays of dipoles in this communication we provide an efficient algorithm for the evaluation of the semi infinite array green s function sagf for a semi infinite planar periodic phased array of dipoles in free space for observation points not too far from the array plane the algorithm uses a hybrid spectral spatial representation of the green s function accelerated with the levin t method that we show to be faster than the shanks method for observation points sufficiently far away from the array plane we show that the sagf is efficiently evaluated by using asymptotic field expressions asymptotics is also used to explain the loss of accuracy of the levin t accelerator in certain regions and a correction procedure is proposed to overcome this problem

a method for detecting damage induced nonlinearities in structures using information theory abstract in this work a new approach is presented for detecting the presence of damage induced nonlinearities in structures from measurements of structural dynamics two different information theoretic it measures the time delayed mutual information and the time delayed transfer entropy are used to provide a probabilistic measure of the coupling between structural components these measures may be used to capture both linear and nonlinear relationships among time series data the formula for both quantities is derived for a linear five degree of freedom system subject to gaussian excitation an algorithm is then described for computing the it metrics from time series data and results are shown to agree with theory we then show that as the coupling between the structure s components changes from linear to nonlinear the information flow can be used to indicate the degree of nonlinearity deviations from a linear model are quantified statistically by generating surrogate data sets that by construction possess only linear second order correlations we then apply the proposed algorithms to both the original data and the surrogates differences in the results are shown to be proportional to the degree of nonlinearity this result is shown to be independent of global changes in stiffness and is therefore unaffected by certain models of environmental variability furthermore the method provides an absolute measure of nonlinearity and therefore does not require a baseline data set for making comparisons this approach is discussed in the context of structural health monitoring where damage is often associated with structural nonlinearity

computation of scattering by db objects with surface integral equation method electromagnetic scattering by objects with a db boundary condition normal components of the electric and magnetic flux densities d and b vanish at the boundary surface is investigated scattering of arbitrary shaped three dimensional objects is analyzed with the surface integral equation method a significant difference compared to the more conventional boundary conditions is that the uniqueness of the solution to the scattering problem with db boundary depends on the connectivity of the object for a simply connected object the solution is unique but for a multiply connected object some additional conditions are required it appears that these additional conditions are satisfied if divergence free basis functions are used to expand the unknown surface current densities the developed method is applied to calculate polarizabilities scattering efficiencies and radar cross sections rcs of the db sphere and cube and the results are compared with those of the pec cube and sphere

well conditioned muller formulation for electromagnetic scattering by dielectric objects numerical solution of electromagnetic scattering by homogeneous dielectric objects with the method of moments mom and rao wilton glisson rwg basis functions is discussed it is shown that the low frequency breakdown associated to the mom solution of scattering by dielectric objects can be avoided by the classical muller formulation without the loop tree or loop star basis functions two variations of the muller formulation t mu spl uml ller and n muller are considered it is demonstrated that only the n muller formulation with the galerkin method and rwg functions gives stable solution discretization of the n muller formulation leads to a well conditioned matrix equation and rapidly converging iterative solutions on a wide frequency range from very low frequencies to microwave frequencies at zero frequency the n muller formulation decouples into the electrostatic and magnetostatic integral equations

identification of coupled non linear modes from free vibration using time frequency representations abstract a new method based on time frequency representations is presented for identifying the non linear modal parameters of a multi degree of freedom non linear lightly damped mechanical system the coupled non linear modes are first introduced it is shown that by using the coupled non linear modes the free response can be expressed as a linear combination of frequency and amplitude modulated components this suggests the use of time frequency methods to characterize these modulation laws and then identify the coupled non linear modes these modulation laws are extracted by using an extended definition of the so called ridges of the continuous gabor transform which enables a more accurate estimation an identification procedure of the coupled non linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non linear elastic dynamic systems

a numerical implementation of a modified form of the electric field integral equation the details of a galerkin discretization scheme for a modified form of the electric field integral equation are outlined for smooth three dimensional perfectly conducting scatterers limitations of the divergence conforming finite element bases in preserving the self stabilizing properties of the electric field integral equation operator are indicated a numerically efficient alternative is outlined which relies on an operator based helmholtz decomposition the condition number of the resulting matrix equation is demonstrated to be frequency independent for scattering from a perfectly conducting sphere at various frequencies

a generalized reaction theorem that eliminates internal resonances in the electric and magnetic field integral equations this paper presents stable magnetic field and electric field integral equation formulations for exterior electromagnetic scattering by either penetrable or perfectly conducting closed bodies of general shape the development relies on an extension of the conventional reciprocity theorem allowing the fields produced by some combination of sources in one environment to be connected with the fields generated by another combination of sources in a different environment by the use of lossy metamaterials the internal resonance problem inherent to the original versions is eliminated and thus the new formulations are amenable to a unique highly accurate and well conditioned solution

a tau approach for solution of the space fractional diffusion equation fractional differentials provide more accurate models of systems under consideration in this paper approximation techniques based on the shifted legendre tau idea are presented to solve a class of initial boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain the fractional derivatives are described in the caputo sense the technique is derived by expanding the required approximate solution as the elements of shifted legendre polynomials using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations from the computational point of view the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use

the third kind chebyshev wavelets collocation method for solving the time fractional convection diffusion equations with variable coefficients in this paper a numerical method based on the third kind chebyshev wavelets is proposed for solving a class of time fractional convection diffusion equations with variable coefficients the third kind chebyshev wavelets operational matrices of the integer order integration and the fractional order integration are derived respectively they are utilized to reduce the problem to a system of linear algebraic equations by combining the collocation method the uniform convergence analysis and error estimation for the third kind chebyshev wavelets expansion are investigated illustrative examples are given and the numerical results are presented to demonstrate the efficiency and accuracy of the proposed method

system identification in frequency domain using wavelets conceptual remarks abstract model identification plays a central role in any activity associated with process operations with control being done on different levels different models are required for the same plant each for a different range of dynamics besides that most identification methods apply to the linear models they also do not allow for selecting a frequency range wavelet based methods have the intrinsic ability to select time and frequency windows and to some extent are also applicable to non linear processes the paper presents an approach in which the wavelet transform is employed for system identification enabling the selection of the particular frequency range of interest we will show the use of some wavelet filters with a property of superior selectivity in the frequency domain and having compact support in the time domain which in turn influences an accurate implementation these properties provide us with a possibility of the measured data analysis in the frequency domain without any loss of information selection of a proper filter allows us to identify the system on a desired frequency range or to identify a number of systems for distinct frequency ranges this is specifically convenient for the systems with dominant modes such as singularly perturbed systems the possibility of selection of the specific frequency range can be utilized for application based identification such as control when only a limited frequency range is required we conclude with a case study where the proposed algorithms are tested and results are presented

finite difference approximations for a fractional advection diffusion problem the use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed fractional space derivatives are used to model anomalous diffusion or dispersion where a particle plume spreads at a rate inconsistent with the classical brownian motion model when a fractional derivative replaces the second derivative in a diffusion or dispersion model it leads to enhanced diffusion also called superdiffusion we consider a one dimensional advection diffusion model where the usual second order derivative gives place to a fractional derivative of order a with 1 a 2 we derive explicit finite difference schemes which can be seen as generalizations of already existing schemes in the literature for the advection diffusion equation we present the order of accuracy of the schemes and in order to show its convergence we prove they are stable under certain conditions in the end we present a test problem

a study of combined field formulations for material scattering for a locally corrected nystro spl uml m discretization a study of the error convergence and condition number of three integral equation formulations derived for penetrable material scattering objects the poggio miller chang harrington wu and tsai pmchwt the mu spl uml ller and the pmchwt formulations is presented for a variety of problems when discretized via a locally corrected nystro spl uml m method the pmchwt formulation is a first kind integral equation with a hypersingular operator the mu spl uml ller formulation leads to a second kind equation consisting of a diagonal term plus a compact operator this form is both frequency and mesh stable however unlike the pmchwt formulation the error grows with the refractive index the pmchwt formulation is in the form of a second kind equation but has a hypersingular term

an approach to parameter identification for a single degree of freedom dynamical system based on short free acceleration response an approach to parameter identification for the single degree of freedom s d o f system is presented it fits into the group of parametric system identification methods that use a structured mathematical model it uses the free acceleration response of the system in order to estimate the parameters of the equation of motion for the model under consideration the approach has been numerically tested on duffing s oscillator with dry friction at different sampling rates of the acceleration time history and at different signal to noise ratios snr the experiment has been carried out on an experimental device with the features of duffing s oscillator the validity and advantages of the approach are presented the results show that this approach offers parameter identification with good quality for short time series using only a modest number of data points for a wide range of s d o f systems

on the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane it is demonstrated by specific examples that eigenvalues of the electric field integral equation efie operator for finite extent objects in lossless media can have branch points in the complex frequency s plane specifically it is shown from the analysis of the spheroidal wave equation in the s plane that branch points are present in the eigenvalues of the integral operator associated with the scalar scattering problem from a perfectly conducting spheroid similarly it is concluded from the analysis of the mathieu s differential equation that branch points besides that associated with the infinite extent of the object exist in the s plane behavior of the eigenvalues of the efie operator for a perfectly conducting infinite elliptic cylinder a proof is given that branch point singularities cannot occur in the eigenvalues of efie operators for structures in which geometrical symmetry completely determines the eigenfunctions and hence they are frequency independent it is conjectured that branch points may always be present when sufficient object symmetry is lacking this conjecture is supported by the fact that branch points appear when a sphere is deformed into a spheroid or when a circular cylinder is deformed into an elliptic one an analogous phenomenon has been observed in circuit and transmission line problems for example it is shown that when the taper parameter of an exponential transmission line goes to zero the line becomes uniform and thus a symmetrical structure the branch points in the eigenvalues of the impedance matrix move away to infinity