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

nonexistence of positive weak solutions of elliptic inequalities abstract in this paper we give sufficient conditions for the nonexistence of positive entire weak solutions of coercive and anticoercive elliptic inequalities both of the p laplacian and of the mean curvature type depending also on u and x inside the divergence term while a gradient factor is included on the right hand side in particular to prove our theorems we use a technique developed by mitidieri and pohozaev in e mitidieri s i pohozaev a priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities proc steklov inst math 234 2001 1 362 which relies on the method of test functions without using comparison and maximum principles their approach is essentially based first on a priori estimates and on the derivation of an asymptotics for the a priori estimate finally nonexistence of a solution is proved by contradiction

efficient finite element solvers for the maxwell equations in the frequency domain the present paper shows that certain instabilities encountered with nedelec type finite element implementations of the vector wave equation can be eliminated by a family of lagrange multiplier methods the considered approaches can be interpreted as coupled vector and scalar potential methods including an ungauged formulation we advocate the latter form for use with iterative solvers we discuss an inexpensive high frequency variant of the method and show how hierarchical finite element bases can be utilized to derive efficient partially gauged formulations of higher order based on the multigrid idea a schwartz type solver is constructed which can overcome a major insufficiency of conventional preconditioners

loop tree implementation of the adaptive integral method aim for numerically stable broadband fast electromagnetic modeling the adaptive integral method aim is implemented in conjunction with the loop tree lt decomposition of the electric current density in the method of moments approximation of the electric field integral equation the representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate broadband electromagnetic em simulation without low frequency numerical instability problems while scaling of computational complexity and memory storage with the size of the problem are of the same order as in the conventional aim algorithm the proposed algorithm is built as an extension to the conventional aim formulation that utilizes roof top expansion functions thus providing direct and easy way for the development of the new stable formulation when the roof top based aim is available a new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested the discussed preconditioner can be used with both roof top and lt formulations of aim and other fast algorithms the resulting aim implementation is validated through its application to the broadband em analysis of large microstrip antennas and planar interconnect structures

preconditioned electric field integral equation using calderon identities and dual loop star basis functions an analytic preconditioner for the electric field integral equation based on the calderon identities is considered it is shown based on physical reasoning that rwg elements are not suitable for discretizing the electric field integral operator appearing in the preconditioner instead the geometrically dual basis functions proposed by buffa and christiansen are used however it is found that this preconditioner is vulnerable to roundoff errors at low frequencies a loop star decomposition of the buffa christiansen basis functions is presented along with numerical results demonstrating its effectiveness

a discontinuous galerkin augmented electric field integral equation for multiscale electromagnetic scattering problems a discontinuous galerkin dg augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full wave solution of multiscale targets the conventional surface integral equation based dg method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low frequency breakdown by augmenting the dg efie with current continuity equation the proposed scheme can alleviate the low frequency breakdown in the augmented system the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including rao wilton glisson rwg and half rwg basis functions since the half rwg basis is not divergence conforming line charge degrees of freedom on the adjoining edges are introduced in this paper it is observed that the resulting linear system is well conditioned at low frequencies which leads to a rapid convergence over wide frequency band numerical examples demonstrate the accuracy and efficiency of the augmented system

stochastic resonance in a tunnel diode we study stochastic resonance in a fast bistable electronic system a tunnel diode we investigate the phenomenon in a higher frequency regime than that studied in previous experiments detailed measurements of the output signal are reported for two values of the frequency of the periodic signal mathit f mathit s 1 khz and mathit f mathit s 10 khz we observe in one case mathit f mathit s 1 khz a nonmonotonic behavior characterized by a sharp dip in the output noise level measured at the frequency of the driving signal

hierarchical bases for nonhierarchic 3 d triangular meshes we describe a novel basis of hierarchical multiscale functions that are linear combinations of standard rao wilton glisson rwg functions when the basis is used for discretizing the electric field integral equation efie for pec objects it gives rise to a linear system immune from low frequency breakdown and well conditioned for dense meshes the proposed scheme can be applied to any mesh with triangular facets and therefore it can be used as if it were an algebraic preconditioner the properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers significantly better than those for the loop tree basis as a byproduct of the basis generation a generalization of the rwg functions to nonsimplex cells is introduced

a helmholtz stable fast solution of the electric field integral equation a new fast matrix vector multiplication scheme for the solution of the electric field integral equation is presented in this work similarly to other fast methods our approach reduces the matrix vector multiplication cost from o n2 to o n logn differently from other fast solvers however the effectiveness of efie preconditioning techniques such as quasi helmholtz decompositions or calderon approaches is maintained by our method even for very high matrix compression rates this is thanks to the fact that in the scheme we are proposing the contribution from the scalar potential when applied to or tested with solenoidal functions is always zero independent of the compression error in addition the new method will take advantage of the redundancies of the efie matrix in the low frequency dense discretization regime and it will further decrease both the memory storage and the multiplication cost with respect to currently available fast solvers numerical results will show the effectiveness of our approach and its impact on the solution of realistic problems

stochastic resonance in overdamped two coupled anharmonic oscillators abstract we consider the overdamped version of two coupled anharmonic oscillators with the external periodic force f sin t and gaussian noise term t added to one of the two state variables of the system linear stability analysis is carried out in the absence of external periodic force and noise then the system with external periodic force only and noise term only are studied in the noise free system four period t orbits are found to co exist one in each of the four wells for small values of forcing amplitude f for fixed values of other parameters at a critical value of f f c cross well periodic orbit appears f c is found to increase with increase in the coupling strength in the absence of forcing the system is found to exhibit intermittent jumping motion between two wells above a particular value of noise strength d d c the noise induced jumping behaviour is characterized by first passage time and residence time distributions next the influence of noise in the presence of the external periodic force is numerically studied the system is found to exhibit stochastic resonance behaviour the observed stochastic resonance dynamics is characterized using power spectrum signal to noise ratio and residence time distribution the plot of maximal lyapunov exponent versus noise strength has shown a stochastic resonance profile the occurrence of stochastic resonance is studied by varying the forcing frequency and the coupling strength finally the influence of addition of external periodic force and noise term to different state variables is also presented

on weak solutions of nonlinear weighted p laplacian elliptic inequalities abstract in this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class w loc 1 p r n c r n of p laplacian elliptic inequalities with possibly singular weights in order to get the results a new omori yau type principle is used we complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite r 0 finally a criterium for the existence of positive entire large radial solutions of class w loc 1 p r n c r n is also established

a nondirective plane wave mlfma stable at low frequencies a novel method called the nondirective stable plane wave multilevel fast multipole algorithm nspwmlfma is presented to evaluate the low frequency lf interactions that cannot be handled by the multilevel fast multipole algorithm mlfma it is well known that the mlfma cannot be used for lf interactions since it suffers from numerical instability contrary to current techniques the proposed technique is not based on the spectral representation of the green function instead the addition theorem of the mlfma is manipulated into a form that allows numerically stable translations along the z axis the translation operator for these translations is derived in closed form a qr based method is devised to allow stable translations in all the other directions interpolations and anterpolations are also provided allowing a full multilevel algorithm since the nspwmlfma is based on the same mathematical foundations as the mlfma it requires limited adaptations to existing mlfma codes the fact that a qr is needed limits this algorithm to lf interactions however a coupling with the mlfma is straightforward allowing the easy construction of a broadband algorithm the dc limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems finally it is shown that the error introduced in the different steps of the algorithm is controllable and a single level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity

embedding calderon multiplicative preconditioners in multilevel fast multipole algorithms calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation efie for perfect electric conductors at lower frequencies previous authors have shown that by using a dense matrix preconditioner based on the calderon identities the low frequency instability is removed while still maintaining the inherent accuracy of the efie it was also demonstrated that the spectral properties of the caldero n preconditioner are conserved during discretization if the efie operator is discretized with rao wilton glisson expansion functions and the preconditioner with buffa christiansen expansion functions in this article we will show how the calderon multiplicative preconditioner cmp can be combined with fast multipole methods to accelerate the numerical solution leading to an overall complexity of o n logn for the entire iterative solution at low frequencies where the cmp is most useful the traditional multilevel fast multipole algorithm mlfma is unstable and we apply the nondirectional stable plane wave mlfma nspwmlfma that resolves the low frequency breakdown of the mlfma the combined algorithm will be called the cmp nspwmlfma applying the cmp nspwmlfma at open surfaces or very low frequencies leads to certain problems which will be discussed in this article

numerical verification of bona fide stochastic resonance the notion of stochastic resonance as an input output synchronization mechanism is reestablished quantitatively based on accurate numerical simulation of a simple two state model namely the schmitt trigger the corresponding phenomenological criterion known as bona fide stochastic resonance is thus proven applicable throughout the entire range of the input parameters claims to the contrary are briefly discussed

stochastic resonance noise enhanced phase coherence we study stochastic resonance in periodically driven stochastic bistable systems in terms of phase synchronization by introduction of an instantaneous phase for the output we show explicitly the effect of phase locking between the input and output the stochastic dynamics of the phase difference between input and output appears to be similar to that of synchronized classical self sustained oscillators the degree of phase coherence is estimated by employing the effective diffusion constant for the phase difference this coherence becomes maximal for optimal noise intensities however phase synchronization effects can only be observed for sufficiently large magnitude of the periodic inputting signal

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

efficient solution of efie via low rank compression of multilevel predetermined interactions this paper describes the predetermined interaction list oct tree pilot algorithm and its application in expediting the solution of full wave electric field integral equation efie based scattering problems for three dimensional arbitrarily shaped conductors pilot combines features of the fast multipole method fmm and qr decomposition based matrix compression techniques to optimize setup times solve times and memory requirements the method is kernel independent and stable for electrically small structures unlike traditional fmm the novel features of the algorithm namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail a complexity estimate is presented to demonstrate the scaling in time and memory requirements examples exhibiting the accuracy and the time and memory performances are also presented finally a quantitative study is included to address the expected but gradual degradation of qr based compression techniques for electrically large structures

stochastic resonance without an external periodic drive in a simple prey predator model we have investigated the effect of noise on a simple prey predator model where the oscillations are triggered by the internal dynamics of the system without the aid of any external periodic drive we report the occurrence of stochastic resonancelike behavior in this system which does not have a threshold or a potential barrier in the absence of an external drive

a multiresolution curvilinear rao wilton glisson basis function for fast analysis of electromagnetic scattering a new set of multiresolution curvilinear rao wilton glisson mr crwg basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems the mr crwg basis functions are constructed as linear combinations of curvilinear rao wilton glisson crwg basis functions which are defined over curvilinear triangular patches thus allowing direct application on the existing mom codes that using crwg basis the multiresolution property of the mr crwg basis can lead to the fast convergence of iterative solvers merely by a simple diagonal preconditioning to the corresponding mom matrices moreover the convergence of iterative solvers can be further improved by introducing a perturbation from the principle value term of the magnetic field integral equation mfie operator to construct diagonal preconditioners for efficient iterative solution of the electric field integral equation efie another important property of the mr crwg basis is that the mom matrices using the mr crwg basis can be highly sparsified without loss of accuracy the mr crwg basis has been applied to the 3 d electromagnetic scattering problems and the numerical results indicate that the mr crwg basis performs much better than the crwg basis

loop star basis functions and a robust preconditioner for efie scattering problems an electric field integral equation efie formulation using the loop star basis functions has been developed for modeling plane wave scattering from perfect conducting objects a stability analysis at the dc limit shows that the use of the rao wilton glisson rwg basis functions results in a singular matrix operator however the use of the loop star basis functions results in a well conditioned matrix moreover a preconditioner constructed from a two step process based on near interactions and an incomplete factorization with a heuristic drop strategy has been proposed in conjunction with the conjugate gradient method to solve the resulting matrix equation the approach is shown to be effective for resolving both the low frequency instability and the bad conditioning of the efie method the computational complexity of the proposed approach is shown to be o n sup 2

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

a single level dual rank ie qr algorithm to model large microstrip antenna arrays a single level dual rank ie qr algorithm is introduced so that the resulting dense method of moments mom matrix is efficiently compressed for a system of n equations an amount of work of the order o n sup 2 has traditionally been required for both matrix assembly and matrix vector multiplication in an iterative matrix solver the algorithm of the present paper reduces the memory requirement and cpu time for both matrix assembly and matrix vector multiplication to o n sup 3 2 making it practical to solve for large antenna arrays with full wave approach in conjunction with a geometric neighboring preconditioner for matrix solution using gmres the current approach solves problems involving large antenna arrays using only a fraction of what are needed by conventional mom both in term of memory and total cpu time

a multiresolution method of moments for triangular meshes this paper presents the construction use and properties of a multiresolution wavelet basis for the method of moments mom analysis of metal antennas scatterers and microwave circuits discretized by triangular meshes several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse mom matrices the proposed basis is organized in hierarchical levels and keeps the different scales of the problem directly into the basis functions representation the current is divided into a solenoidal and a quasi irrotational part which allows mapping these two vector parts onto fully scalar quantities where the wavelets are defined as a byproduct this paper also presents a way to construct hierarchical sets of rao wilton glisson rwg functions on a family of meshes obtained by subsequent refinement i e with the rwg of coarser meshes expressed as linear combinations of those of finer meshes

a priori estimates for nonlinear differential inequalities and applications the aim of the paper is to derive a priori estimates and obtain the harnack type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain by using the test function method developed by mitidieri and pohozaev we extend and improve some known results proved by serrin and zou bidaut veron and pohozaev

a hierarchical fast solver for efie mom analysis of multiscale structures at very low frequencies we present an efie fast solver that is stable down to very low frequencies for very dense meshes and multi scale problems the proposed approach uses a split potentials formulation in association to a hierarchic pre conditioner for the underlying low rank fast factorization potential splitting prevents the numerical cancellation problem that undermines the effectiveness of the low rank factorization negatively impacting on the necessary factorization tolerance the fast method presented in this work can be directly implemented into existing codes