efficient analysis of em scattering from bodies of revolution via the aca in this communication the adaptive cross approximation aca algorithm is utilized to analyze the scattering from arbitrary metallic bodies of revolution bors that is formulated by the electric field integral equation approach for a given mode a multilevel partitioning is used to group the basis functions of the bors along the longitudinal dimension the interactions of the adjacent groups are calculated directly by the method of moments mom and the interactions of well separated groups are compressed by the aca algorithm the memory requirement and cpu time consumption are reduced drastically

electromagnetic multiple pec object scattering using equivalence principle and addition theorem for spherical wave harmonics a novel domain decomposition procedure is presented to analyze the electromagnetic wave multiple scattering among separate pec objects the method is based on the equivalence principle algorithm epa that transfers the primary unknowns on the objects to the unknowns on the equivalence surfaces each equivalence surface is considered to be a spherical surface encompassing a pec object inside the equivalence spheres the analysis is performed based on the rao wilton glisson rwg basis functions where the electromagnetic interactions outside them are considered by means of the addition theorem for spherical wave harmonics swhs the translation procedures are presented to translate the rwg basis functions to swhs and vice versa the reduction of unknowns in the presented method versus the conventional epa which uses translation operators among equivalence surfaces shows its efficiency some numerical examples are presented to evaluate the efficacy of the proposed approach the acceptable consistency among the results of the proposed method and the conventional epa as well as the direct method of moments validates the proposed method

numerical properties of a gaussian translation operator for the 2d fmm a diagonal gaussian translation operator for the time harmonic fast multipole method fmm in two dimensions is examined numerically the gaussian translation operator depends on a beam parameter that determines its sharpness when the beam parameter is set to zero the gaussian translation operator reduces to the standard fmm translation operator the sampling rate can be determined straightforwardly to achieve any desired accuracy the directionality of the gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy the required number of plane waves depends strongly on the actual source receiver locations not just on the diameter of the source and receiver regions

the generalized method of moments for electromagnetic boundary integral equations the generalized method of moments gmm is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations past work on gmm for electromagnetics was confined to geometries modeled by piecewise flat tessellations and suffered from spurious internal line charges in the present article we redesign the gmm scheme and demonstrate its ability to model scattering from pec scatterers composed of mixtures of smooth and non smooth geometrical features furthermore we demonstrate that because the partition of unity provides both functional and effective geometrical continuity between patches gmm permits mixtures of local geometry descriptions and approximation function spaces with significantly more freedom than traditional moment methods

construction of starting algorithms for the rk gauss methods in this paper starting algorithms for the numerical solution of stage equations in runge kutta gauss formulae with 2 3 and 4 stages are constructed for each of these formulae three types of starting algorithms are given according to their requirement of none one or two additional function evaluations per step numerical experiments with hamiltonian systems are presented to show the superior performance of the new starting algorithms of high order

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

non conformal domain decomposition method with second order transmission conditions for time harmonic electromagnetics non overlapping domain decomposition dd methods provide efficient algorithms for solving time harmonic maxwell equations it has been shown that the convergence of dd algorithms can be improved significantly by using high order transmission conditions in this paper we extend a newly developed second order transmission condition sotc which involves two second order transverse derivatives to facilitate fast convergence in the non conformal dd algorithms however the non conformal nature of the dd methods introduces an additional technical difficulty which results in poor convergence in many real life applications to mitigate the difficulty a corner edge penalty method is proposed and implemented in conjunction with the sotc to obtain truly robust solver performance numerical results verify the analysis and demonstrate the effectiveness of the proposed methods on a few model problems finally drastically improved convergence compared to the conventional robin transmission condition was observed for an electrically large problem of practical interest

accurate and efficient computation of the modal green s function arising in the electric field integral equation for a body of revolution we present a computationally efficient way to compute the modal green s function arising in the electric field integral equation for a body of revolution the computation of this function is time consuming due to its singular and oscillating nature especially for high fourier mode indices efficient and accurate computation of this function is important to arrive at a fast numerical method for analyzing the scattering problem of a body of revolution we compute the modal green s function up to machine precision in a well controlled way with limited effort even for large bodies

integral equation based domain decomposition method for solving electromagnetic wave scattering from non penetrable objects the integral equation ie method is commonly utilized to model time harmonic electromagnetic em problems one of the greatest challenges in its applications arises in the solution of the resulting ill conditioned matrix equation we introduce a new domain decomposition method ddm for the ie solution of em wave scattering from non penetrable objects the proposed method is a non overlapping non conformal ddm and it provides a computationally efficient and effective preconditioner for the ie matrix equations moreover the proposed approach is very suitable for dealing with multi scale electromagnetic problems since each sub domain has its own characteristics length and will be meshed independently furthermore for each sub domain we are free to choose the most effective ie sub domain solver based on its local geometrical features and electromagnetic characteristics additionally the multilevel fast multi pole algorithm mlfma is utilized to accelerate the computations of couplings between sub domains numerical results demonstrate that the proposed method yields rapid convergence in the outer krylov iterative solution process finally simulations of several large scale examples testify to the effectiveness and robustness of the proposed ie based ddm

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

modal characteristic basis function method for solving scattering from multiple conducting bodies of revolution the analysis of scattering from multiple bodies of revolution bors has important applications in microwave remote sensing radar imaging and other areas for single bor three dimensional problem can be degenerated into 2 5 dimensional problem based on the modal green functions mgfs reducing the solving time and storage remarkably however it is difficult to extend the mgf to multiple arbitrarily orientated bors this paper presents a modal characteristic basis function method for solving the scattering from multiple bors it combines the mgf of bor with the characteristic basis function method named as the bor cbf method here the mgf of bor is first applied to efficiently solve the current distribution on the surface of each bor the singular value decomposition is then used to construct the global modal characteristic basis functions mcbfs for each bor finally the mcbfs are transformed into the rwg basis functions using a basis function mapping technique so that the filling of the interaction matrix can be accelerated by the multilevel fast multipole algorithm by using the bor cbf method the scattering of multiple arbitrarily orientated bors can be solved efficiently numerical results are presented to demonstrate the accuracy and efficiency of the bor cbf method

a spectral integral method for smooth multilayered bodies of revolution a spectral integral method sim is developed to solve the scattering problem from smooth multilayered bodies of revolution bors this sim is a spectral method to improve the accuracy and efficiency of the sim by the fast fourier transform fft algorithm this method can achieve high accuracy and greatly reduce the computational time consumption in our bor sim the bor generatrix current is expanded by the truncated fourier series then the impedance matrix is generated in the spectral domain to solve the scattering problem unlike the conventional methods that need eight to ten segments per wavelength in the bor sim two points per wavelength are adequate to achieve high accuracy according to the nyquist theorem being accelerated by fft this method shows a significant efficiency advantage over the conventional bor method numerical results demonstrate the accuracy and efficiency of our new method by combining with the poggio miller chang harrington wu tsai surface integral equations this method can be used to solve many practical scattering problems

a domain decomposition method for the vector wave equation a nonoverlapping domain decomposition method ddm is presented for the finite element fe solution of electromagnetic scattering problems by inhomogeneous three dimensional 3 d bodies the computational domain is partitioned into concentric subdomains on the interfaces of which conformal vector transmission conditions are prescribed and that can be implemented in the inhomogeneous part the ddm is numerically implemented when a conformal vector absorbing boundary condition abc is utilized on the outer boundary terminating the fe mesh while employing the standard edge based fe formulation then numerical experiments are performed on a sphere and a cone sphere that emphasize the advantages of this technique in terms of memory storage and computing times especially when the total number of unknowns is very large also these numerical experiments serve as a severe test for the performances of the abc

a generalized surface integral equation formulation for analysis of complex electromagnetic systems a novel method is presented to analyze the electromagnetic characteristics of systems consisting of a large number of scatterers with different shapes and materials in the method nearly located scatterers are grouped together while large bulk materials are divided into subblocks with adequate sizes a scatterer group or a subblock forms a basic block of the system and each block is contained with a virtual reference surface a generalized transition matrix defined on the reference surface is used to characterize the electromagnetic characteristics of the block the generalized transition matrix relates the rotated tangential components of the scattered fields or the equivalence sources to the rotated tangential components of the incident fields directly the generalized transition matrix can be calculated for each block independently using proper methods according to its structure and material surface integral equations are established on all the virtual reference surfaces which can be solved by moment method to get the electromagnetic characteristics of the whole system characteristic basis functions and synthetic basis functions can be applied to further reduce the unknown number while fast multipole method can be used to accelerate the evaluation of interactions two dimensional examples are provided to verify the method

a reverse operation self consistent evaluation approach for singular integrals in the sie analysis of pec targets discussed herein is a novel approach entitled reverse operation self consistent evaluation rose specifically we applied rose for the treatment of weak singular and hypersingular kernels in surface integral equations sies for the computation of electromagnetic em scattering from perfect electrical conductors pecs different from the existing forward methods rose is based on reverse operations the singular entries are not evaluated directly by analytical or numerical evaluation instead they are introduced as unknowns and are solved algebraically for em scattering from pec sies can be set up by using the stratton chu representation formula an auxiliary problem with the same meshed boundary is then formulated of which any plane waves are the self consistent solutions it is shown that by applying a consistent discretization the matrix of the auxiliary problem can be made identical with the original one as a consequence these self consistent solutions can be utilized to solve the singular entries of the original system explicitly a set of plane waves are interpolated using the appropriate basis functions subsequently the corresponding coefficient vectors are utilized to construct small linear systems to solve the troublesome singular entries in the underlying matrix the proposed rose approach is applicable to different singular kernels as well as different discretization schemes in this paper we restrict our discussion to the weak singular and hypersingular kernels using respectively div conformal rao wilton glisson basis functions and nonconformal piecewise constant vector basis functions accelerated by the multilevel fast multipole algorithm the proposed method is applicable for real life applications

truncation strategies for optimal krylov subspace methods optimal krylov subspace methods like gmres and gcr have to compute an orthogonal basis for the entire krylov subspace to compute the minimal residual approximation to the solution therefore when the number of iterations becomes large the amount of work and the storage requirements become excessive in practice one has to limit the resources the most obvious ways to do this are to restart gmres after some number of iterations and to keep only some number of the most recent vectors in gcr this may lead to very poor convergence and even stagnation therefore we will describe a method that reveals which subspaces of the krylov space were important for convergence thus far and exactly how important they are this information is then used to select which subspace to keep for orthogonalizing future search directions numerical results indicate this to be a very effective strategy

initializers for rk gauss methods based on pseudo symplecticity symplectic runge kutta rk methods for general hamiltonian systems are implicit and an iterative scheme must be used to obtain the solution at each step in this paper the classical order and the pseudo symplecticity order pseudo symplectic runge kutta methods bit 38 1998 439 461 of the one step method that results after s fixed point iterations for solving the implicit equations of stages in an implicit rk method are studied in the numerical experiments with some rk gauss methods s is chosen so that the pseudo symplecticity order is twice the classical order thus the pseudo symplectic method retains some important properties of the original symplectic one further new starting algorithms are constructed taking into account their pseudo symplecticity properties and are compared with other initializers existing in the literature

direct solve of electrically large integral equations for problem sizes to 1 m unknowns when unknowns are spatially grouped for electrically large bodies the blocked method of moments mom z matrix and its lu factors are comprised of blocks which can be well approximated by matrices of low rank expressed as the outer product of a column matrix times a row matrix this approximation is called matrix compression and can save significant memory and operations count and for monostatic scattering where there are many right hand sides rhs for electrically large bodies the blocked rhs v and current solution j are also well approximated by this low rank outer product form the blocked system equation zj luj v is lu factored and solved using this compressed block form where each outer product approximant is computed using the adaptive cross approximation aca this approach has been applied to a frequency domain efie rwg galerkin integral equation for 3 d pec surfaces preliminary results for this compressed block lu factor and solve technique are presented and compared to measured data bor code predictions and the same code without matrix compression complexity of this approach is studied numerically for an open pipe geometry with specific error tolerances using a pc workstation with unknowns n ranging from 2592 to 1 025 109 and the number of rhs varying from 310 to 6162 matrix fill time scales as n1 34 lu matrix memory storage scales as n1 5 lu factor time scales as n2 0 and the time per rhs solve scales as n1 67 complete solution wall time scales as n1 8

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

starting algorithms for irk methods in this paper some classes of starting algorithms for the iterations of irk methods are studied they are of three types according to their additional cost by means of b series the order conditions for them are obtained the maximum order attained by these algorithms and their construction are derived too

fast direct solution of method of moments linear system a novel algorithm the compressed block decomposition cbd is presented for highly accelerated direct noniterative method of moments mom solution of electromagnetic scattering and radiation problems the algorithm is based on a block wise subdivision of the mom impedance matrix impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly but approximated in a compressed form subsequently the matrix is decomposed preserving the compression examples are presented of typical problems in the range of 5000 to 70000 unknowns the total execution time for the largest problem is about 1 h and 20 min for a single excitation vector the main strength of the method is for problems with multiple excitation vectors monostatic rcs computations due to the negligible extra cost for each new excitation for radiation and scattering problems in free space the numerical complexity of the algorithm is shown to be n 2 and the storage requirements scale with n 3 2

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

linear embedding via green s operators a modeling technique for finite electromagnetic band gap structures we propose a modular electromagnetic modeling procedure for large finite electromagnetic band gap ebg structures called linear embedding via green s operators it is a diakoptic method based on the huygens schelkunoff principle involving equivalent boundary current sources that electromagnetically characterize the enclosed domain of arbitrary shapes as if it were a multiport system in a cascade of embedding steps separate reusable domains are combined to form larger domains device design often involves tuning local medium properties in a compact designated domain with a large environment through an additional embedding step the equivalent sources describing the environment can be transferred to the boundary of the designated domain rendering subsequent design steps very fast this two stage optimization process is applied in the design of an ebg power splitter

a new dual primal domain decomposition approach for finite element simulation of 3 d large scale electromagnetic problems a novel dual primal non overlapping domain decomposition method ddm for the finite element solution of three dimensional 3d large scale electromagnetic problems is proposed this method reduces the computational complexity from solving the original 3d problem to an equivalent interface problem by utilizing the idea of the dual primal finite element tearing and interconnecting feti dpem method the new method which is referred to as the feti dpem2 combines the dual primal idea with two lagrange multipliers and implements robin type transmission condition at the subdomain interfaces to significantly improve the convergence of the interface solution in the high frequency region similar to the original version a global coarse problem related to the degrees of freedom at the subdomain corner edges is designed to propagate the residual error to the whole computational domain at each iteration which further increases the convergence numerical examples are presented to demonstrate the validity and the capability of this method the results show that the proposed method produces fast solutions to large scale problems in any frequency band

backward error analysis for numerical integrators backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods this is true in particular for the integration of hamiltonian systems where backward error analysis can be used to show that a symplectic method will conserve energy over exponentially long periods of time such results are typically based on two aspects of backward error analysis i it can be shown that the modified vector fields have some qualitative properties which they share with the given problem and ii an estimate is given for the difference between the best interpolating vector field and the numerical method these aspects have been investigated recently for example by benettin and giorgilli in j statist phys 74 1994 pp 1117 1143 by hairer in ann numer math 1 1994 pp 107 132 and by hairer and lubich in numer math 76 1997 pp 441 462 in this paper we aim at providing a unifying framework and a simplification of the existing results and corresponding proofs our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit taylor series expansion of the numerical method and the corresponding flow maps as in the above cited works as an application we discuss the long time integration of chaotic hamiltonian systems and the approximation of time averages along numerically computed trajectories

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

one way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems non overlapping domain decomposition dd methods with complex first order robin type transmission conditions tcs provide an efficient iterative solution for maxwell s equation unfortunately the first order tcs do not effectively account for some eigenmodes of the system matrix which limits the scalability of the methods in this work we examine two tcs with a second order transverse derivative to improve the method s performance a detailed convergence analysis of the two tcs is presented we then investigate the use of the two second order tcs in non conformal and non overlapping one way dd methods numerical results illustrate the effectiveness of the proposed methods on some model problems and on several problems of practical interest

efficient solution of integral equation based electromagnetic problems with the use of macromodels the idea of so called macromodels is applied to problems of computational electromagnetics involving integral equation method of moments formulations it is shown that with the use of equivalence principles it is possible to exclude a part of the problem calculate its wideband response without an a priori knowledge of the excitations and then efficiently combine the result into the original situation the idea is validated using examples involving slot excited dielectric resonator antennas

efie modeling of high definition multiscale structures we propose a method to significantly improve the spectral properties of the efie mom matrix for broad band analysis of structures with fine details non uniform meshes and large overall sizes a multilevel approach allows to overlay fine meshes and quasi nyquist sampled meshes the fine mesh conditioning is solved via hierarchical basis functions and the quasi nyquist sampled part is treated by an algebraic incomplete lu preconditioner numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten twenty wavelengths and levels of detail from very moderate to extending over the whole structure

on the convergence of the eigencurrent expansion method applied to linear embedding via green s operators lego the scattering from a large complex structure comprised of many objects may be efficiently tackled by embedding each object within a bounded domain brick which is described through a scattering operator upon electromagnetically combining the scattering operators we arrive at an equation which involves the total inverse scattering operator s 1 of the structure we call this procedure linear embedding via green s operators lego to solve the relevant equation we then employ the eigencurrent expansion method eem essentially the method of moments with a set of basis and test functions that are approximations to the eigenfunctions of s 1 termed eigencurrents we have investigated the convergence of the eem applied to lego in cases when all the bricks are identical our findings lead us to formulate a simple and practical criterion for controlling the error of the computed solution a priori

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

a generalized transition matrix model for open ended cavity with complex internal structures in this paper a novel generalized transition matrix gtm algorithm is proposed to analyze the electromagnetic problems of open ended cavity structures an artificial reference surface is applied to seal the slots and or apertures to reshape the target cavity into an interior domain containing inner metallic surface and internal structures and an exterior domain containing the outer surface of the cavity special junctions at the transitional connection of the two domains are applied to guarantee the current continuity on the metallic surface based on the huygens principle an associated gtm is constructed on the reference surface and the special junctions to extract the characteristics of the interior region of the cavity the gtm is independent of the outer shape of the cavity and the exterior electromagnetic environment the computational complexity can be effectively reduced especially when the interior region is with fine structures and internal sources to investigate the feasibility and effectiveness of the proposed approach several numerical examples are presented

starting algorithms for a class of rk methods for index 2 daes when semiexplicit differential algebraic equations are solved with implicit runge kutta methods rk the computational effort is dominated by the cost of solving the nonlinear systems and therefore it is important to have good starting values to begin the iterations for semiexplicit index 2 daes starting algorithms without additional cost for rk methods with regular matrix coefficient were studied in a previous paper however the regularity condition on the matrix coefficient excludes some interesting methods like lobatto iiia and esdirk methods in this paper we study starting algorithms without additional computational cost for a class of runge kutta methods in the case of index 2 daes

modeling long range memory with stationary markovian processes in this paper we give explicit examples of long range correlated stationary markovian processes y t where the stationary probability density function pdf shows tails which are gaussian or exponential these processes are obtained by simply performing appropriate coordinate transformations of a specific power char21 law correlated additive process x t already known in the literature whose pdf shows power law tails we give analytical and numerical evidences that although the new processes are markovian and have gaussian or exponential tails their autocorrelation function shows a power law decay with logarithmic corrections for a generic continuous and monotonously increasing coordinate transformation we also analytically investigate what is the relationship between the asymptotic decay of the autocorrelation function and the tails of the stationary pdf extreme events seem to be associated to long range correlated processes with power law decaying autocorrelation function however the occurrence of extreme events is not necessary in order to have more general long range correlated processes in which the autocorrelation shows a slow decay characterized by a power law times a correction function such as the logarithm our results help in clarifying that even in the context of stationary markovian processes long range dependencies are not necessarily associated to the occurrence of extreme events moreover our results can be relevant in the modeling of complex systems with long memory in fact we provide simple stationary processes associated to langevin equations with white noise thus confirming that long memory effects can be modeled in the context of continuous time stationary markovian processes

improved synthetic basis functions method for nonperiodic scaling structures with arbitrary spatial attitudes synthetic basis functions method sbfm is an improved approach of method of moment which utilizes fewer high order synthetic functions to replace rao wilton glisson functions to discretize surface currents and make inner products thus this approach can drastically decrease the number of unknowns and lower the requirements of pc s memory especially for periodic structures computational efficiency will be improved sharply since synthetic functions defined on different subblocks can be set identical and the process of constructing synthetic functions needs to be calculated only once however for nonperiodic structures this advantage no longer exists due to the diversities of synthetic functions defined on different subblocks in that case synthetic functions need to be calculated block by block targeted at this problem an improved sbfm is proposed for nonperiodic scaling structures whose subblocks only share identical similar contour features but spatial attitudes spatial positions and geometrical sizes can be arbitrary based on theoretical analysis the improved sbfm employs a special triangulating method for each subblock which makes synthetic functions defined on them reusable in this way synthetic functions need to be calculated only once too for nonperiodic scaling structures compared to traditional sbfm this approach decreases the elapsed time of constructing synthetic functions and memory cost of synthetic functions expansion coefficients to 1 n n is the number of subblocks and is of great help in the analysis of large scale targets such as complex nonperiodic arrays finally accuracy of this approach is validated by both simulating and measured results

starting algorithms for gauss runge kutta methods for hamiltonian systems abstract among the symplectic integrators for the numerical solution of general hamiltonian systems implicit runge kutta methods of gauss type rkg play an important role to improve the efficiency of the algorithms to be used in the solution of the nonlinear equations of stages accurate starting values for the iterative process are required in this paper a class of starting algorithms which are based on numerical information computed in two previous steps is studied for two and three stages rkg methods explicit starting algorithms for the stage equations with orders three and four are derived finally some numerical experiments comparing the behaviour of the new starting algorithms with the standard first iterant based on lagrange interpolation of stages in the previous step are presented

equivalence principle algorithm with body of revolution equivalence surface for the modeling of large multiscale structures we propose a multiscale solver of equivalence principle algorithm with a body of revolution bor equivalence surface es first the whole object is decomposed into subdomains the ess are defined as proper bors e g spheres in this work to enclose each subdomain the rao wilton glisson rwg and bor basis functions are defined on each sphere respectively second the octree is constructed in each nonzero subdomain the multilevel fast multipole algorithm mlfma is employed to solve the equivalent currents on the es individually and then the equivalent currents are projected from rwg onto the bor basis functions the couplings between neighboring subdomains are evaluated directly using mlfma and the separated subdomains are substituted by the es to es couplings and are evaluated efficiently by the bor method of moments bor mom to solve the equation system a hybrid inner and outer iterative solver is employed where the inner iteration is used to solve each local subdomains and the outer iteration is used to update the global solutions by collecting all the local solutions numerical results and discussions demonstrate the validity of the proposed work

a domain decomposition finite difference method for parallel numerical implementation of time dependent maxwell s equations a domain decomposition technique together with an implicit finite difference scheme is used to design a parallel algorithm to solve for electromagnetic scattering in the time domain by an infinite square metallic cylinder the implicit difference scheme yields second order accuracy unconditional stability and at each time step a large system of linear equations the domain decomposition technique reduces the solution of this large system to that of many independent smaller subsystems the present algorithm can be easily implemented on coarse grain parallel vector supercomputers to obtain a speedup close to the number of available central processing units cpus

understanding the determinants of volatility clustering in terms of stationary markovian processes abstract volatility is a key variable in the modeling of financial markets the most striking feature of volatility is that it is a long range correlated stochastic variable i e its autocorrelation function decays like a power law for large time lags in the present work we investigate the determinants of such feature starting from the empirical observation that the exponent of a certain stock s volatility is a linear function of the average correlation of such stock s volatility with all other volatilities we propose a simple approach consisting in diagonalizing the cross correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts as a result the diagonalized volatilities result to share with the original volatilities either the power law decay of the probability density function and the power law decay of the autocorrelation function this would indicate that volatility clustering is already present in the diagonalized un correlated volatilities we therefore present a parsimonious univariate model based on a non linear langevin equation that well reproduces these two stylized facts of volatility the model helps us in understanding that the main source of volatility clustering once volatilities have been diagonalized is that the economic forces driving volatility can be modeled in terms of a smoluchowski potential with logarithmic tails

application of the characteristic basis function method utilizing a class of basis and testing functions defined on nurbs patches a novel implementation of the characteristic basis function method cbfm is given in which the high level basis functions called characteristic basis functions cbfs are represented in terms of curved rooftops generated from nonuniform rational b splines nurbs in the parametric u v domain the associated macro testing functions are defined by using curved razor blade functions corresponding to each rooftop the underlying objective of the cbfm is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments mom the result is therefore an approach which can handle many complex cases via direct solvers without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill conditioned matrices as a result of the combination of the cbfm with the special class of low level basis and testing functions directly located over nurbs surfaces complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the cpu time as well as required memory resources

a nonconformal domain decomposition scheme for the analysis of multiscale structures we present a domain decomposition dd framework for the analysis of impenetrable structures it allows for the electric field integral equation efie and combined field integral equation cfie and for open closed and open closed structures the dd results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations the dd employs specialized transmission conditions among the domains and the use of discontinuous galerkin dg allows conformal as well as nonconformal discretizations of domain boundaries the nonconformal nature of the decomposition gives considerable flexibility in the meshing the strategy is highly parallelizable as all the operations involving the subdomains can be performed in parallel the proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes

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

a recursive green s function method for boundary integral analysis of inhomogeneous domains the recursive green s function method rgfm for computation of fields scattered by two dimensional 2 d inhomogeneous dielectric bodies is presented the algorithm efficiently constructs the green s function for the inhomogeneous region by recursively combining known green s functions from smaller subdomains the fields on the scatterer surface are then computed using a boundary integral formulation proper implementation of the rgfm results in computational and storage complexities which scale as n sup 1 5 and n respectively where n is the total number of discrete cells in a domain comparisons of results obtained using the rgfm with those computed from moment method and exact solutions show the efficiency and accuracy of the technique

integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme an integral equation approach is presented to analyze the two dimensional 2 d scattering from multilayered periodic array the proposed approach is capable of handling scattering from the array filled with different media in different layers combining the equivalence principle algorithm epa and connection scheme epacs it can be avoided to find and evaluate the multilayered periodic green s functions for 2n identical layers the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm more importantly based on epacs an approach is proposed to effectively handle the semi infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction

a saim faffa method for efficient computation of electromagnetic scattering problems a novel method is proposed through an effective combination of the subdomain adaptive integral method saim with the fast far field approximation faffa for efficient computation of electromagnetic scattering problems in the saim technique the whole perfectly electrically conducting structure is decomposed into subdomains and each subdomain is properly handled by the aim with its local cartesian grid individually a current continuity boundary condition is introduced on the interface between contiguous subdomains to guarantee the accuracy moreover the faffa technique is utilized to speed up the process of updating the modified excitation vectors numerical results show that the present hybrid method can not only significantly decrease the number of auxiliary grid points and the memory requirement of green s function matrix but also improve the convergence of the iterative process compared to the conventional aim

an efficient marching on in degree solution of transient multiscale em scattering problems a marching on in degree mod based time domain domain decomposition method is proposed to efficiently analyze the transient electromagnetic scattering from electrically large multiscale targets the algorithm starts with an octree that divides the whole scattering target into several subdomains then using the equivalence principle algorithm each subdomain is enclosed by an equivalence sphere es where both the rwg and bor spatial basis functions are employed to expand the unknown currents the interactions of the near field subdomains are directly calculated by the method of moments while the far field interactions can be converted into the interactions of corresponding ess this scheme implicitly satisfies the current continuity condition and the convergence can be accelerated as well by harnessing the rotational symmetry of the ess the computational resources are reduced significantly compared with the traditional mod method several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm

nested equivalent source approximation for the modeling of multiscale structures we introduce a method to compress the impedance matrix of the method of moments mom for the modeling of high fidelity multiscale structures at low to moderate frequencies we start from a method recently proposed to compress static scalar problems proved to have o n computational complexity we represent far coupling between groups through equivalent source distributions on properly defined automatically generated equivalence surfaces the equivalent sources are obtained via an inverse source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy and are intrinsically multiscale this results in an o n complexity scaling of matrix vector products but reduces multiplicative constants i e reduces time and memory requirements for all structures it affords an improved representation of couplings in multiscale structures resulting in a fast convergence of iterative solvers our approach is green s function independent and easy to be implemented in existing mom codes the present version is based on the electric field integral equation efie numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures

automatic basis function regularization for integral equations in the presence of ill shaped mesh elements bad meshes are a common problem in using computational electromagnetics codes often much of an engineer s or analyst s time ids wasted improving a mesh until the solver finally converges we investigate the problem as it comes up in integral equation methods and observe that its effects can be detected by analyzing the singular values of the electric field integral equation matrix armed with this information we automatically remove the undesirable degrees of freedom caused by the ill shaped mesh elements so that the iterative solver behaves as if they were not present all without any extra effort by the user an a posteriori error estimator is developed which verifies the improved accuracy for test problems and also suggests potential future applications in adaptive mesh refinement for integral equation methods further numerical examples demonstrate the improved solution convergence

marching on in degree solution of the transient scattering from multiple bodies of revolution an efficient marching on in degree mod scheme is proposed to analyze the transient em scattering from multiple conducting bodies of revolution mbors with arbitrary axis using the equivalence principle algorithm epa the self acting of each bor is calculated by taking advantage of the rotationally symmetrical property in its local bor coordinate system the interaction between any two bors is replaced by the one between their equivalence spheres which enclose corresponding bor with epa in this way the transient scattering properties of the randomly distributed mbors can be obtained with high efficiency by the use of the bor basis functions and the weighted laguerre polynomial numerical results are presented to demonstrate the accuracy and efficiency of proposed algorithm

recycling krylov subspaces for sequences of linear systems many problems in science and engineering require the solution of a long sequence of slowly changing linear systems we propose and analyze two methods that significantly reduce the total number of matrix vector products required to solve all systems we consider the general case where both the matrix and right hand side change and we make no assumptions regarding the change in the right hand sides furthermore we consider general nonsingular matrices and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix our methods work well under these general assumptions and hence form a significant advancement with respect to related work in this area we can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems we consider two approaches that allow for the continuous improvement of the recycled subspace at low cost we consider both hermitian and non hermitian problems and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling we also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics materials science and computational physics

integral equation based nonoverlapping ddm using the explicit boundary condition a new integral equation based nonoverlapping domain decomposition method nddm is proposed for analyzing electromagnetic em scattering from electrically large pec objects whose mlfma models are too large for the user s computer to accommodate the integral equation is first built on the entire pec surface and the entire surface is partitioned into some nonoverlapping subsurfaces the rwg functions are used to expand the surface current on the entire surface then each full rwg function across some boundary curve is split into two half rwg functions whose unknown coefficients are constrained by the boundary current continuity using the explicit boundary condition the convergence of the outer iterative scheme of the proposed nddm is investigated theoretically and demonstrated to be very good and hence a very large problem can be effectively solved in an ordinary computer some numerical examples are provided to demonstrate the correctness and robustness of the proposed method and to compare the proposed method with the existing overlapping ddms having similar attributes

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

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

the use of the fft for the efficient solution of the problem of electromagnetic scattering by a body of revolution the enhancement of the computational efficiency of the body of revolution scattering problem is discussed with a view of making it practical for solving large body problems the problem of the electromagnetic scattering by a perfectly conducting body is considered although the methods provided can be extended to multilayered dielectric bodies as well typically the generation of the elements of the moment method matrix consumes a major portion of the computational time it is shown how this time can be significantly reduced by manipulating the expression for the matrix elements in a manner that allows one to compute them efficiently by using the fast fourier transform fft a technique for extracting the singularity of the green s function that appears within the integrands of the matrix diagonal is also presented further enhancing the usefulness of the fft it is shown that with the use of the method discussed here the computational time can be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms

a domain decomposition method for boundary integral equations using a transmission condition based on the near zone couplings a domain decomposition method ddm for the solution of boundary integral equations for impenetrable objects is presented the approach uses a transmission condition which is based on the near range couplings in order to obtain close approximations of the global solution on the subdomains the comparatively strong near zone interactions are taken into account to avoid unphysical reflections from the domain interfaces the algorithm can be accelerated by fast integral solvers such as the multilevel fast multipole method mlfmm by creating local subtrees which coincide with the different computing domains this concept is embedded in an inner outer iterative solution algorithm in which the ddm acts as a preconditioner in the inner iterations by introducing small overlap regions the convergence of the iterative solver is further improved this results in a very robust ddm which can be integrated into existing codes with reasonable effort and which is suited for parallelization numerical results for various open and closed objects demonstrate the effectiveness and the excellent performance of the proposed ddm for the solution of electromagnetic radiation and scattering problems

an iterative solution for electrically large problems combining the characteristic basis function method and the multilevel fast multipole algorithm an iterative scheme for the rigorous computation of electrically large problems is presented the approach is based on a combination of the characteristic basis function method cbfm and the multilevel fast multipole algorithm mlfma that can deal with very large problems that require an iterative solution process even considering that the application of the cbfm entails an important reduction of the number of unknowns when compared to method of moments approaches based on subdomain functions this reduction is due to the fact that the number of macro basis functions called characteristic basis functions cbfs is lesser than the number of low level subsectional functions used to sample the geometry in addition the use of the mlfma avoids the need to calculate and store the coupling terms in the reduced matrix that are not on or close to the diagonal thereby optimizing the cpu time and the memory storage requirements non uniform rational b splines nurbs surfaces are employed for the representation of the geometry and the cbfs are described in terms of curved rooftops generated in the parametric space the associated macro testing functions are defined as aggregations of curved razor blade functions

a discontinuous galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets we present a discontinuous galerkin surface integral equation method herein referred to as iedg for time harmonic electromagnetic wave scattering from nonpenetrable targets the proposed iedg algorithm allows the implementation of the combined field integral equation cfie using square integrable trial and test functions without any considerations of continuity requirements across element boundaries due to the local characteristics of basis functions it is possible to employ nonconformal surface discretizations of the targets furthermore it enables the possibility to mix different types of elements and employ different order of basis functions within the same discretization therefore the proposed iedg method is highly flexible to apply adaptation techniques numerical results are included to validate the accuracy and demonstrate the versatility of the proposed iedg method in addition a complex large scale simulation is conducted to illustrate the potential benefits offered by the proposed method for modeling multiscale electrically large targets

role of conditional probability in multiscale stationary markovian processes the aim of the paper is to understand how the inclusion of more and more time scales into a stochastic stationary markovian process affects its conditional probability to this end we consider two gaussian processes i a short range correlated process with an infinite set of time scales bounded from above and ii a power law correlated process with an infinite and unbounded set of time scales for these processes we investigate the equal position conditional probability p x t ensuremath mid x 0 and the mean first passage time t x ensuremath lambda the function p x t ensuremath mid x 0 can be considered as a proxy of the persistence i e the fact that when a process reaches a position x then it spends some time around that position value the mean first passage time can be considered as a proxy of how fast is the process in reaching a position at distance ensuremath lambda starting from position x in the first investigation we show that the more time scales the process includes the larger is the persistence specifically we show that the power law correlated process shows a slow power law decay of p x t ensuremath mid x 0 to the stationary probability density function by contrast the short range correlated process shows a decay dominated by an exponential cutoff moreover we also show that the existence of an infinite and unbounded set of time scales is a necessary but not sufficient condition for observing a slow power law decay of p x t ensuremath mid x 0 in fact in the context of stationary markovian processes such a form of persistence seems to be associated with the existence of an algebraic decay of the autocorrelation function in the second investigation we show that for large values of ensuremath lambda the more time scales the process includes the larger is the mean first passage time i e the slower is the process on the other hand for small values of ensuremath lambda the more time scales the process includes the smaller is the mean first passage time i e when a process statistically spends more time in a given position the likelihood that it reached nearby positions by chance may also be enhanced

power law tail distributions and nonergodicity we establish an explicit correspondence between ergodicity breaking in a system described by power law tail distributions and the divergence of the moments of these distributions

analysis of large complex structures with the synthetic functions approach an innovative procedure is presented that allows the method of moments mom analysis of large and complex antenna and scattering problems at a reduced memory and cpu cost bounded within the resources provided by a standard 32 bit personal computer the method is based on the separation of the overall geometry into smaller portions called blocks and on the degrees of freedom of the field the blocks need not be electrically unconnected on each block basis functions are generated with support on the entire block that are subsequently used as basis functions for the analysis of the complete structure only a small number of these functions is required to obtain an accurate solution therefore the overall number of unknowns is drastically reduced with consequent impact on storage and solution time these entire domain basis functions are called synthetic functions they are generated from the solution of the electromagnetic problem for the block in isolation under excitation by suitably defined sources the synthetic functions are obtained from the responses to all sources via a procedure based on the singular value decomposition because of the strong reduction of the global number of unknowns one can store the mom matrix and afford a direct solution the method is kernel free and can be implemented on existing mom codes

efficient electromagnetic scattering computation using the random auxiliary sources method for multiple composite 3 d arbitrary objects the electromagnetic em scattering problem from three dimensional 3 d arbitrary composite objects is proposed using the random auxiliary sources ras method based on direct application of the boundary conditions with the uniqueness theorem and the use of random equivalent problems concept more degrees of freedom to the sources positions are added resulting in significantly efficient solutions with lower memory requirements the technique does not require any singularity treatment due to placing the equivalent sources away from the boundaries while boundary conditions are not enforced exactly an iterative framework is introduced that can achieve an acceptable level of error in their satisfaction for an arbitrary randomly generated set of equivalent sources the presented technique promises a significant reduction in the execution time and memory requirements compared to the surface equivalent based method of moments mom the solution stability repeatability and numerical noise susceptibility are investigated thoroughly through this work also a novel edge correction scheme has been implemented to extend the capabilities of this procedure to structures with sharp edges the results of the presented technique are compared to series solutions for conducting spheres and a commercially available mom code for arbitrarily shaped objects and combinations of different materials

electromagnetic scattering for multiple pec bodies of revolution using equivalence principle algorithm an equivalence principle algorithm epa method is extended to analyze the electromagnetic scattering from multiple bodies of revolution mbor with the axes arbitrarily oriented equivalence spheres are used to enclose each bor and the equivalence currents are expanded by the basis functions of bodies of revolution bor to obtain the scattering operators and translation operators of epa for fourier modes independently the rotational symmetry systems are established in local bor coordinate systems the origin of the local bor coordinate system is located at the center of the equivalence sphere and the z axis coincides with the axis of the enclosed bor to obtain the scattering operator of each equivalence sphere whereas the origin is located at the observation sphere and z axis passes through the center of the source sphere to obtain the translation operator of each pair of equivalence spheres the current coefficient transformation algorithm is used to transform the equivalence currents among local bor coordinate systems the total equation is iteratively solved in the global coordinate system the proposed scheme is especially efficient for the analysis of scattering from mbor randomly distributed in electrically large scale region numerical results are given to demonstrate the efficiency

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

fast computation of angular responses of large scale three dimensional electromagnetic wave scattering many applications in electromagnetic engineering require predicting the currents induced by a wide range of incident plane waves on a given object this paper proposes a way to efficiently and accurately compute the angular responses for electrically large targets since the targets of concern are electrically large we have employed the newly developed non conformal domain decomposition method ddm as the direct maxwell equation solver the proposed fast angular sweep algorithm is then applied in conjunction with the ddm solver to produce wide range of angular responses there are basically three main ingredients in the proposed fast angular sweep algorithm the use of fourier harmonics to interpolate the right hand sides rhss over a given angular range the number of independent coefficient vectors in the fourier harmonics can be further reduced through the application of singular value decomposition svd and finally the matrix solution of multiple rhss can be solved efficiently using a recently proposed krylov recycling method gcro dr three numerical results are presented and compared to measurements and direct computations to validate the numerical solutions and to illustrate the effectiveness of the proposed approach

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

a domain decomposition method with nonconformal meshes for finite periodic and semi periodic structures we present a domain decomposition method as a preconditioner for krylov type solvers to model complex electromagnetic problems containing periodicities the method reduces memory requirements by decomposing the original problem into several nonoverlapping sub domains the 1st order transmission condition is employed on interfaces between adjacent sub domains to enforce continuity of electromagnetic fields and to ensure the sub domain problems are well posed by following the spirit of duality paring a symmetric system is obtained to reduce the computational burdens of the present method the finite element tearing and interconnecting like algorithm is adopted this algorithm results in the computation of the so called numerical green s function which can be compressed efficiently via a rank revealing matrix factorization algorithm the final system matrix is solved by krylov solvers instead of classical stationary solvers to improve the convergence of iterative solvers several robust implementation details are discussed and the choice of some popular krylov subspace solvers is studied through numerical examples

modular fast direct electromagnetic analysis using local global solution modes local global solution logos modes provide a computationally efficient framework for developing fast direct solution methods for electromagnetic simulations logos modes provide a single basis for which both electromagnetic operators and their inverses are sparse with a controllable accuracy for fixed frequency modeling with h refinement efficient application of this observation is shown to provide efficient factorization algorithms for both integral equation and finite element methods in addition to providing fast direct solutions the logos framework is also shown to provide a new strategy for modular electromagnetic analysis the possibility of developing efficient direct solution strategies at high frequencies using the logos framework is also discussed

connected patch array analysis using the characteristic basis function method the characteristic basis function method cbfm is extended to apply to efficient analysis of dual polarized connected patch arrays where neighboring patches are connected via two wire transmission lines and a groundplane comparison with a reference solution shows that the use of tertiary basis functions can significantly improve the cbfm approximation to the array currents and radiation patterns a simple procedure for estimating the error in the cbfm current is shown to produce good approximations to the true error and therefore may be useful more generally in determining suitable parameters of the cbfm basis the technique is applied to a prototype phased array feed for a next generation radio telescope a thin dielectric supporting the array patches is shown to produce a loading effect that modifies the radiation patterns good agreement with the results of other techniques and measured data has been obtained

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

wave field interaction with complex structures using equivalence principle algorithm a domain decomposition scheme based on the equivalence principle similar to huygens principle for integral equation solvers and the method of moments is introduced the equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume it also allows the dissociation of the solution of one region from that of another region in this manner problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns it can aid in parallel algorithms reusability of solutions as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed the challenge arises when an equivalence surface intercepts a current carrying conductor because the breakup of the current into separate pieces gives rise to charge singularity a junction basis can be used to mitigate this singularity however a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces using this scheme the current continuity is conserved and the singularity of the charges is avoided the solution is shown to be accurate