growing radial basis neural networks merging supervised and unsupervised learning with network growth techniques this paper proposes a framework for constructing and training radial basis function rbf neural networks the proposed growing radial basis function grbf network begins with a small number of prototypes which determine the locations of radial basis functions in the process of training the grbf network gross by splitting one of the prototypes at each growing cycle two splitting criteria are proposed to determine which prototype to split in each growing cycle the proposed hybrid learning scheme provides a framework for incorporating existing algorithms in the training of grbf networks these include unsupervised algorithms for clustering and learning vector quantization as well as learning algorithms for training single layer linear neural networks a supervised learning scheme based on the minimization of the localized class conditional variance is also proposed and tested grbf neural networks are evaluated and tested on a variety of data sets with very satisfactory results

fast multipole method for scattering from an arbitrary pec target above or buried in a lossy half space the fast multipole method fmm was originally developed for perfect electric conductors pecs in free space through exploitation of the spectral properties of the free space green s function in the work reported here the fmm is modified for scattering from an arbitrary three dimensional 3 d pec target above or buried in a lossy half space the near terms in the fmm are handled via the original method of moments mom analysis wherein the half space green s function is evaluated efficiently and rigorously through application of the method of complex images the far fmm interactions which employ a clustering of expansion and testing functions utilize an approximation to the green s function dyadic via real image sources and far field reflection dyadics the half space fmm algorithm is validated through comparison with results computed via a rigorous mom analysis further a detailed comparison is performed on the memory and computational requirements of the mom and fmm algorithms for a target in the vicinity of a half space interface

a novel multilevel matrix compression method for analysis of electromagnetic scattering from pec targets we present a new multilevel matrix compression method mlmcm and its application to the analysis of scattering problems from three dimensional 3 d arbitrary shaped conductors the compression is achieved without generating the full subblocks of the matrix by the rank based method unlike the conventional rank based method incoming compression matrix and outgoing compression matrix are defined when coupling with a cluster of its far interaction groups only a small translation matrix is redefined for every two coupling groups the merits of the proposed method are 1 it is kernel function independent and can be applied to arbitrary complex media 2 it is more efficient than conventional rank based methods this paper shows numerical results to demonstrate the validity of the proposed method

efficient inversion of the galerkin matrix of general second order elliptic operators with nonsmooth coefficients this article deals with the efficient approximate inversion of finite element stiffness matrices of general second order elliptic operators with l coefficients it will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices h matrices furthermore numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity

a fast analysis of scattering from large scale finite periodic microstrip patch arrays arranged on a non orthogonal lattice using sub entire domain basis functions a sub entire domain sed basis function method which was first introduced for modeling large scale finite periodic pec structures in free space has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array the microstrip array may have a nonrectangular layout and non orthogonal lattice configurations e g hexagons or quadrangles based on the mixed potential integral equation and utilizing the proposed sed basis function algorithm the original large scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions the first is to construct the sed basis functions for the corresponding microstrip arrays with orthogonal non orthogonal lattices three kinds of the sed basis functions are constructed including those related to the edge patch elements the interior patch elements and the corner patch elements the second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem based on the obtained sed basis functions the reduced matrix equation of small size can be generated by the galerkin procedure and solved by use of the lu lower upper decomposition based direct solver which results in a fast solution the accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large scale finite periodic arrays of microstrip patches with rectangular non orthogonal lattices

a fast directional algorithm for high frequency electromagnetic scattering this paper is concerned with the fast solution of high frequency electromagnetic scattering problems using the boundary integral formulation we extend the o nlogn directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case we also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm when combined with a standard iterative method this results in an almost linear complexity solver for the combined field integral equations in addition the butterfly algorithm is utilized to compute the far field pattern and radar cross section with o nlogn complexity

interaction of electromagnetic waves with 3 d arbitrarily shaped homogeneous chiral targets in the presence of a lossy half space the interaction of electromagnetic waves with an arbitrarily shaped three dimensional 3 d homogeneous chiral object located above a lossy half space is investigated using the method of moments mom via the coupled mixed potential integral equations mpies based on the surface equivalence principle the equivalent surface electric and magnetic currents are used to replace the homogeneous chiral target in the presence of the half space two coupled mpies are developed for the unknown equivalent surface electric and magnetic currents by utilizing the continuity condition of the tangential total electric and magnetic field components on the chiral body s surface the well known galerkin procedure with rao wilton glisson rwg basis functions is applied to solve this problem the spatial domain half space green s functions are obtained from the corresponding spectral domain green s functions via the discrete complex image method dcim combined with the generalized pencil of function gpof technique the reciprocity theorem is employed to calculate the far zone scattered field numerical results are presented for characterizing electromagnetic scattering by a 3 d arbitrarily shaped homogenous chiral object located above a lossy half space so as to demonstrate the accuracy and efficiency of the proposed technique

an effective mom solution with nested complex source beam method for electromagnetic scattering problems a nested complex source beam ncsb method based on octree structure is proposed to accelerate the method of moments mom solution for three dimensional 3 d electromagnetic scattering analysis at the finest level the far field contribution of each basis function is expressed with that of complex source beams csbs distributed on the equivalent sphere surface for every group furthermore the far field radiated by csbs of the source group at child level can be represented by that radiated by csbs of the source group at parent level similarly the received field of csbs for each observation group at the parent level can be expressed with that of csbs belong to their child level group an equivalent relationship of csbs between every two adjacent levels is built to obtain the nested equivalent process for ncsb method and only the csbs at the finest level have the direct association with the basis functions in their group the ncsb method is shown to be o nlogn computational complexity for both matrix vector product mvp time and memory storage by numerical examples with appropriate parameters and numerical results demonstrate the better efficiency of the proposed method than the current multilevel csb method

fast rcs computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique the method of moments mom in conjunction with the asymptotic waveform evaluation awe technique is applied to obtain the radar cross section rcs of an arbitrarily shaped three dimensional 3 d perfect electric conductor pec body over a frequency band the electric field integral equation efie is solved using the mom to obtain the equivalent surface current on the pec body in the awe technique the equivalent surface current is expanded in a taylor s series around a frequency in the desired frequency band the taylor series coefficients are then matched via the pade approximation to a rational function using the rational function the surface current is obtained at any frequency within the frequency range which is in turn used to calculate the rcs of the 3 d pec body a rational function approximation is also obtained using the model based parameter estimation mbpe method and compared with the pade approximation numerical results for a square plate a cube and a sphere are presented over a frequency bandwidth good agreement between the awe and the exact solution over the bandwidth is observed

co evolutionary algorithm for structural damage identification using minimal physical testing the problem of damage identification using minimum test data is studied in this work data sparsity in damage identification applications commonly results in inverse problems that are mathematically ill posed e g non unique solutions although solution non uniqueness may be addressed by performing multiple tests on a structure it is not trivial to decide which tests to carry out given that actual physical testing is costly this problem is addressed in this work through a new co evolutionary algorithm that interactively searches for damage scenarios and optimum physical tests the algorithm is composed of two stages the estimation phase which searches for damage scenarios that can predict current physical tests and the exploration phase which searches for tests that increase the level of information about the damaged system the feasibility of the methodology is demonstrated using numerical examples copyright 2006 john wiley sons ltd

an cal h 2 matrix based integral equation solver of reduced complexity and controlled accuracy for solving electrodynamic problems using an h 2 matrix as the mathematical framework we compactly represent a dense system matrix by a reduced set of parameters thus enabling a significant reduction in computational complexity the error bound of the h 2 matrix based representation of an electrodynamic problem was derived we show that exponential convergence with respect to the number of interpolation points can be achieved irrespective of the electric size in addition we show that a direct application of h 2 matrix based techniques to electrodynamic problems would result in a complexity greater than o n with n being the matrix size due to the need of increasing the rank when ascending an inverted tree in order to keep a constant order of accuracy a rank function was hence developed to maintain the same order of accuracy in a wide range of electric sizes without compromising computational complexity with this rank function we demonstrate that given a range of electric sizes which lead to a range of n the dense system of o n 2 parameters can be compactly stored in o n units and the dense matrix vector multiplication can be performed in o n operations moreover the same order of accuracy can be kept across this range the method is kernel independent and hence is suitable for any integral equation based formulation in addition it is applicable to arbitrary structures numerical experiments from small electric sizes to 64 wavelengths have demonstrated the performance of the proposed method

on the treatment of arbitrary boundary conditions using a fast direct mathcal h matrix solver in mom this communication adapts the formalism of hierarchical mathcal h matrices to the direct solution process lu decomposition of the method of moments mom in the frequency domain a novel clustering approach based on physical constraints is presented and extended to treat dielectric bodies as well as arbitrary boundary conditions comparisons with other numerical methods are provided the analyses show a considerable speedup of the computation times and a significant reduction of required memory compared with the traditional mom solution process especially for highly resonant structures where iterative solvers like the multilevel fast multipole algorithm show poor convergence

a fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered media a newly developed iterative method the stabilized biconjugate gradient fast fourier transform bcgs fft method is applied to simulate electromagnetic scattering from large inhomogeneous objects embedded in a planarly layered medium in this fast solver the weak form formulation is applied to obtain a less singular discretization of the volume electric field integral equation several techniques are utilized to speed up the dyadic green s function evaluation to accelerate the operation of the dyadic green s function on an induced current i e the green s operation the green s function is split into convolutional and correlational components so that fft can be applied the cpu time and memory cost of this bcgs fft method is o nlogn and o n respectively where n is the number of unknowns significantly more efficient than the method of moments mom as a result this method is capable of solving large scale electromagnetic scattering problems in a planarly layered background a large scale scattering problem in a layered medium with more than three million unknowns has been solved on a sun ultra 60 workstation with 1 2 gbytes memory

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

pareto optimal sensor locations for structural identification theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling for a single model class the information entropy is used as the optimality criterion for selecting the best sensor configuration for multiple model classes the problem is formulated as a multi objective optimization problem of finding the pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices a heuristic algorithm is proposed for constructing effective pareto optimal sensor configurations that are superior in terms of computational efficiency and accuracy to the pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi objective optimisation problems the theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10 dof chain like spring mass model and a 32 dof truss structure

a decision theoretic rough set approach for dynamic data mining uncertainty and fuzziness generally exist in real life data approximations are employed to describe the uncertain information approximately in rough set theory certain and uncertain rules are induced directly from different regions partitioned by approximations approximation can further be applied to data mining related task hbox e g attribute reduction nowadays different types of data collected from different applications evolve with time especially new attributes may appear while new objects are added this paper presents an approach for dynamic maintenance of approximations hbox w r t objects and attributes added simultaneously under the framework of decision theoretic rough set dtrs equivalence feature vector and matrix are defined first to update approximations of dtrs in different levels of granularity then the information system is decomposed into subspaces and the equivalence feature matrix is updated in different subspaces incrementally finally the approximations of dtrs are renewed during the process of updating the equivalence feature matrix extensive experimental results verify the effectiveness of the proposed methods

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

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 mixed form thin stratified medium fast multipole algorithm for both low and mid frequency problems a mixed form thin stratified medium fast multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid frequencies the newly developed matrix friendly formula of layered medium green s function is applied in this algorithm for well separated interactions the path deformation technique is implemented to achieve a smoother and exponentially convergent integral the two dimensional addition theorem is then incorporated into the integrand to expedite the matrix vector product in our approach multipole expansion low frequency fast multiple algorithm as well as the plane wave expansion mid frequency fast multipole algorithm of the translational addition theorem are combined into a single multilevel tree to capture quasi static physics and wave physics simultaneously the outgoing wave is represented first in terms of multipole expansion at leafy levels and then switched to plane wave expansion automatically at higher levels this seamless connection makes the algorithm applicable in simulations where subwavelength interaction and wave physics both exist

a fast full wave analysis of scattering and radiation from large finite arrays of microstrip antennas a fast full wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented the technique discretizes the mixed potential integral equation mpie in the spatial domain by means of a full wave discrete complex image method the del operators on the green s functions are transferred from the singular kernel to the expansion and testing functions the resultant system of equations is solved using the biconjugate gradient bcg method in which the matrix vector product is evaluated efficiently using the fast fourier transform fft this results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas several numerical results are presented demonstrating the accuracy efficiency and capability of this technique

self adaptive hp finite element method with iterative mesh truncation technique accelerated with adaptive cross approximation abstract to alleviate the computational bottleneck of a powerful two dimensional self adaptive h p finite element method fem for the analysis of open region problems which uses an iterative computation of the integral equation over a fictitious boundary for truncating the fem domain we propose the use of adaptive cross approximation aca to effectively accelerate the computation of the integral equation it will be shown that in this context aca exhibits a robust behavior yields good accuracy and compression levels up to 90 and provides a good fair control of the approximants which is a crucial advantage for h p adaptivity theoretical and empirical results of performance computational complexity comparing the accelerated and non accelerated versions of the method are presented several canonical scenarios are addressed to resemble the behavior of aca with h p and h p adaptive strategies and higher order methods in general

volume surface integral equation method based on higher order hierarchical vector basis functions for em scattering and radiation from composite metallic and dielectric structures this paper presents a novel galerkin type method of moments solution of the volume surface integral equation vsie which is developed for the analysis of electromagnetic scattering and radiation from composite metallic and dielectric structures our new scheme utilizes curved tetrahedral elements and curved triangular patches for geometric modeling and the associated higher order hierarchical vector hohv basis functions for volume surface current modeling in contrast to the previous studies on higher order vsie our scheme which is reported for the first time in vsie is much more flexible in comparison with the conventional low order scheme our scheme requires much less memory and computational time for the same accuracy level numerical results are provided to demonstrate the accuracy efficiency and flexibility of our scheme

a neural fuzzy modelling framework based on granular computing concepts and applications fuzzy and neural fuzzy systems have successfully and extensively applied to solve problems in many research areas such as those associated with industrial medical and academic applications however recent trends reveal a demand for a workflow with a particular emphasis on transparency simplicity system interpretability as well as on a strong link with human cognition such requirement is mainly driven by research areas where expert knowledge is of very high importance and any new proposed modelling system falls under the interpretability scrutiny of experts in order to confirm the system s validity the relatively recent paradigm of granular computing grc offers an ideal opportunity for a transparent knowledge discovery methodology to be combined with fuzzy logic thereby towards a systematic modelling framework with a focus on the overall transparency of the system such transparency in the workflow allows for better interaction between the expert process knowledge and the system design which translates into a better performing system in this paper a systematic modelling approach using granular computing grc and neural fuzzy modelling is presented in this research study a grc algorithm is used to extract relational information and data characteristics out of an initial database the extracted knowledge and granular features are then translated into a linguistic rule base of a fuzzy system this rule base is finally elicited and optimised via a neural fuzzy modelling structure during the various steps of this methodology the transparency features are highlighted and it is shown here how the system designer can take advantage of such features to enhance the system the proposed modelling framework is applied to a multi dimensional and complex data set consisting of measurements of mechanical properties of heat treated steel the data set is collected from a real industrial process and the measurements are dictated by customer production demands and the data set is very sparse with many discontinuities the proposed framework successfully models the mechanical properties of heat treated steel and it further improves upon the performance of previously established modelling structures

mining association rules from imprecise ordinal data categorical data can generally be classified into ordinal data and nominal data although there have been numerous studies on finding association rules from nominal data few have tried to do so from ordinal data additionally previous mining algorithms usually assume that the input data is precise and clean which is unrealistic in practical situations real world data tends to be imprecise due to human errors instrument errors recording errors and so on therefore this paper proposes a new approach to discovering association rules from imprecise ordinal data experimental results from the survey data show the feasibility of the proposed mining algorithm performance analyses of the algorithms also show that the proposed approach can discover interesting and valuable rules that could never be found using the conventional approach the apriori algorithm

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

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

mom matrix generation based on frequency and material independent reactions fmir mom a novel and efficient method of moments mom matrix generation technique called the frequency and material independent reactions for the method of moments fmir mom technique is presented this new matrix generation algorithm efficiently calculates impedance matrices while sweeping through frequency permittivity conductivity and or permeability values for frequency sweeps it has computational and memory costs comparable to those of interpolation techniques it has the advantage over interpolation techniques in that it does not divide the frequency range into segments and allows one to dynamically update the precision the technique expands the exponential of the green s function into a taylor series this allows the problem to be formulated as a summation where each term consists of a real valued matrix depending only on the geometry discretization multiplied by a scalar dependent on the propagation constant the algorithm s efficiency is obtained by calculating the geometry dependent matrices prior to sweeping through frequency or material parameters

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

compensatory neurofuzzy systems with fast learning algorithms in this paper a new adaptive fuzzy reasoning method using compensatory fuzzy operators is proposed to make a fuzzy logic system more adaptive and more effective such a compensatory fuzzy logic system is proved to be a universal approximator the compensatory neural fuzzy networks built by both control oriented fuzzy neurons and decision oriented fuzzy neurons cannot only adaptively adjust fuzzy membership functions but also dynamically optimize the adaptive fuzzy reasoning by using a compensatory learning algorithm the simulation results of a cart pole balancing system and nonlinear system modeling have shown that 1 the compensatory neurofuzzy system can effectively learn commonly used fuzzy if then rules from either well defined initial data or ill defined data 2 the convergence speed of the compensatory learning algorithm is faster than that of the conventional backpropagation algorithm and 3 the efficiency of the compensatory learning algorithm can be improved by choosing an appropriate compensatory degree

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

fast dual mgs block factorization algorithm for dense mom matrices a robust method is introduced for efficiently compressing dense method of moments mom matrices using a dual modified gram schmidt block qr factorization algorithm based on low rank singular value decomposition the compression is achieved without generating the full matrix or even full subblocks of the matrix the compressed matrix may then be used in the iterative solution of the mom problem the method is very robust because it uses a reduced set of the original matrix entries to perform the compression furthermore it does not depend on the analytic form of the green s function so it may be applied to arbitrarily complex media

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

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

on the relationship between multiple scattering macro basis functions and krylov subspace iterative methods a mathematical link is provided between the krylov subspace iterative approach based on the full orthogonalization method fom and the macro basis functions mbf approach based on a multiple scattering methodology the link refers to the subspaces created by those methods as well as to the orthogonality conditions which they satisfy both approaches are applied to the same method of moments mom system of equations that is preconditioned based on a closest interaction rule and where blocks of the mom impedance matrix are compressed using a rank revealing method mbf and fom approaches are compared numerically with a special attention given to accuracy for perfectly conducting objects comprising an array of tapered slot antennas spheres and an aircraft the respective advantages of both methods are briefly discussed and further prospects are given

study of mixed order basis functions for the locally corrected nystro spl uml m method a high order locally corrected nystro spl uml m lcn method employing the mixed order basis functions proposed by c 80al spl iota s 80kan and peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies an integral operator based on a combined field formulation for conducting surfaces and a mu spl uml ller formulation for dielectric surfaces is used it is found that for general scattering objects mixed order basis functions accelerate the convergence of the lcn solution can eliminate spurious charges and can significantly reduce the condition number of the impedance matrix

scattering by conducting bodies coated with bi isotropic materials electromagnetic scattering by arbitrarily shaped conducting bodies coated with general bi isotropic materials is formulated in terms of the surface integral equation method in order to facilitate the implementation of the surface equivalence principle a field decomposition scheme is utilized to split a bi isotropic media into two equivalent isotropic media by enforcing the boundary condition on the interfaces of the body a set of coupled integral equations is finally obtained for the unknown surface currents and then numerically solved using the moment methods combined with the vector triangular basis function the fast multipole technique has been embedded into the algorithm to accelerate the solution process the validity of theoretical formulations is verified by numerical results and their comparisons the calculated results for bi isotropically coated conducting spheres and oblate spheroids are compared with the exact solution and the existing data and excellent agreements are observed

numerical simulation of vector wave scattering from the target and rough surface composite model with 3 d multilevel uv method numerical simulation of vector wave scattering from three dimensional 3 d target and rough surface composite model is investigated with a 3 d multilevel uv method due to the adoption of rwg basis functions for accurate modeling of vector current the oscillation of the interaction matrix elements brings difficulty to directly apply the uv decomposition method based on the reordering of the interaction strength and the sampling according to the characteristics distribution of the interaction an em interaction based sampling algorithm is developed for the accurate reconstruction of the far interaction submatrix with uv decomposition method combined with multilevel division of the total composite model the 3 d multilevel uv method incorporating the new sampling algorithm is developed for vector wave scattering from 3 d complex target above or on a random rough surface the 3 d multilevel uv method yields a complexity of o n log n for the setup time of the impedance matrix the solve time of the matrix iterative solution and also for the memory requirements the accuracy and the efficiency of the 3 d multilevel uv method is compared and validated with the full mom method and the aca method in the tested cases finally the applications of a target above or on the rough surface for example a ship on the sea surface have been accomplished and analyzed

a single level low rank ie qr algorithm for pec scattering problems using efie formulation this paper presents a single level matrix compression algorithm termed ie qr based on a low rank approximation to speed up the electric field integral equation efie formulation it is shown with the number of groups chosen to be proportional to n sup 1 2 where n is the number of unknowns the memory and cpu time for the resulting algorithm are both o n sup 1 5 the unique features of the algorithm are a the ie qr algorithm is based on the near rank deficiency property for well separated groups this near rank deficiency assumption holds true for many integral equation methods such as laplacian radiation and scattering problems in electromagnetics em the same algorithm can be adapted to other applications outside em with few or no modifications and b the rank estimation is achieved by a dual rank process which ranks the transmitting and receiving groups respectively thus the ie qr algorithm can achieve matrix compression without assembling the entire system matrix also a geometric neighboring preconditioner is presented in this paper this geometric neighboring preconditioner when used in conjunction with gmres is proven to be both efficient and effective for solving the compressed matrix equations

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

a fast technique applied to the analysis of resistive wall modes with 3d conducting structures this paper illustrates the development of a fast technique for the analysis of resistive wall modes rwms in fusion devices with three dimensional conducting structures by means of the recently developed carma code thanks to its peculiar features the computational cost scales almost linearly with the number of discrete unknowns some large scale problems are solved in configurations of interest for the international thermonuclear experimental reactor iter

complex source beam moment method procedure for accelerating numerical integral equation solutions of radiation and scattering problems a new hybrid complex source beam moment method csb mom procedure is presented to accelerate the matrix vector product mvp computation in the iterative solution of moment method integral equation problems the scattering object in this csb mom algorithm is partitioned into groups in a manner similar to the fast multipole method fmm however unlike fmm the interactions between well separated groups are computed by using the complex source beams csbs which represent the radiation from the basis elements in the group the directional properties of csbs allow a fast evaluation for these interactions such that the overall mvp is computed very efficiently the direct solution time and the storage requirement of the csb mom method is numerically shown to be o n3 2 by optimally selecting the number of groups a low memory version of a new hybrid complex source beam moment method csb mom procedure is presented to accelerate the matrix vector product mvp computation in the iterative solution of moment method integral equation problems the scattering object in this csb mom algorithm is partitioned into groups in a manner similar to the fast multipole method fmm however unlike fmm the interactions between well separated groups are computed by using the complex source beams csbs which represent the radiation from the basis elements in the group the directional properties of csbs allow a fast evaluation for these interactions such that the overall mvp is computed very efficiently the direct solution time and the storage requirement of the csb mom method is numerically shown to be o n3 2 by optimally selecting the number of groups a low memory version of the csb mom method is also presented wherein separated group interactions are computed on the fly the csb mom method is also presented wherein separated group interactions are computed on the fly

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

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

identification of fuzzy models using a successive tuning method with a variant identification ratio the paper is concerned with the identification of fuzzy inference systems fuzzy models realized with the aid of the successive tuning method using a variant identification ratio that is based on hierarchical fair competition based parallel genetic algorithms hfc pga and information granulation the hfc pga is a certain multi population version of parallel genetic algorithms pga which is suitable for a simultaneous optimization of both the structure of the fuzzy model as well as its parameters the granulation of information is realized with the aid of the c means clustering algorithm information granules formed in this way become essential at further stages of the construction of the fuzzy models by forming the centers modal values of the fuzzy sets constituting individual rules of the inference schemes further optimization of the fuzzy model deals with an adjustment of a suite of parameters such as the number of input variables to be used in the model a collection of specific subsets of the input variables and the number of membership functions being used by these variables and the order and parameters of the polynomial occurring in the conclusions of the corresponding rules an iterative development of the fuzzy model deals with its structural as well as parametric optimization via hfc pga the c means algorithm and a standard least square estimation method to evaluate the performance of the proposed model we exploit well known and commonly used data sets such as gas furnace mackey glass time series as well as medical imaging system a comparative analysis demonstrates that the proposed model leads to the superior performance when compared with other fuzzy models reported in the literature

fast analysis of large finite arrays with a combined multiresolution sm aim approach we present a synthesis of the sparse matrix adaptive integral method sm aim and the multiresolution mr approach for the analysis of electrically large finite arrays with planar or 3 d radiating elements the two methods were separately introduced previously the use of the mr has the effect of a preconditioner and speeds up the convergence rate of the sm aim of almost two orders of magnitude with a total reduction of the numerical complexity with respect to the standard mom of almost three orders of magnitude

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 calderon multiplicative preconditioner for the pmchwt equation for scattering by chiral objects scattering of time harmonic electromagnetic waves by chiral structures can be modeled via an extension of the poggio miller chan harrington wu tsai pmchwt boundary integral equation for analyzing scattering by dielectric objects the classical pmchwt equation however suffers from dense discretization breakdown the matrices resulting from its discretization become increasingly ill conditioned when the mesh density increases this contribution revisits the pmchwt equation for chiral media it is demonstrated that it also suffers from dense discretization breakdown this dense discretization breakdown is mitigated by the construction of a calderon multiplicative preconditioner a stable discretization scheme is introduced and the resulting algorithm s accuracy and efficiency are corroborated by numerical examples

on the representation of fuzzy rules in terms of crisp rules there are two classical ways of viewing a fuzzy set in terms of a combination of crisp sets either as a weighted max aggregation of its level cuts or as a convex combination of the latter these views are applied to the particular case of fuzzy relations which are induced by fuzzy rules where the rules are modeled by implication connectives defined on a finite subset of the unit interval the paper studies more closely the representation of such fuzzy rules in terms of a convex combination of gradual rules a special type of implication based fuzzy rule inducing a crisp relation this representation which might be interpreted in a probabilistic way is shown to be unique on the assumption that the implication operator used for modeling the fuzzy rule does not satisfy a special kind of strict monotonicity condition in this case the crisp relations induced by the involved gradual rules correspond to level cuts of the fuzzy relation associated with the fuzzy rule however other representations might exist if the aforementioned property is not satisfied under a slightly stronger strict monotonicity condition the existence of further non consonant representations is even guaranteed then the crisp relations induced by gradual rules do not necessarily correspond to level cuts of the underlying fuzzy relation in this sense the decomposition of a fuzzy rule into a class of crisp implication based rules is more general than the classical decomposition of fuzzy sets

optimal sensor placement methodology for parametric identification of structural systems abstract theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the information entropy measuring the uncertainty in the system parameters is used as the performance measure of a sensor configuration a useful asymptotic approximation for the information entropy valid for a large number of measured data is derived the asymptotic estimate is then used to rigorously justify that selections of the optimal sensor configuration can be based solely on a nominal structural model ignoring the time history details of the measured data which are not available in the experimental design stage it is further shown that the lower and upper bounds of the information entropy are decreasing functions of the number of sensors based on this result two algorithms are proposed for constructing effective sensor configurations that are superior in terms of computational efficiency and accuracy to the sensor configurations provided by genetic algorithms the theoretical developments and the effectiveness of the proposed algorithms are illustrated by designing the optimal configuration for a 10 degree of freedom d o f chain like spring mass model and a 240 d o f three dimensional truss structure

a multilevel implementation of the qr compression for method of moments we present a multilevel version of a previously reported compression technique for the method of moments poirier j r et al ibid vol 46 p 1175 6 1998 this method is based on qr compression of the impedance matrix off diagonal blocks the block structure of the matrix is built up to optimize the compression rate it results from the study that the compression threshold is the unique adjustment parameter which makes this method very easy to handle some results are presented which stress the improvement in memory storage and computation time obtained through this approach with respect to the mono level algorithm

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

efficient analyzing em scattering of objects above a lossy half space by the combined mlqr mlssm a large dense complex linear system is obtained when solving an electromagnetic scattering of arbitrary shaped object located above a lossy half space with the surface integral equation approach to analyze the large dense complex linear system efficiently the multilevel qr mlqr is used to accelerate the matrix vector multiplication when the corresponding matrix equation is solved by a krylov subspace iterative method although the mlqr is more efficient than the direct solution this paper presents a novel recompression technique to further reduce computation time and storage memory the technique applies the multilevel simply sparse method mlssm to the matrices of mlqr using the mlssm a sparser representation of the impedance matrix is obtained and a more efficient matrix vector multiplication is implemented the combined mlqr mlssm is comparable to the mlqr and the adaptive cross approximation singular value decomposition aca svd in terms of computation time and memory requirement remarkably the new formulation can reduce the computational time and memory by about one order of magnitude with excellent accuracy

multilevel fast adaptive cross approximation algorithm with characteristic basis functions this paper presents a multilevel fast adaptive cross approximation mlfaca algorithm for accelerated iterative solution of the method of moments mom matrix equation for electrically large targets the mlfaca compresses the impedance submatrices between well separated blocks into products of sparse matrices constructed with the aid of the fast adaptive cross sampling facs scheme and the butterfly algorithm as a result the mlfaca can reduce both the computational time and the storage of the mom to mathbf o mathbf n mathbf log mathbf 2 text n where mathbf n is the number of the rao wilton glisson rwg basis functions in the analyzed target meanwhile the mlfaca maintains the adaptive and kernel independent properties furthermore the characteristic basis function method cbfm is employed to decrease the size of the outer matrices of the mlfaca to further reduce the storage and iteration time numerical results are presented to demonstrate the advantages of the proposed method including a successful solution of a scattering problem involving 10 861 668 rwg basis functions

cluster centric fuzzy modeling in this study we propose a cluster oriented development of fuzzy models an overall design process is focused on an efficient usage of fuzzy clustering fuzzy c means fcm in particular to form information granules clusters that are used in the construction of the fuzzy model fuzzy models are regarded as mappings from information granules expressed in the input and output spaces this position motivates us to look at the development of the models through the perspective of the construction and efficient usage of information granules this study directly associates fuzzy clustering with fuzzy modeling both in terms of conceptual and algorithmic linkages the augmented fcm method is formed predominantly for modeling purposes so that a balance between the structural content present in the input and output spaces is achieved and this way the performance of the resulting fuzzy model is optimized it is shown that the cluster oriented modeling gives rise to the mamdani like fuzzy rules and a zero order takagi sugeno model under a certain decoding scheme we identify an interesting and direct linkage between the developed fuzzy models and a fundamental idea of encoding decoding or granulation degranulation encountered in processing fuzzy sets and granular computing in general furthermore refinements of zero order fuzzy models are investigated leading to first order fuzzy models with linear functions standing in the conclusions of the rules a series of experiments is reported where we used synthetic and real world data using which an issue of generalization capabilities is elaborated in detail

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

self regularized pseudo time marching schemes for structural system identification with static measurements we explore the application of pseudo time marching schemes involving either deterministic integration or stochastic filtering to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response solutions of such non linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping an important yet inadequately understood aspect in dynamic system identification problems the usual method of least square solution is through a regularized gauss newton method gnm whose results are known to be sensitively dependent on the regularization parameter and data noise intensity finite time recursive integration of the pseudo dynamical gnm pd gnm update equation addresses the major numerical difficulty associated with the near zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration therefore we also propose a pseudo dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo dynamic ensemble kalman filter pd enkf for multiple sets of measurements involving various load cases we expedite the speed of thepd enkf by proposing an inner iteration within every time step results using the pseudo dynamic strategy obtained through pd enkf and recursive integration are compared with those from the conventional gnm which prove that the pd enkf is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small

learning based fast iterative convergence of 3 d mom via eigen agmres method three dimensional 3 d full wave electromagnetic simulation using method of moments mom under the framework of fast solver algorithms like fast multipole method fmm is often bottlenecked by the speed of convergence of the krylov subspace based iterative process this is primarily because the electric field integral equation efie matrix even with cutting edge preconditioning techniques often exhibits bad spectral properties arising from frequency or geometry based ill conditioning which render iterative solvers slow to converge or stagnate occasionally in this communication a novel technique to expedite the convergence of mom matrix solution at a specific frequency is proposed by extracting and applying eigen vectors from a previously solved neighboring frequency in an augmented generalized minimum residual agmres iterative framework this technique can be applied in unison with any preconditioner numerical results demonstrate up to 40 speed up in convergence using the proposed eigen agmres method

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

on the use of the singular value decomposition in the fast multipole method the authors present a new matrix compression algorithm to improve the efficiency of the fast multipole method fmm the method is based on the application of the singular value decomposition svd to the plane wave fmm aggregation matrices these matrices are low ranked which is exploited to provide alternative sets of orthonormal singular basis functions obtained as linear combinations of the original basis by choosing only the most relevant singular functions a much more compact representation is obtained to accurately handle the interactions between the fmm groups the new formulation provides a reduction close to one order of magnitude both in computational cost and memory requirements with a moderate impact on the accuracy of the solution

multilevel adaptive cross approximation mlaca the multilevel adaptive cross approximation mlaca is proposed as a fast method to accelerate the matrix vector products in the iterative solution of the linear system that results from the discretization of electromagnetic integral equations ie with the method of moments mom the single level aca already described in the literature is extended with a multilevel recursive algorithm in order to improve the asymptotical complexity of both the computational cost and the memory requirements the main qualities of aca are maintained it is purely algebraic and independent of the integral equation kernel green s function as long as it produces pseudo rank deficient matrix blocks the algorithm is presented in such a way that it can be easily implemented on top of an existing mom code with most commonly used green s functions

efficient learning algorithms for three layer regular feedforward fuzzy neural networks a key step of using gradient descend methods to develop learning algorithms of a regular feedforward fuzzy neural network fnn is to differentiate max min functions which contain max spl or and min spl and operations the paper aims at several objectives first investigate further the differentiation of spl or spl and functions second employ general fuzzy numbers which include triangular and trapezoidal fuzzy numbers as special cases to define a three layer regular fnn the general fuzzy numbers related can be approximately determined by their corresponding finite level sets so we can approximately represent the input output i o relationship of the regular fnn as functions of the endpoints of all finite level sets third a fuzzy back propagation algorithm is presented and to speed up the convergence of the learning algorithm a fuzzy conjugate gradient algorithm for fuzzy weights and biases is developed furthermore the convergence of the algorithm is analyzed systematically finally some real simulations demonstrate the efficiency of our learning algorithms the regular fnn is applied to the approximate realization of fuzzy inference rules and fuzzy functions defined on given compact sets

multilevel fast multipole algorithm for general targets on a half space interface the multilevel fast multipole algorithm mlfma is considered for scattering from an electrically large conducting or dielectric target resting on the interface of a dielectric half space we focus on analysis of the half space green s function such that it is computed efficiently and accurately while retaining a form that is applicable to an mlfma analysis attention is also directed toward development of a simple preconditioner to accelerate convergence of the conjugate gradient solver the utility of the model is examined for several applications including scattering from an electrically large vehicle trees and rough dielectric interfaces in the presence of a dielectric half space background

input selection and partition validation for fuzzy modelling using neural network a simple and effective method for selecting significant input variables and determining optimal number of fuzzy rules when building a fuzzy model from data is proposed in contrast to the existing clustering based methods in this approach both input selecting and partition validating are determined on the basis of a class of sub clusters created by a self organising network instead of on the data the important input variables which independently and significantly influence the system output can be extracted by a fuzzy neural network on the other hand the optimal number of fuzzy rules can be determined separately via the fuzzy c means algorithm with a modified fuzzy entropy as the criterion of cluster validation the simulation results show that the proposed method can provide good model structures for fuzzy modelling and has high computing efficiency

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

a sparse factorization for fast computation of localizing modes localizing modes provide an effective basis for developing efficient error controlled factorizations of the dense matrices encountered in integral equation formulations of wave phenomena at low to moderate frequencies an essential component of these factorization algorithms is the numerical determination of the underlying localizing modes this communication describes the details of an efficient procedure for computing the so called non overlapping localizing modes the principle component of the procedure is a qr like factorization of the sparse multilevel data structure used to compress discrete integral operators numerical examples demonstrate the performance of the algorithm

long term learning for type 2 neural fuzzy systems abstract the development of a new long term learning framework for interval valued neural fuzzy systems is presented for the first time in this article the need for such a framework is twofold to address continuous batch learning of data sets and to take advantage the extra degree of freedom that type 2 fuzzy logic systems offer for better model predictive ability the presented long term learning framework uses principles of granular computing grc to capture information knowledge from raw data in the form of interval valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long term learning fashion the latter is to accommodate new input output mappings and new classes of data without significantly disturbing existing input output mappings therefore maintaining existing performance while creating and integrating new knowledge rules this is achieved via an iterative algorithmic process which involves a two step operation iterative rule base growth capturing new knowledge and iterative rule base pruning removing redundant knowledge for type 2 rules the two step operation helps create a growing but sustainable model structure the performance of the proposed system is demonstrated using a number of well known non linear benchmark functions as well as a highly nonlinear multivariate real industrial case study simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model s performance following the incremental learning routine the study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed

robust structural damage identification based on multi objective optimization structural damage identification is an inverse problem which often is formulated as an optimization problem the design variables are degrees of damage in computational model and the objective is the discrepancies between the computed responses and the measured responses conventional single objective optimization approach defines the objective function by combining multiple error terms into a single one which leads to a weaker constraint in solving the identification problem an alternative approach explained in this paper is a multi objective approach that simultaneously minimizes multiple error terms a stronger constraint from multiple objectives promotes the solutions to converge to the correct solution numerical examples based on static testing are provided to illustrate the multi objective approach also conceptual explanations are given to extend the approach to include both the static testing and the dynamic testing expected challenges will also be explained

formal concept analysis based on fuzzy granularity base for different granulations this paper introduces granular computing grc into formal concept analysis fca it provides a unified model for concept lattice building and rule extraction on a fuzzy granularity base for different granulations one of the strengths of grc is that larger granulations help to hide some specific details whereas fca in a grc context can prevent losses due to concept lattice complexity however the number of superfluous rules increases exponentially with the scale of the decision context to overcome this we present some inference rules and maximal rules and prove that the set of all these maximal rules is complete and nonredundant thus users who want to obtain decision rules should generate maximal rules examples demonstrate that application of the method is valid and practicable in summary this approach utilizes fca in a grc context and provides a practical basis for data analysis and processing

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

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