optimal network configuration for maximal coherence resonance in excitable systems we analyze the coherence resonance phenomenon in an ensemble of noise driven excitable neurons giving special attention to the role of the interaction topology the neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale free like with dominating long range connections and a network with mostly adjacent neurons connected we found that besides an optimal noise intensity also an optimal network configuration exists at which the largest average coherence of noise induced spikes is achieved furthermore we show that long as well as short range interactions between neurons should exist in order to achieve the optimal response of the neuronal network

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

bounding the firing synchronization problem on a ring in this paper we improve the upper and lower bounds on the complexity of solutions to the firing synchronization problem on a ring in this variant of the firing synchronization problem the goal is to synchronize a ring of identical finite automata initially all automata are in the same state except for one automaton that is designated as the initiator for the synchronization the goal is to define the set of states and the transition function for the automata so that all machines enter a special fire state for the first time and simultaneously during the final round of the computation in our work we present two solutions to the ring firing synchronization problem an 8 state minimal time solution and a 6 state non minimal time solution both solutions use fewer states than the previous best known minimal time automaton a 16 state solution due to culik we also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem we show that there is no 3 state solution and no 4 state symmetric minimal time solution for the ring

complex multipole beam approach to acoustic scattering problems a novel approach to reducing the matrix size associated with the boundary element moment method solution of the problem of acoustic scattering from arbitrarily shaped closed bodies is presented in this paper the key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space on the scatterer boundary the fields generated by these multipole sources resemble the gabor basis functions by utilizing the properties of the gabor series guidelines for selecting the orders as well as locations of the multipole sources are developed the present approach not only reduces the number of unknowns but also generates a generalized impedance matrix with a banded structure the accuracy of the proposed method is verified by using internal accuracy checks and by comparing the numerical results with the analytic solutions for spherical scatterers

a six state minimal time solution to the firing squad synchronization problem abstract from balzer s work 1967 we know that the firing squad synchronization problem has a minimal time solution with eight states we show that such a solution exists with only six states our method is somewhat different from all previous ones the initial line is iteratively divided in two inequal parts so that each new right part can be treated as the homothetical image of a shorter initial line

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

printed antennas analysis by a gabor frame based method of moments gabor frame based discretization is proposed for the first time as a fully rigorous and flexible tool in the context of antenna analysis a rigorous discretization procedure based on frame theory is presented and applied to integral equations solution through a method of moments mom in this approach the unknown field or current is expanded in a set of spatially and spectrally translated elementary functions the use of a gaussian window function as basis element allows for the representation of radiated fields as a superposition of shifted and rotated gaussian beams by exploiting the well understood propagation and transformation features of gaussian beams the fields can be evaluated by summations of analytic terms at any observation point this method seems well suited to model antennas embedded in complex systems including arbitrary interfaces numerical results are presented for slot antennas at the interface between two dielectric half spaces and compared to a standard mom to validate the approach and illustrate its attractive characteristics

detecting non uniqueness of solutions to biharmonic integral equations through svd we consider the singular values of an integral operator and of a corresponding square matrix derived from the integral operator by means of a quadrature formula and a collocation the integral operator and also the matrix depend on a real parameter which may also enter the singular values of the operator and the matrix when a singular value drops to zero for a certain critical value of the parameter the corresponding homogeneous integral equation or matrix equation has a nontrivial solution based on several examples with biharmonic integral operators we conjecture that the order of approximation of the critical value for the matrix is at least equal to the order of the quadrature formula used it is therefore possible with a reasonable accuracy to detect such critical values for the integral operator simply through a singular value decomposition of the matrix derived by a quadrature and collocation

the firing squad synchronization problem on ca with multiple updating cycles abstract classical cellular automata have a single global clock that allows all the cells to update their states simultaneously at every clock cycle here we overturn this assumption and we study cellular automata where different cells can use different clocks cycles and as a consequence they update at different times we show how it is possible to solve the firing squad synchronization problem in this new setting and propose a synchronization algorithm operating in time linear with respect to the automata size

seven state solutions to the firing squad synchronization problem abstract we show that seven states are enough to implement minsky like solutions to the firing squad synchronization problem in a linear network of n finite state cellular automata with null transmission delay

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

fully asynchronous behavior of double quiescent elementary cellular automata in this paper we propose a probabilistic analysis of the fully asynchronous behavior i e two cells are never simultaneously updated as in a continuous time process of elementary finite cellular automata i e 0 1 states radius 1 and unidimensional for which both states are quiescent i e 0 0 0 0 and 1 1 1 1 it has been experimentally shown in previous works that introducing asynchronism in the global function of a cellular automata was perturbing its behavior but as far as we know only few theoretical work exists on the subject the cellular automata we consider live on a ring of size n and asynchronism is introduced as follows at each time step one cell is selected uniformly at random and the transition is made on this cell while the others stay in the same state among the 64 cellular automata belonging to the class we consider we show that 9 of them diverge on all non trivial configurations while the 55 other converge almost surely to a random fixed point we show that the exact convergence time of these 55 automata can only take the following values either 0 n ln n n2 n3 or n2n furthermore the global behavior of each of these cellular automata is fully determined by reading its code

a note on the construction of synthetic basis functions for antenna arrays construction of synthetic basis functions sbfs for analyzing the radiation problems of antenna arrays is discussed the sbfs of a block are generated from two separate solution spaces with one space to account for the effect of the feeding voltages and the other space to account for the responses of the block to incident electromagnetic fields from its environment singular value decomposition svd method is used to extract the characteristic modes of the block examples show that using sbfs constructed in this way may cause better efficiency

one way cellular automata on cayley graphs the notion of one dimensional one way cellular automata has been introduced to model cellular automata with only a one way communication between two neighbor cells in this paper we generalize this notion to cellular automata working on different communication graphs we present some sufficient conditions for a cellular automaton to be stimulated by a one way cellular automaton having the same underlying graph and we give some bounds on the simulation time of this mimic

the firing squad synchronization problem on cayley graphs the firing squad synchronization problem fssp for short has been intensively studied in the one dimensional space the problem consists in the synchronization of a segment of automata we generalize this problem on cayley graphs we give minimal time solutions for a synchronizing all cells in all minimal paths between any pair of cells of a cayley graph b synchronizing all cells in all minimal paths starting at a given cell g the general and leading to all cells at a given distance from g in a cayley graph in solutions for b in some cases all cells of a ball in a cayley graph will be synchronized in other cases this is not possible because of the existence of culs de sac

time optimal solution of the firing squad synchronization problem for n dimensional rectangles with the general at an arbitrary position a time optimal solution to the firing squad synchronization problem of n dimensional rectangles with the general at an arbitrary position is presented the solution uses one dimensional time optimal fssp algorithms which have a symmetrical transition function and use as few states as the best known non symmetrical transition functions the n dimensional case is demonstrated for n 2 and the straightforward generalization to larger n is outlined

the recursive aggregate interaction matrix algorithm for multiple scatterers the recursive aggregate interaction matrix algorithm raima for calculating a wave scattering solution is developed this algorithm combines the strength of both the recursive aggregate t matrix algorithm ratma and the recursive interaction matrix algorithm rima that have been previously developed the resultant algorithm is robust for scattering problems involving highly singular green s functions by avoiding the violation of the addition theorem it also has reduced computational complexity for inverting the volume integral equation of scattering the computational complexity of raima is o n sup 7 3 in three dimensions and o n sup 2 in two dimensions

the firing squad synchronization problem for graphs abstract in this paper we give a solution of the firing squad synchronization problem for graphs the synchronization times of solutions which have been obtained are proportional to the number of nodes of a graph the synchronization time of our solution is proportional to the radius rg of a graph g 3rg 1 or 3rg time units where rg is the longest distance between the general and any other node of g this synchronization time is minimum for an infinite number of graphs

the minimum firing time of the generalized firing squad synchronization problem for squares for almost all variations of the firing squad synchronization problem for elementary geometric figures such as lines rings squares rectangles and cubes minimal time solutions are known however in 2012 umeo and kubo introduced a very simple variation of this type and pointed out that its minimal time solutions are unknown in that variation a problem instance is a square array of n columns and n rows and the position of the general is arbitrary for this variation they constructed a solution that fires at time 2n 2 for any position of the general and wrote that it is not known whether this solution is minimal time or not we determine the exact value of the minimum firing time of this variation for some problem instances this value is smaller than 2n 2 and hence the 2n 2 time solution is not minimal time our result does not solve the problem of existence or non existence of minimal time solutions of the variation however the result gives one necessary condition for solutions to be minimal time

protecting efie based scattering computations from effects of interior resonances a numerical method based on the standard matrix formulation of the electric field integral equation efie for calculating the scattering from conducting bodies near resonant frequencies is given for both stabilizing the numerical calculations and finding the form of the resonant fields when this method is used along with a direct solution to the original matrix equation it requires insignificant additional computation an additional advantage of this approach is that it can easily be implemented in existing computer codes by using a single standard but general plug in module

analysis of an infinite current source above a semi infinite lossy ground using fictitious current auxiliary sources in conjunction with complex image theory techniques the canonical problem of an infinitely long electric current line radiating above a lossy infinite half space is examined the solution is based on the method of auxiliary sources mas in this method one can in general apply a numerical solution by introducing sets of fictitious current sources whose fields are elementary analytical solutions to the boundary value problem in order to approximately describe the actual electromagnetic em fields in each domain in general the convergence rate and the accuracy of the mas solution depend on the spatial distributions of the fictitious current sources sets and their locations in regard to the singularities of the actual em field simulated by each set here both the accuracy and the convergence rate of the method are examined investigating complex image approximations in order to optimally choose the auxiliary sources placements it is proved that the convergence rate and the accuracy of the method are significantly improved by utilizing the complex images as locations of the auxiliary sources the main contribution of the paper consists in the application of mas to an open structure which involves lossy dielectrics excited by a nonuniform em field as well as in the optimal choice of the locations of the fictitious current sources according to complex image techniques

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

crossovers in scale free networks on geographical space complex networks are characterized by several topological properties degree distribution clustering coefficient average shortest path length etc using a simple model to generate scale free networks embedded on geographical space we analyze the relationship between topological properties of the network and attributes fitness and location of the vertices in the network we find there are two crossovers for varying the scaling exponent of the fitness distribution

on time optimal solutions of the firing squad synchronization problem for two dimensional paths the firing squad synchronization problem for two dimensional paths 2 path fssp for short is a variation of the firing squad synchronization problem where finite automata are placed along a path in the two dimensional array space whether 2 path fssp has a time optimal solution or not is an open problem we introduce a combinatorial problem which we call the two dimensional path extension problem 2 pep for short and show that if 2 path fssp has a time optimal solution then 2 pep has a polynomial time algorithm the computational complexity of 2 pep is not well understood and the exhaustive search requiring exponential time is the only algorithm we know for it at present

a fast solver for the helmholtz equation on long thin structures we present a fast solver for the helmholtz equation on long thin structures it operates on an integral equation formulation of the problem in which the solution is represented as a superposition of fields generated by sources on the structure usually on the boundary or boundaries of the structure it uses a standard iterative solver for linear equations in conjunction with a novel method for applying the forward matrix whose computational complexity is o n where n is the number of points on which the integral equation is solved the algorithm is suitable for structures in either two dimensions 2 d or three dimensions it does not depend in any great detail on the specifics of the helmholtz equation and thus is also suitable for similar equations we demonstrate the algorithm by using it to simulate scattering in 2 d from dielectric structures using an integral equation formulation constructed using a combination of single layer and double layer potentials yielding a second kind integral equation numerical results show the algorithm to be efficient and accurate

generation of characteristic basis functions defined over large surfaces by using a multilevel approach an efficient procedure for the generation of characteristic basis functions cbfs over large arbitrary surfaces is presented in this work the first step is to partition the original object into subdomains and then derive the cbfs for these domains by solving for the currents induced by a set of components of the planewave spectrum pws next we aggregate the adjacent domains to obtain enlarged cbfs by expanding the original ones in terms of the weighted planewaves used to compute them this process can be performed iteratively and involves fast non expensive matrix manipulation we obtain a progressive decrease of the number of unknowns as we increase the domain size by following the procedure described above

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

a hybrid wavelet expansion and boundary element analysis of electromagnetic scattering from conducting objects a new wavelet approach is presented for treating the two dimensional electromagnetic scattering problems over curved computation domains the wavelet expansion method in combination with the boundary element method bem is applied to solve the integral equation for the unknown surface current the unknown surface current is expanded in terms of a basis derived from a periodic orthogonal wavelet in interval 0 1 the geometrical representation of the bem is employed to establish the map between the curved computation domain and the interval 0 1 this technique exhibits the advantages of both the wavelet expansion method and the boundary element method sparse matrix system and accurately modeling of curved surfaces comparisons of the results from the new technique with the moment method solutions the analytical solutions or the data in previous publications are provided good agreements are observed

on the complexity of network synchronization we show that if a minimal time solution to a fundamental distributed computation primitive synchronizing a network path of finite state processors exists on the three dimensional undirected grid then we can conclude the purely complexity theoretic result p np every previous result on network synchronization for various network topologies either demonstrates the existence of fast synchronization solutions or proves that a synchronization solution cannot exist at all to date it is unknown whether there is a network topology for which there exists a synchronization solution but for which no minimal time synchronization solution exists under the assumption that p neq np this paper solves this longstanding open problem in the affirmative

application of a new theoretical treatment to an old problem sinusoidal pressure release boundary scattering the scattering of sound from a sinusoidal pressure release boundary has long been the subject of study among researchers recently r l holford j acoust soc am 70 1116 1128 1981 outlined an exact solution to a variant of the helmholtz integral equation that permits calculation of the unknown velocity potential on the surface by the solution to a matrix equation application of this solution is made to the sinusoid to generate plane wave reflection coefficients the reflection coefficients are then compared with two sets of model tank data as well as with the approximate solutions of kirchhoff eckart rayleigh and brekhovskikh the exact solution compares most favorably with the data particularly on the rougher surfaces the principal errors produced by the approximate solutions are a shift in the location of the reflection nulls an inability to correctly predict unity when all side orders are evanescent and the absence of rayleigh reflection anomalies these errors appear regardless of the

a multilevel formulation of the method of moments em scattering the modeling of electromagnetic scattering and radiation problems using the method of moments mom is limited to resonant frequencies because of the extensive computational requirements of solving large matrix equations in this study a multilevel formulation of mom which allows substantial computational savings and thus extends the application of mom to higher frequencies is presented using a hierarchy of discretization levels the multilevel technique extracts different modal components of the solution by focusing on a specific portion of the spectrum of the solution at a given level the fundamental features of this process for the mom solution of the electric field integral equation efie are developed and implemented this multilevel mom allows the rapid evaluation of the current distributions on a variety of 2 d scatterers with thousands of unknowns in fewer than ten cycles and in fractions of the normal cpu times the method is stable fast suitable for multiple excitations and adaptable as a solve module for almost any mom code

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

superlinear and sublinear urban scaling in geographical networks modeling cities using a geographical scale free network to describe relations between people in a city we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city the urban indicator y n of a city with the population size n is analytically calculated by summing up all individual activities produced by person to person relationships our results show that the urban indicator scales superlinearly with the population namely y n n with 1 if y n represents a creative productivity and the indicator scales sublinearly 1 if y n is related to the degree of infrastructure development these results coincide with allometric scaling observed in real world urban indicators we also show how the scaling exponent depends on the strength of the geographical constraint in the network formation

an iteration free mom approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems we describe a numerically efficient strategy for solving a linear system of equations arising in the method of moments for solving electromagnetic scattering problems this novel approach termed as the characteristic basis function method cbfm is based on utilizing characteristic basis functions cbfs special functions defined on macro domains blocks that include a relatively large number of conventional sub domains discretized by using triangular or rectangular patches use of these basis functions leads to a significant reduction in the number of unknowns and results in a substantial size reduction of the mom matrix this in turn enables us to handle the reduced matrix by using a direct solver without the need to iterate in addition the paper shows that the cbfs can be generated by using a sparse representation of the impedance matrix resulting in lower computational cost and that in contrast to the iterative techniques multiple excitations can be handled with only a small overhead another important attribute of the cbfm is that it is readily parallelized numerical results that demonstrate the accuracy and time efficiency of the cbfm for several representative scattering problems are included in the paper

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

the synchronization of nonuniform networks of finite automata abstract the generalized firing squad synchronization problem gfssp is the well known firing squad synchronization problem fssp extended to arbitrarily connected networks of finite automata here the transmission delays associated with the links of a network are assumed to be 0 i e a signal can get through a link in no time when the delays are allowed to be arbitrary nonnegative integers the problem is called gfssp nud i e gfssp with nonuniform delays we give for the first time a solution of gfssp nud the solution is independent of the structure of the network and the actual delays of the links the firing time of the solution is bounded by o 3 max where max is the maximum transmission delay of any single link and is the maximum transmission delay between the general and any other node of a given network this answers an open question in mazoyer in automata networks c choffrut ed pp 82 93 springer verlag berlin new york 1986 our result is based on a strategy different from the one of balzer and waksman which is used in almost all existing solutions of fssp and gfssp the extension of gfssp and gfssp nud to networks with more than one general is also considered we show that 1 for any fixed k 2 gfssp with at most k generals has a solution whose firing time is bounded by o d where d is the maximum distance between any two nodes of a given network and gfssp nud with at most k generals has a solution whose firing time is bounded by o max 3 where is the maximum transmission delay between any two nodes of a given network 2 there are no solutions for gfssp and gfssp nud with an arbitrary number of generals

efficient multilevel approach for the generation of characteristic basis functions for large scatters an efficient approach for deriving the characteristic basis functions cbfs for analyzing radiation and scattering problems is proposed the spectrum of the incident plane waves is partitioned into several angular regions that are progressively enlarged in a multilevel procedure to generate orthogonal functions the cbfs are obtained at the final orthogonalization level so that they cover the entire angular range this approach to generating the cbfs is better suited for electrically large objects than the conventional approach which utilizes the entire angular range visible of the plane wave spectrum in a single level

combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution the purpose of this work is to combine an extrapolation technique with the method of moments mom to solve scattering problems involving large bodies it has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms based on this concept a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer complemented by subdomain basis functions near edges and discontinuities an extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional mom next a set of entire domain basis functions whose behaviour could be extrapolated with an increase in the size of the scatterer is extracted from this original solution the procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased allowing for large scatterers to be handled with a relatively small number of unknowns the extrapolation technique is applied to scattering problems from bodies of revolution bors and numerical results for an open cylinder and a barrel shaped bor are presented

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 comparison of spherical wave boundary value matching versus integral equation scattering solution for a perfectly conducting body a spherical wave expansion spex technique for calculating the scattering from a smooth perfectly conducting body is presented sample case results are compared with the well known lawrence livermore national laboratory numerical electromagnetics code nec which is based on the integral equation formulation the internal fields are computed for both results using a third surface current integration program which is totally independent of both spex and nec the internal fields which would be zero for a perfect solution are much more sensitive to the currents than the scattered fields the spex solution which uses fewer unknowns and less computer time than nec also produces a lower internal field the spex technique also allows a direct check on satisfaction of the boundary condition at any set of points on the surface independent of the points used to obtain the solution this provides a valuable built in test feature for quickly validating results which is one of the most attractive features of the technique

adaptive multiscale moment method ammm for analysis of scattering from three dimensional perfectly conducting structures the adaptive multiscale moment method ammm is presented for the analysis of scattering from three dimensional 3d perfectly conducting bodies this algorithm employs the conventional moment method mm using the subsectional triangular patch basis functions and a special matrix transformation which is derived from solving the fredholm equation of the first kind by the multiscale technique this methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time the widely used triangular patch vector basis functions developed by rao et al 1982 are used for expansion and testing functions in the conventional mm the objective here is to compress the unknowns in existing mm codes which solves for the currents crossing the edges of the triangular patch basis functions by use of a matrix transformation the currents source terms and impedance matrix can be arranged in the form of different scales from one scale to another scale the initial guess for the solution can be predicted according to the properties of the multiscale technique ammm can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional mm the basic difference between this methodology and the other wavelet based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown two numerical results are presented which demonstrate that the ammm is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3d perfectly conducting bodies

improved computational efficiency via near field localization the coefficient matrix which results when one applies the method of moments to the solution of the electric field integral equation is rendered sparse by appropriate selection of basis functions these new basis functions arise when equivalent sources are arranged in such a manner as to produce a field focused on the bounding surface the local nature of the focused fields reduces to a negligible level the interactions represented by many of the off diagonal elements of the coefficients matrix moreover the resulting basis appears to represent the surface fields more efficiently than many of the commonly used bases the technique is currently limited to closed structures its application is demonstrated in two dimensions by computing the scattering of a plane wave by circular and square perfectly conducting cylinders as the electrical size of the structure is increased and the number of unknowns is correspondingly increased that the number of significant matrix elements per row is shown to remain approximately constant

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

on the use of svd improved point matching in the current model method em scattering an approach which uses the singular value decomposition svd to improve the accuracy of the numerical solution obtained with fictitious current models is introduced in this approach the svd is essentially facilitating a systematic way to optimally reduce the generalized inverse matrix used in the solution to a submatrix of smaller rank this reduction strikes a balance between the fulfillment of the boundary conditions at the matching points and that between them clearly the boundary conditions errors at the matching points are no longer strictly zero however the previously discernible errors between the matching points are markedly suppressed the approach is efficacious not only when the impedance matrix is inherently singular or highly ill conditioned but also when this matrix is entirely well conditioned it can be generalized and implemented in any method of moments code which uses point matching for testing the approach has been incorporated into an existing solution based on the current model method for the problem of scattering from periodic sinusoidal surfaces and is shown to render the solution more accurate

smaller solutions for the firing squad in this paper we improve the bounds on the complexity of solutions to the firing squad problem also known as the firing synchronization problem in the firing synchronization problem we consider a one dimensional array of n identical finite automata initially all automata are in the same state except for one automaton designated as the initiator for the synchronization our results hold for the original problem where the initiator may be located at either endpoint and for the variant where any one of the automata may be the initiator called the generalized problem in both cases the goal is to define the set of states and transition rules for the automata so that all machines enter a special fire state simultaneously and for the first time during the final round of the computation in our work we improve the construction for the best known minimal time solution to the generalized problem by reducing the number of states needed and give non minimal time solutions to the original and generalized problem that use fewer states than the corresponding minimal time solutions

complex multipole beam approach to electromagnetic scattering problems a novel approach to reducing the matrix size associated with the method of moments mom solution of the problem of electromagnetic scattering from arbitrary shaped closed bodies is presented the key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space on the scatterer boundary the fields generated by these multipole sources resemble the gabor basis functions by utilizing the properties of the gabor series guidelines for selecting the orders as well as locations of the multipole sources are developed it is shown that the present approach not only reduces the number of unknowns but also generates a generalized impedance matrix with a banded structure and a low condition number the accuracy of the proposed method is verified by comparing the numerical results with those derived by using the method of moments

analytic continuation considerations when using generalized formulations for scattering problems a generalized operator equation has been developed for a simple scattering problem for which a closed form solution exists the operator equation has been solved numerically via the method of moments using spatially impulsive fictitious sources as expansion functions together with a simple point matching testing procedure the study focused on the convergence and accuracy of the solution and examined how they are dependent on the location and distance of the fictitious sources relative to the area containing the singularities of the actual field simulated by these sources as expected it was found that when the actual field simulated by the fictitious impulsive sources has singularities lying between the physical boundary and the closed surface over which the sources are placed the impulsive expansion does not yield a uniformly convergent solution in this case instabilities are encountered as the number of sources increases in the sense that a small improvement of the boundary error requires a considerable change in the currents the moment matrix is then difficult to invert and easily susceptible to large round off errors conversely if the actual field has no singularities lying between the physical boundary and the closed surface over which the sources are placed the impulsive expansion does yield a uniformly convergent solution to any degree of precision

fmm accelerated source model technique for many scatterer problems motivated by the lack of scalability of the source model technique smt to many scatterer problems a new smt based method for 3 d many scatterer problems is developed the large time complexity of the smt is reduced by deriving an implicit compact representation of the scattering problem via a fast multipole formulation which divides the interactions into far and near ones while grouping and approximating the far interactions this results in significant acceleration of classical smt which is demonstrated in a variety of 3 d many body scattering problems the improvement is notable already at the minimal number of unknowns necessary and grows with the size of the problem

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems