the multifrontal method for sparse matrix solution theory and practice this paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems the method is formulated in terms of frontal matrices update matrices and an assembly tree formal definitions of these notions are given based on the sparse matrix structure various advances to the basic method are surveyed they include the role of matrix reorderings the use of supernodes and other implementatjon techniques the use of the method in different computational environments is also described

preconditioned conjugate gradient methods for solving electromagnetic problems it is shown that appropriately chosen preconditioners can significantly improve the convergence rate of the conjugate gradient cg algorithm as applied to electromagnetic problems preconditioners are constructed for the problems of scattering from frequency selective surfaces and scattering from infinite cylinders

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

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

reduction of the number of unknowns in large stacked planar structures by a fringe aperture formulation for scattering problems comprising a combination of planar structures the total number of unknowns may be significantly reduced if an aperture formulation is employed rather than a patch formulation the rationale behind using the aperture formulation is based on the recognition that the decay rate of the scattered aperture field is independent of the size of the scatterer therefore any scatterer may be surrounded by an aperture of fixed width over which an integral equation is formulated the area of this aperture is proportional to the perimeter of the scatterer rather than its area and it becomes much smaller compared with the entire scatterer area as the size of the scatterer increases hence the reduction in the number of independent unknowns a truncation criterion for the finite aperture is determined via a numerical study of the aperture field behavior for various angles of incidence in addition the a priori knowledge of the physical optics component is also taken into account reducing the unknown function to an aperture field component that is the outcome of the remaining fringe current only the total current distribution can be subsequently derived from this field by adding the known physical optics field and invoking the inverse of the green s function in the spectral domain this analysis of isolated planar scatterers results in a spectral scattering matrix representation that is subsequently used for cascading of stacked structures

part based 3d descriptions of complex objects from a single image volumetric 3d part based descriptions of complex objects in a scene can be highly beneficial for many tasks such as generic object recognition navigation and manipulation however it has been difficult to derive such descriptions from image data there has been some progress in getting such descriptions from range data or from perfect contours but analysis of a real intensity image presents many difficulties the object and part boundaries do not completely correspond to image boundaries the detected boundaries are often fragmented and many boundaries due to surface markings shadows and noise are present in addition inference of 3d from a 2d image is difficult the paper describes a method to compute the desired descriptions from a single image by exploiting projective properties of a class of generalized cylinders and of possible joints between them experimental results on some examples are given

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

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

a spectral iteration technique for analyzing a corrugated surface twist polarizer for scanning reflector antennas an analysis of the corrugated surface twist polarizer which finds application in the design of scanning reflector antennas is presented the spectrai interation technique a novel procedure which combines the use of the fourier transform method with an iterative procedure is employed the first step in the spectral iteration method is the conversion of the original integral equation for the interface field into a form which is suitable for iteration using a method developed previously an important feature of the technique is that it takes advantage of the discrete fourier transform dft type of kernel of the integral equation and evaluates the integral operators efficiently using the fast fourier transform fft algorithm thus in contrast to the conventional techniques e g the moment method the spectral iteration approach requires no matrix inversion and is capable of handling a large number of unknowns furthermore the method has a built in check on the satisfaction of the boundary conditions at each iteration

singular basis functions and curvilinear triangles in the solution of the electric field integral equation basis functions are formulated that account for singularities in the charge density near an edge on a conducting body the formulation is general and the basis functions are valid for planar as well curvilinear geometries in principle singularities of any order can be treated but best results are obtained for so called knife edge singularities results are compared with exact solutions or measurements where available for some simple problems

the field feedback formulation for electromagnetic scattering computations a new procedure is described for the solution of electromagnetic scattering problems in unbounded regions using this technique a spatial region enclosing the scatterer is initially decoupled from the exterior region and the fields therein are considered as the solution of an interior dirichlet boundary value problem the interior region solution is then recoupled to the unbounded exterior region by use of the equivalence principle such a process can be symbolically represented as a simple feedback system the formulation is demonstrated for the case of plane wave scattering by finite metallic circular cylinders a finite element solution of the interior problem is utilized in this example in conjunction with a field representation using a special case of coupled azimuthal potentials

singular higher order divergence conforming bases of additive kind and moments method applications to 3d sharp wedge structures we present new subsectional singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges the bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood singular bases of this kind complete to arbitrarily high order are described in a unified and consistent manner for curved quadrilateral and triangular elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components adequate modelling of the divergence and removal of spurious solutions these singular high order bases provide more accurate and efficient numerical solutions of surface integral problems several test case problems are considered in the paper thereby obtaining highly accurate numerical results for the current and charge density induced on 3d sharp wedge structures the results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problems

iterative computational techniques in scattering based upon the integrated square error criterion an iterative technique is developed to rigorously compute the electromagnetic time and frequency domain scattering problems the method is based upon a wave function expansion technique this also includes the integral representation techniques in which the electromagnetic field equations and causality conditions are satisfied analytically while the boundary conditions or the constitutive relations have to be satisfied in a computational manner the latter is accomplished by an iterative minimization of the integrated square error for the solution of an integral equation it is shown how to obtain optimum convergence some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method

a concise conjugate gradient computation of plate problems with many excitations one of the major difficulties in the application of the conjugate gradient algorithm for the analysis of electromagnetic scattering problems is the necessity to carry out the calculation separately for each incident wave in the approach suggested rather than handling the incident waves directly a class of possible excitations is represented by a set of strip type basis functions for these functions convergence is predictable and rapid because the majority of the strips are located away from the edges of the scatterer this choice also facilitates the use of the physical optics approximation as a good initial guess once the solutions for all the unit basis functions over the body are known they can be combined to synthesize the solution for any excitation using the weighting coefficients associated with the expansion of the incident field numerical examples are given and they demonstrate the substantial savings achieved by adopting this approach for the analysis of multiple excitations

a generalization of van den berg s integral square error iterative computational technique for scattering van den berg shows a way of using spectral iteration si within a scheme that shows good convergence his method can be reinterpreted as a global expansion of the field quantities in terms of a set of basis functions it is shown here that the orthogonalization of these basis functions can considerably improve convergence rates this involves extra storage requirements but only a negligible decrease in speed of computation

a computational approach to soliton solutions of the kadomtsev petviashvili equation in this paper we present a computational approach to develop soliton solutions of the nonlinear kadomtsev petviashvili equation our approach rests mainly on the adomian decomposition method to include few components of the decomposition series the proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type numerical examples are tested to illustrate the proposed scheme

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

singular hierarchical scalar basis functions for triangular cells a new family of hierarchical basis functions is proposed for triangular cells these functions incorporate singular behavior to model fields with corner singularities the functions are of the additive kind and combine a traditional polynomial complete representation on triangles with additional singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest the condition numbers arising from the use of these functions is investigated

a weak form of the conjugate gradient fft method for plate problems a number of electromagnetic field problems for planar structures can be formulated in terms of a hypersingular integral equation in which a grad div operator acts on a vector potential the vector potential is a convolution of the free space green s function and some surface current density over the domain of interest a weak form of this integral equation is obtained by testing it with subdomain basis functions defined over the plate domain only as a next step the vector potential is expanded in a sequence of subdomain basis functions and the grad div operator is integrated analytically over the plate domain only for the problem of electromagnetic scattering by a plate the method shows excellent numerical performance the numerical difficulties encountered in some previous conjugate gradient fast fourier transform cgfft methods have been eliminated

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

hierarchical matrix techniques based on matrix decomposition algorithm for the fast analysis of planar layered structures the matrix decomposition algorithm mda provides an efficient matrix vector product for the iterative solution of the integral equation ie by a blockwise compression of the impedance matrix the mda with a singular value decomposition svd recompression scheme i e so called mda svd method shows strong ability for the analysis of planar layered structures however iterative solution faces the problem of convergence rate an efficient hierarchical h lu decomposition algorithm based on the h matrix techniques is proposed to handle this problem exploiting the data sparse representation of the mda svd compressed impedance matrix h lu decomposition can be efficiently implemented by h matrix arithmetic h matrix techniques provide a flexible way to control the accuracy of the approximate h lu factors h lu decomposition with low accuracy can be used as an efficient preconditioner for the iterative solver due to its low computational cost while h lu decomposition with high accuracy can be used as a direct solver for dealing with multiple right hand side rhs vector problems particularly numerical examples demonstrate that the proposed method is very robust for the analysis of various planar layered structures

on the geometric interpretation of image contours abstract in this paper we suggest a computational model for the 3d interpretation of a 2d view based on contour classification and contour interpretation we concentrate on those contours arising from discontinuities in surface orientation we combine a generic surface description well suited for visual tasks with a model of the image formation process in order to derive image contour configurations that are likely to be interpreted in terms of surface contours next we describe a computer algorithm which attempts to interpret image contours on the following grounds first an image analysis process produces a description in terms of contours and relationships between them second among these contours we select those which form a desired configuration third the selected contours are combined with constraints available with the image formation process in order to be interpreted in terms of discontinuities in surface orientation as a consequence there is a dramatic reduction in the number of possible orientations of the associated scene surfaces

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

a spectral iteration technique for analyzing scattering from arbitrary bodies part ii conducting cylinders with h wave incidence the stacked two dimensional spectral iteration technique sit introduced in an accompanying paper is further developed and extended to the case of an h polarized field incident on an arbitrary conducting cylinder as before the method takes advantage of the simplicity with which the relationships between planar sources and fields are expressed in the spectral domain

rcs computation of large inhomogeneous objects using a fast integral equation solver in this paper we apply a fast fourier transform fft accelerated volume integral equation solver to compute the radar cross section of large scale inhomogeneous objects this method is related to bojarski s k space method and the subsequent conjugate cg and biconjugate gradient bcg fft algorithms the method developed here combines the weak form discretization with the bcg and stabilized bcg bcgs solvers we show that this method has marked improvements over related algorithms the numerical method has been validated by mie series for multilayer spheres and applied to some practical problems with this method we are currently able to solve a three dimensional problem with a volume of size 3648 spl lambda sup 3 21 23 million unknowns on a single workstation

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

perturbation technique for matrix equations and its application in the computation of internal fields in a three dimensional arbitrarily shaped biological body a novel matrix perturbation technique for the matrix equation a u b is presented one of its applications the computation of internal fields in a three dimensional arbitrarily shaped heterogeneous biological body illuminated by a plane wave is further investigated by using the technique if one regards a normal biological body as the primary model and stores its computation results when small perturbations in the dielectric characteristics or the shape of the body occur the internal fields in the perturbed biological body can be rapidly computed using the stored results compared with the usual moment methods the new technique has an equivalent precision yet takes only 1 70 the execution time this technique is especially suitable for pathological cases in which the dielectric characteristics or the shape of the biological body vary due to disease

an add on method for the analysis of scattering from large planar structures a so called add on procedure is proposed to deal with the data analysis problem resulting from the collection of scattering data from large planar structures the computations involving of the order of a few thousand unknowns is undertaken in a gradual manner by building up the body from small patches which are added sequentially the procedure is based on an initial expansion of the unknown current distribution into subsectional pulse type basic functions each segment of the scatterer carries an unknown amplitude which is the response to an incident wave however rather than forming a matrix equation for these responses they are computed in a gradual manner where the scatterer is built up from these segments as they are added one at a time at the end of each addition of a segment the result for scattering from a partial body is obtained at each stage the problem solved reflects the size of the small addition only and the solution to an actual partial body is obtained an important feature of this method is its ability to utilize a priori known information on a portion of the scatterer as an initial stage for the economic analysis of the entire structure the process takes into account the interactions between all segments of the body the process proves to be very efficient both in terms of computation time and storage requirements as seen in the computed examples on of the order of 1000 to 6000 unknowns

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

hamiltonian structure of the integrable couplings for the multicomponent dirac hierarchy a scheme for deducing hamiltonian structures of the integrable couplings for the multicomponent hierarchies of evolution equations is presented which is devoting to obtaining the hamiltonian structures of the integrable couplings of the multicomponent dirac hierarchy

a new integrable hierarchy and constrained flows its expanding integrable system abstract a new subalgebra of loop algebra a 2 is first constructed it follows that an isospectral problem is established using tu pattern gives rise to a new integrable hierarchy which possesses bi hamiltonian structure furthermore by making use of bi symmetry constraints the generalized hamiltonian regular representations for the hierarchy are obtained finally we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five dimensional loop algebra g

scattering from frequency selective surfaces an efficient set of v dipole basis functions in this paper a novel set of v dipole basis functions is introduced these basis functions are used to approximate the induced surface current density on an infinite plane frequency selective surface fss the elements of the fss are supposed to consist of straight sections and bends two groups of elements which the present v dipole basis functions can be applied to are identified namely the center connected elements and the loop type elements using the established spectral galerkin method where the method of moment mom procedure is carried out in the spectral domain we determine the reflection and transmission coefficients of the fss the convergence of the solution is demonstrated both for existing bases and the present v dipole basis functions it is found that the double infinite floquet sum diverges when existing discontinuous basis functions are used but that convergence is obtained for the present basis functions therefore care needs to be exercised and it would seem discontinuous bases should be avoided

low frequency scattering through an aperture in a rigid screen some numerical results abstract the penetration of a plane wave through an aperture in a rigid screen is investigated the first three terms of the low frequency expansion are evaluated numerically for both simply connected and annular apertures in the numerical method use is made of a division of the aperture into arbitrary triangles the singular behaviour at the edges is incorporated in the shape functions which yields good accuracy and fast convergence special attention has been given to the thin ring which can serve as a model for e g imperfectly shielded windows

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

a dual field domain decomposition method for the time domain finite element analysis of large finite arrays a novel dual field time domain finite element domain decomposition method is presented for an efficient and broadband numerical simulation of electromagnetic properties of large finite arrays instead of treating the entire array as a single computation domain the method considers each array element as a smaller subdomain and computes both the electric and magnetic fields inside each subdomain adjacent subdomains are related to each other by the equivalent surface currents on the subdomain interfaces in an explicit manner furthermore the method exploits the identical geometry of the array elements and further reduces the memory requirement and cpu time the proposed method is highly efficient for the simulation of large finite arrays numerical stability and computational performance of the method are discussed several radiation examples are presented to demonstrate the accuracy and efficiency of the method

iterative analysis of finite sized planar frequency selective surfaces with rectangular patches or perforations frequency selective surfaces fss and other periodic gratings are often analyzed under the assumption that they are infinite in extent most existing methods for analyzing periodic structures are based on the use of a floquet type representation of the fields in a unit cell whose dimensions are typically comparable to the wavelength in this work a finite truncated version of an infinite periodic structure is dealt with directly without the benefit of the assumption that the structure is periodic this in turn requires the handling of a large number of unknowns and makes it difficult to solve the problem using conventional matrix methods two different iteration approaches to solving the finite fss problem are discussed in the paper both of which employ the spectral domain formulation the first of these employs the spectral iteration technique and the second one uses the conjugate gradient cg iteration algorithm convergence characteristics of both of these methods are investigated and the results are reported

a new fractional order soliton equation hierarchy and its integrable coupling system a fractional order soliton equation hierarchy is presented which is a new liouville integrable hierarchy and possesses bi hamiltonian structure finally we obtain a integrable coupling system of this fractional order soliton equation hierarchy by applying a upper triangular matrix of lie algebras

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

a spectral iteration technique for analyzing scattering from arbitrary bodies part i cylindrical scatterers with e wave incidence in the past methods for solving electromagnetic scattering problems in the frequency domain have been developed largely for the low frequency moment method and high frequency asymptotic techniques regimes the intermediate frequency range has been analyzed by combinations of these two approaches or by separation of variables when possible this paper is devoted to the development of an independent approach viz the stacked spectral iteration technique which is capable of handling arbitrary scatterers with dimensions ranging from small to moderately large the method takes advantage of the simplicity with which the planar source planar field relationships are expressed in the spectral domain the boundary conditions or constitutive relationships on the other hand are expressed most simply in the spatial domain alternating between the two domains is carried out with the aid of the fast fourier transform fft algorithm the spectral iteration technique sit was applied in the past to thin planar structures which allow the analysis to be carried out on a plane the generalization of the two dimensional formulation to arbitrary three dimensional bodies can be accomplished by sampling the current distribution on the scatterer over a number of parallel planes and using the simple spectral domain interaction relationships between the planes this new approach involves no matrix inversion and is capable of analyzing scatterers whose sizes far exceed those treatable by the moment method in addition to being arbitrarily shaped the scatterer may be conducting dielectric or lossy dielectric thus the sit provides an efficient approach to filling the much needed gap between low and high frequency conventional techniques e g the moment method mom and the geometrical theory of diffraction gtd and to extending the range of applicability to dielectric scatterers with or without loss though the concepts presented herein are applicable to arbitrary three dimensional scatterers the problem of arbitrary cylinders with e polarized excitation is addressed in this paper while the h case is treated in an accompanying work the three dimensional case is to be reported in a future communication which treats the problem of scattering by a lossy inhomogeneons dielectric cylinder of finite length

spectral domain iterative analysis of single and double layered microstrip antennas using the conjugate gradient algorithm an analysis for single and double layered microstrip antennas is described the planarity of these structures makes it possible to construct a general spectral representation for any number of layers and to derive the spectral green s dyad in a compact fashion using a transmission line analogy a formulation of the antenna problem in the spectral domain incorporating this dyad is coupled with the conjugate gradient algorithm whose applicability as an efficient way of analyzing a number of microstrip antennas is studied results are quite accurate conclusions pertaining to the applicability of the method including effects of problem parameters on convergence rates are drawn

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

a powerful approach to generate new integrable systems in this paper an effective algorithm to generate integrable systems is given as a result many new integrable equations are derived in a systematic way

moment method calculations on apertures using basis singular functions the transmission properties of perforated perfectly conducting screens are of practical interest the treatment of nonperiodical structures by numerical techniques such as the method of moments is very computer intensive in this paper it is shown that using basis functions that incorporate the edge as well as the corner singularities the number of unknowns can be drastically reduced the advantages and limitations of the method are discussed numerical results are presented illustrating the transmission properties of arrays of square and rectangular apertures

on a class of finite step iterative methods conjugate directions for the solution of an operator equation arising in electromagnetics a class of finite step iterative methods for the solution of linear operator equations is presented specifically the basic principles of the method of conjugate directions are developed gaussian elimination and the method of conjugate gradients are then presented as two special cases with an arbitrary initial guess the method of conjugate gradient always converges to the solution in at most n iterations where n is the number of independent eigenvalues for the operator in the finite dimensional space in which the problem is being solved the conjugate gradient method requires much less storage sim 5n than the conventional matrix methods sim n 2 in the solution of problems of higher complexity also after each iteration the quality of the solution is known in the conjugate gradient method the conjugate gradient method is also superior to the spectral iterative method as the latter does not always converge and it doubles the complexity of a given problem unnecessarily four versions of the conjugate gradient method are presented in detail and numerical results for a thin wire scatterer are given to illustrate various properties of each version

recursive algorithms for calculating the scattering from n strips or patches using the definition of recursive relations for the reflection operator for n strips or patches two easily programmable recursive algorithms are developed to calculate the electromagnetic scattering by n strips or patches one algorithm is for arbitrary excitation and the other is for a fixed excitation the recursive algorithms require the inversion of small matrices at each stage and hence are suitable for programming on smaller computers if the n strips or patches are identical and equally spaced symmetry can be exploited to speed up the algorithms a program was developed to calculate scattering by n strips and the result is shown to converge to scattering by a large strip when the n strips are contiguous

a conjugate gradient procedure for the analysis of planar conductors with alternating patch and aperture formulations em scattering the formulation of an electromagnetic scattering problem by an operator equation can be done in different ways leading to different rates of convergence when the conjugate gradient algorithm is used the convergence can tend to slow down at certain stages depending on the formulation used thus whenever the error tends to level off in one formulation it is advisable to switch to another one to this end a procedure that alternates repeatedly between formulations is presented it is shown to accelerate the convergence rate during the earlier stages of the iterative process making it possible to arrive at a prescribed practical error criterion faster a substantial saving in storage allocation is attained

fourier transform of a linear distribution with triangular support and its applications in electromagnetics a three dimensional fourier transform ft of a linear function with triangular support is derived in its coordinate free representation the fourier transform of this distribution is derived in three steps first the 2 d ft of a constant top hat function is obtained next the distribution is generalized to a linearly varying function finally the formulation is extended to a coordinate free representation which is the 3 d ft of the 2 d function defined over a surface this formulation is applied to the near field computation yielding accurate numerical solutions

recovery of 3 d objects with multiple curved surfaces from 2 d contours abstract inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision often techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well in this paper we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously though it is limited to objects made of zero gaussian curvature surfaces our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them and from other boundaries this technique uses some of the constraints developed in an earlier paper that was limited to examining a zero gaussian curvature surface cut by parallel planes this restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces results on some complex examples are shown

a direct method for integrable couplings of td hierarchy a direct method for establishing integrable couplings is proposed in this paper as an example illustration integrable couplings of td hierarchy are obtained by constructing a suitable transformation of lax pairs and a new lie algebra

feedback control of fractional nonlinear differential algebraic systems with hamiltonian function method abstract in this paper we first present a fractional hamiltonian function then based on the dissipative hamiltonian realization using the fractional hamiltonian function method as a static measurable feedback a criterion for the fractional nonlinear differential algebraic systems fndas is proposed to stabilize the multi machine power system finally fndas in presence of disturbance a fractional h control strategy is constructed the proposed stabilization and robust controller can effectively take advantage of the structural characteristics of fndas and is simple in form

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

a spectral iteration approach for analyzing scattering from frequency selective surfaces a novel technique called the spectral iteration approach for analyzing the problem of scattering from periodically perforated screens which find useful applications as radomes optical filters artificial dielectrics and so on is applied the formulation is carried out in the spectral domain where a set of algebraic equations is obtained directly for the spectral coefficients of the aperture field distribution or the induced current density rather than via an integral equation formulation these equations are then solved simultaneously using an iterative procedure developed in this paper that circumvents the need for matrix inversion because the matrix solution is avoided in the spectral approach it is capable of handling large aperture sizes in a computationally efficient manner the efficiency of computation results from the use of the fast fourier transform fft algorithm which is employed in the derivation of the algebraic equations and in the iteration procedure a unique feature of the spectral iteration approach is that it has a built in boundary condition check which provides a reliable indication of the accuracy of the solution it is also shown that the spectral domain technique can be applied to even a wider class of geometries e g the step discontinuity in a waveguide

survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems

singular higher order complete vector bases for finite methods this paper presents new singular curl and divergence conforming vector bases that incorporate the edge conditions singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements the curl divergence conforming singular bases guarantee tangential normal continuity along the edges of the elements allowing for the discontinuity of normal tangential components adequate modeling of the curl divergence and removal of spurious modes solutions these singular high order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems sample numerical results confirm the faster convergence of these bases on wedge problems

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

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

numerical analysis of finite frequency selective surfaces with rectangular patches of various aspect ratios the finite frequency selective surface studied consists of a two dimensional array finite in one dimension and infinite in the other of perfectly electrically conducting plates in free space the analysis uses a green s function formulation in the spectral domain and the resulting equation is solved using the method of moments techniques are demonstrated for increasing the speed of the numerical computation so that the problem can be solved on a vax 11 780 in a reasonable amount of time two types of basis functions one subsectional and the other complete domain are used to represent the currents on the patches both yield similar results and both are suitable for use in this problem techniques are demonstrated for approximating the tails of the infinite integrations which allow a more accurate solution than truncation results for scattered power density and patch currents illustrate the edge effect and incident angle dependencies results showing 3 db bandwidth resonance peak versus frequency and scattered power versus frequency are plotted for patches with aspect ratios varying from 0 1 to 1

constructing a multi function equation hierarchy and its integrable coupling system with maple in this article by considering a multi dimensional lie algebra system a new multi function integrable equation hierarchy is presented with the help of maple then the integrable coupling system of the new multi function integrable equation hierarchy is obtained through enlarging matrix spectral problem