the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

fast periodic interpolation method for periodic unit cell problems a fast periodic interpolation method fpim is presented for rapidly computing fields in a unit cell of an infinitely periodic array for low and moderate frequencies for unit cells smaller than or on the order of the wavelength the fpim has the computational cost of o n and it requires only o 1 periodic green s function pgf evaluations for n sources and observers for higher mixed frequencies the computational cost scales as o d 3 log d n where d is the domain size within the unit cell and is the wavelength fpim is based on splitting the field into the near field from the sources around the unit cell and the far field from the remaining sources the near field component can be evaluated rapidly using any available fast method the far field component is computed by tabulating the pgf at sparse source and observer grids using this table to calculate the field at the observation grid and interpolating from the observation grid to the actual observers the fpim is kernel independent and allows using any method for evaluating the pgf including simple floquet expansions the computational times can be comparable to those of conventional non periodic n body electromagnetic problems the presented method can be used to accelerate integral equations for periodic unit cell problems with many applications in microwave engineering and optics

positive steady states of the holling tanner prey predator model with diffusion this paper is concerned with the holling tanner prey predator model with diffusion subject to the homogeneous neumann boundary condition we obtain the existence and non existence of positive non constant steady states

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

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

solution of arbitrarily dimensional matrix equation in computational electromagnetics by fast lifting wavelet like transform a new wavelet matrix transform wmt operated by lifting wavelet like transform lwlt is applied to the solution of matrix equations in computational electromagnetics the method can speedup the wmt without allocating auxiliary memory for transform matrices and can be implemented with the absence of the fast fourier transform furthermore to handle the matrix equation of arbitrarily dimension a new in space preprocessing technique based on lwlt is constructed to eliminate the limitation in matrix dimension complexity analysis and numerical simulation show the superiority of the proposed algorithm in saving cpu time numerical simulations for scattering analysis of differently shaped objects are considered to validate the effectiveness of the proposed method in particular due to its generality the proposed preprocessing technique can be extended to other engineering areas and therefore can pave a broad way for the application of the wmt

pattern formation in a general two cell brusselator model abstract in this article we are concerned with the following general coupled two cell brusselator type system d 1 u a b 1 u f u v c w u in d 2 v b u f u v in d 1 w a b 1 w f w z c u w in d 2 z b w f w z in u v w z 0 on here r n n 1 is a smooth and bounded domain a b c d 1 d 2 are positive constants and f c 1 0 c 0 is a nonnegative and nondecreasing function such that f 0 in 0 when f u u 2 this system corresponds to the coupled two cell brusselator model in the present work we exhibit the crucial role played by the nonlinearity f in generating the stationary patterns our conclusions show that if f has a sublinear growth then no stationary patterns occur while if f has a superlinear growth stationary patterns may exist

strategy and stationary pattern in a three species predator prey model abstract in this paper we study a strongly coupled system of partial differential equations which models the dynamics of a two predator one prey ecosystem in which the prey exercises a defense switching mechanism and the predators collaboratively take advantage of the prey s strategy we demonstrate the emergence of stationary patterns for this system and show that it is due to the cross diffusion that arises naturally in the model as far as the authors are aware this is the first example of stationary patterns in a predator prey system arising solely from the effect of cross diffusion

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

electromagnetic degrees of freedom in 2 d scattering environments the electromagnetic em degrees of freedom dof of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous dof theory first developed by miller and piestun for optical systems the received em fields are efficiently calculated by fast multipole method fmm and the ensemble average of the dof number is obtained through monte carlo simulation technique the results show that the average em dof number is strongly dependent on the sizes of the transmit volume the receive volume and the scattering region in particular the average number of dof generally increases with both the transmit and receive volumes however this increase is a non linear process and will not continue indefinitely as the transmit volume or the receive volume expands an upper bound of the average dof number is expected due to noise effects due to the lack of criteria for choosing a critical parameter involved in miller and piestun s original dof definition a modified definition is also considered even though the modified definition is snr dependent it provides a clearer physical meaning of the dof in addition the simulations also suggest that it might not be appropriate to ignore the influence of the snr on the dof number when the system concerned is of general form and relative small where no critical point of the channel quality can be identified a logarithmic dependence of the dof number on the total source power is demonstrated for such systems

improving error bounds for multipole based treecodes rapid evaluation of potentials in particle systems is an important time consuming step in many physical simulations over the past decade the development of treecodes such as the fast multipole method and barnes hut method has enabled large scale simulations in astrophysics molecular dynamics material science etc these methods use fixed degree polynomial approximations of the potential at a point due to a set of particles in a hierarchical representation of the particle system in this paper we present analysis and experiments to illustrate that fixed degree multipole approximations can lead to large aggregate errors we describe an alternate strategy based on careful selection of the multipole degree that leads to asymptotically lower errors while incurring minimal computation overhead first we estimate the error associated with each particle cluster interaction and the aggregate error for each particle then we describe a technique for computing the multipole degree of each interaction with a view to reducing aggregate error and establish the computational complexity of the new method following this we discuss numerical experiments that demonstrate favorable error properties of the new method at the expense of marginal increase in computation finally we report a parallel implementation on the sgi origin 2000 that achieves excellent speedup for problems from domains such as astrophysics and boundary element solvers

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

application of normal forms to the lorenz model in the subcritical region abstract it is shown that within a certain parameter interval below the hopf bifurcation the lorenz equations can be decoucpled in the normal form representation we normalize only up to monomials of finite order and combine the unnormalized part of the flow in a remainder the formalism avoids small denominators and is well defined if the inverse of a finite polynomial map exists numerical results are presented for the basin of attraction in some neighborhood of the stable fixed points and for the hopf limit cycle

the multiple sweep method of moments msmm analysis of electrically large bodies this paper presents the multiple sweep method of moments msmm analysis of the radiation and scattering from electrically large smooth perfectly conducting bodies the msmm is an o n sup 2 recursive method for solving the large matrix equations which arise in the method of moments mm analysis of electrically large bodies in the msmm the body is split into p sections and the currents on these sections are found in a recursive fashion the first msmm recursion or sweep includes the dominant scattering mechanisms and each subsequent recursion or sweep includes higher order mechanisms thus as the electrical size of the body increases fewer and fewer sweeps are required to accurately compute the current on the body

truncated floquet wave full wave t fw sup 2 analysis of large periodic arrays of rectangular waveguides a new hybrid technique has been recently proposed for the analysis of large periodic arrays this method is based on a high frequency representation of the active green s function of a finite array involving a floquet wave fw expansion with the relevant edge and vertex diffracted ray fields originating at the array border using this representation the unknown current of an appropriate fringe integral equation is expanded in terms of a few basis functions shaped as fw induced diffracted rays this representation drastically reduces the numerical effort and provides a physical insight into the mechanism of the array truncation in this paper this method is applied to the analysis of large arrays of rectangular waveguides opened on an infinite ground plane numerical results are shown to demonstrate the effectiveness and the numerical efficiency of the method

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

scattering from very large randomly rough surfaces using a markov random field equivalent current a markov random field mrf model is employed to learn the statistical properties of an equivalent current situated above a rough surface where this equivalent current represents near field electromagnetic scattered fields the mrf parameters are learned by considering numerical scattering from a relatively small rough surface which can be solved efficiently via existing numerical methods the mrf parameters may then be used to synthesize multiple realizations of the equivalent current associated with scattering from a much larger rough surface these equivalent currents may be used to efficiently calculate the far field scattered field statistics for large surfaces the advantages of this approach are manifested in the fact that once the mrf parameters are learned a forward model is no longer needed to generate random realizations of the equivalent currents and the mrf model can be employed to generate equivalent surfaces of size beyond the capability of existing numerical models to improve the accuracy of the mrf model a narrowband filter is used to preprocess the computed current distributions prior to mrf model training one dimensional rough surfaces are considered here to demonstrate the idea and the method of ordered multiple interactions momi is employed to perform the numerical forward modeling promising mrf generated results are demonstrated with comparison to direct momi solutions

stationary patterns for a prey predator model with prey dependent and ratio dependent functional responses and diffusion abstract we study a reaction diffusion system arising from a three species prey predator model with prey dependent and ratio dependent functional responses the main aim of this paper is to study the global existence and bifurcation of non constant positive steady states in particular we will show that even though the unique positive constant steady state is stable for the ode dynamics non constant positive steady states exist for the reaction diffusion system this demonstrates that stationary patterns arise as a result of diffusion

qualitative analysis of steady states to the sel kov model in this work we are concerned with a reaction diffusion system well known as the sel kov model which has been used for the study of morphogenesis population dynamics and autocatalytic oxidation reactions we derive some further analytic results for the steady states to this model in particular we show that no nonconstant positive steady state exists if 0 1 and large where nonconstant positive steady states can occur thus these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants the a priori estimates are fundamental to our mathematical approaches

a highly accurate fgg fg fft for the combined field integral equation in this paper a novel realization of the integral equation in combination with the fast fourier transform for the cfie is established by fitting both the green s function and its gradient onto the nodes of a uniform cartesian grid the new method has been compared with several existing popular fft based methods including the aim the ie fft and the p fft the accuracy of the proposed method is significantly higher than other fft based methods and the method is not sensitive to both the grid spacing and the expansion order the outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions therefore when the higher order basis functions would be adopted in the method of moments only one fitting procedure for the green s function and its gradient on a basis function support is needed to meet all of basis functions defined on this support some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method

a study of wavelets for the solution of electromagnetic integral equations the use of wavelet basis functions for the efficient solution of electromagnetic integral equations is studied it has previously been demonstrated that the use of wavelets for expansion and testing functions produces a sparse moment method matrix here this effect is examined and analyzed in terms of the radiation receiving characteristics of the wavelet basis functions the limitations of wavelets as an efficient solution technique are discussed and a comparison is made to other fast algorithms

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

stationary patterns caused by cross diffusion for a three species prey predator model we study a system arising from a three component prey predator model with prey dependent and ratio dependent functional responses where cross diffusion is included in such a way that predator chases the prey and the prey runs away from the predator we prove that the cross diffusion can generate the stationary patterns nonconstant positive steady states

robust exponential convergence of hp fem in balanced norms for singularly perturbed reaction diffusion problems corner domains abstract the h p version of the finite element method is applied to singularly perturbed reaction diffusion type equations on polygonal domains the solution exhibits boundary layers as well as corner layers on a class of meshes that are suitably refined near the boundary and the corners robust exponential convergence in the polynomial degree is shown in both a balanced norm and the maximum norm

short note moore s law and the saffman taylor instability ten years ago hou lowengrub and shelley 4 published a state of the art boundary integral simulation of a classical viscous fingering problem the saffman taylor instability 12 in terms of complexity and level of detail those computations 4 are still among the most ramified and accurately computed interfacial instability patterns that have appeared in the literature since 1994 the computational power of a standard workstation has increased a hundredfold as predicted by moore s law 7 the purpose of this note is to consider moore s law and its consequences in computational science and in particular its impact on studying the saffman taylor instability we illustrate moore s law and fast algorithms in action by presenting the worlds largest viscous fingering simulation to date viscous fingering is one of the fundamental interfacial instabilities in fluid dynamics perturbations to an expanding circular air bubble displacing a viscous fluid in a thin gap flow device become unstable resulting in intricate densely branched interfacial patterns the viscous fingering problem is governed by the three dimensional incompressible navier stokes equations with moving free boundaries at the fluid air interface without simplification this problem is computationally intractable and will remain so for the foreseeable future the simulations in this note build upon decades of advances in mathematical modeling and numerical methods i the fluid dynamics in a thin gap is reduced from the threedimensional navier stokes equations by asymptotic analysis to a darcy s law 12

recursive bifurcation formulae for normal form and center manifold theory abstract applicable recursive formulae are obtained for n dimensional bifurcation problems these formulae give a reduced system corresponding to the center manifold theorem in brjuno s normal form up to an arbitrary order previous formulae by i d hsu n d kazarinoff and b hassard y h wan can be essentially included as particular cases

spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law in this paper a reaction diffusion bimolecular model with autocatalysis and saturation law is investigated firstly we provide some conditions for the stability turing instability of the constant positive solution then we mainly consider hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive solution of the system our results suggest the existence of spatially non homogeneous periodic orbit and non constant positive steady state solutions which implies the possibility of rich spatiotemporal patterns in this diffusive bimolecular model numerical examples are presented to support our theoretical analysis furthermore non existence of non constant steady state is investigated in terms of parameters

a novel fdtd time stepping scheme to calculate rcs of curved conducting objects using adaptively adjusted time steps the chief shortcoming of the conventional conformal finite difference time domain cfdtd method is a global time step reduction to ensure stability due to the small irregular cells truncated by the curved conducting geometry introducing the local time stepping into the cfdtd method is an efficient way and has been numerically proven in our previous work in this paper we further employ the concept of the equivalent material constants into the integral form of faraday s law to analyze the curved configuration with or without the coating hence we can theoretically derive the stability criterion of each irregular cell based on the same procedure for the courant friedrichs lewy cfl stability criterion therefore the local time step size of each small irregular cell can be chosen adaptively an adaptively adjusted time stepping procedure is presented and is theoretically proven to ensure numerical stability the radar cross section rcs results of various curved conducting objects with the coating are computed comparisons of accuracy and efficiency of our method with other established methods are performed

a fast algorithm for the multiplication of generalized hilbert matrices with vectors on presente un algorithme rapide de complexite logarithmique pour la multiplication des matrices de hilbert generalisees par des vecteurs

a fast multi level boundary element method for the helmholtz equation abstract most recently we have developed a novel multi level boundary element method mlbem for the solution of the steady heat diffusion equation involving asymptotically decaying non oscillatory log singular and strongly singular kernels this hierarchical approach generalizes the pioneering work of brandt and lubrecht on multi level multi integration mlmi and c cycle multi grid to the broader class of mixed boundary value problems the result is a fast accurate and efficient boundary element method the present paper extends this new computational methodology to the solution of the helmholtz equation involving oscillatory log singular and strongly singular kernels for two dimensional problems we consider a direct boundary element formulation and due to the nature of the fundamental solutions split the corresponding boundary integral equation into real and imaginary parts then we introduce double noded corners to facilitate a patch by patch application of the mlmi algorithm for fast matrix vector and matrix transpose vector multiplications within bi conjugate gradient methods the performance of the proposed fast mlbem is investigated using a numerical example that possesses an exact solution for wave numbers 20 and below we demonstrate that the fast mlbem algorithm for the helmholtz equation is robust accurate and exceptionally efficient

on the use of fourier series fft s as global basis functions in the solution of boundary integral equations for em scattering current methods for the solution of the surface integral equations of interest to practical electromagnetic scattering appear to have reached an impasse plagued by disputes concerning the suitability and performance of various competing choices for piecewise basis functions and facing horribly complicated piecewise quadratures for the construction of influence matrix elements it has become quite commonplace for these methods to be matrix build time limited rather than matrix solve time limited an extremely simple alternative to all this is described below and demonstrated in an introductory sense on some 2 d problems in this procedure the fft method the basis functions are all global fourier series in a suitably chosen parameter and one attempts to estimate the coefficients describing the unknown surface current directly from the integral equation this format circumvents all of the shortcomings discussed above there are no singular integrals to evaluate furthermore since the fft algorithm is used throughout the computation is extremely efficient the results shown below suggest that so far this approach is very effective

efficient fast multipole method for low frequency scattering the solution of the helmholtz and maxwell equations using integral formulations requires to solve large complex linear systems a direct solution of those problems using a gauss elimination is practical only for very small systems with few unknowns the use of an iterative method such as gmres can reduce the computational expense most of the expense is then computing large complex matrix vector products the cost can be further reduced by using the fast multipole method which accelerates the matrix vector product for a linear system of size n the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to n log n there exist two versions of the fast multipole method one which is based on a multipole expansion of the interaction kernel exp ikr r and which was first proposed by v rokhlin and another based on a plane wave expansion of the kernel first proposed by w c chew in this paper we propose a third approach the stable plane wave expansion spw fmm which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion the computational complexity is n log n as with the other methods

the method of ordered multiple interactions for closed bodies boundary integral methods for calculating bistatic scatter start with a specified sample grid over the surface that defines the scatterer whereas standard method of moments mom implementations can be applied independent of the mesh structure the method of ordered multiple interactions momi effectively defines a surface trajectory over the sample grid this paper introduces source directed slice sampling whereby a variant of the momi method applied to three dimensional 3d objects becomes a strict forward backward recursion applications of momi to 1d rough surfaces first demonstrated the rapid convergence that can be obtained when the surface sampling follows the projected direction of the incident radiation with a 3d object source directed sampling can be implemented with no projection although the surface must be resampled for each new source direction the first iteration of the momi recursion makes a partial backward correction with strict forward backward sampling the initial forward sweep which we call the forward approximation often provides a good approximation to the source currents the results are demonstrated for the scalar problem but the extension to the vector problem is straightforward

separation of horizontal and vertical dependencies in a surface volume integral equation approach to model quasi 3 d structures in multilayered media a new and efficient integral equation approach is presented to model heterogeneous dielectric volumes in a multilayered environment the dielectric volumes can be vertically large they can cross dielectric interfaces and they should be quasi 3 d which means that the contour faces should be placed either horizontally or vertically in the multilayered environment in this way a perpendicular prismatic mesh can be fitted on the volumes and the 3 d displacement currents can be expanded in generalized rooftop functions with separated horizontal x y and vertical z dependencies this makes it possible to evaluate all z z reaction integrals fully analytically in the spectral domain and ensures an efficient implementation the formulation of the source field relations is adapted to the quasi 3 d geometries as a hybrid dyadic mixed potential form additionally the electromagnetic coupling between dielectric volumes and metal sheets is included using a coupled volume surface formulation this turns the implementation into a complete full wave solver for planar antennas containing both finite and infinite dielectric regions in order to illustrate and validate the presented approach two patch antennas with a local volumetric inhomogeneity under the patch are numerically analyzed in a multilayered environment eventually a matrix fill time comparison is used to demonstrate the improvement in computation efficiency

optimal grouping of basis functions when using the method of moments to solve scattering problems a crucial factor is the appropriate choice of basis functions a judicious choice of the basis functions can lead to a sparse impedance matrix or to a sparse solution vector both of which will reduce the computational burden however pulse basis functions are usually used both due to their simple description and because there are already many software tools written for this aim therefore some efforts have been invested in transforming a formulation that is the result of using pulse basis functions to one using preferred basis functions this transform produces grouping of the pulse functions into a new more appropriate set of basis functions this paper discusses the search for an optimal grouping where optimality is measured in terms of the sparseness of the resulting solution vector various options are demonstrated and discussed and numerical examples are given it is important to note that the optimal grouping suggested herein is expected to be optimal on the average when tried on many sample problems adjusting the optimization to a more specific set of problems and scenarios will lead to even better performances and is a viable option in practical cases

analysis of critical and post critical behaviour of non linear dynamical systems by the normal form method part i normalization formulae abstract a method based on normal form theory is presented to study the dynamical behaviour of a system in the neighbourhood of a nearly critical equilibrium state associated with a bifurcation condition explicit formulae for the normalization procedure are derived these formulae can be numerically programmed avoiding usual complicated algebraic calculations and making the method effectively applicable for n dimensional systems rather general bifurcations can be included e g non linear flutter hopf bifurcation divergence and internal resonance

a high performance upgrade of the perfectly matched layer multilevel fast multipole algorithm for large planar microwave structures an improvement of the perfectly matched layer multilevel fast multipole algorithm pml mlfma for simulating large planar microwave structures is presented by exploiting the low rank property of the pml mlfma multimodal aggregation and disaggregation matrices considerable reductions in memory usage and computation time are obtained the method has been extensively validated demonstrating complete error controllability when simulating large planar microwave structures reductions in memory requirements and cpu time of more than 60 and 40 have been achieved

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

calderon s preconditioning for periodic fast multipole method for elastodynamics in 3d summary preconditioning methods based on calderon s formulae for the periodic fast multipole method for elastodynamics in 3d are investigated three different types of formulations are proposed the first type is a preconditioning just by appropriately ordering the coefficient matrix without multiplying preconditioners the other two types utilise preconditioners constructed using matrices needed in the main fast multipole method algorithms we make several numerical experiments with proposed preconditioners to confirm the efficiency of these proposed methods we also conclude that the preconditioning of the first type is faster with respect to the computational time than other preconditioning methods discussed in this article copyright 2012 john wiley sons ltd

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

non constant positive steady states of the sel kov model abstract this paper deals with the reaction diffusion system known as the sel kov model with the homogeneous neumann boundary condition this model has been applied to various problems in chemistry and biology we first give a priori estimates positive upper and lower bounds of positive steady states and then study the non existence bifurcation and global existence of non constant positive steady states as the parameters and are varied

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

an efficient numerical method for studying interfacial motion in two dimensional creeping flows we present new methods for computing the motion of two dimensional closed interfaces in a slow viscous flow the interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex variable theory for the biharmonic equation the numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole based iterative solution procedure which requires only o n operations where n is the number of nodes in the discretization of the interface the interface is described spectrally and we use evolution equations that preserve equal spacing in arclength of the marker points a small scale decomposition is performed to extract the dominant term in the evolution of the interface and we show that this dominant term leads to a cfl type stability constraint when in an equal arclength frame this term is linear and we show that implicit time integration schemes that are explicit in fourier space can be formulated we verify this analysis through several numerical examples

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

fast algorithms for large scale periodic structures using subentire domain basis functions two efficient algorithms are proposed to analyze a large scale periodic structure with finite size using the subentire domain sed basis functions and the conjugate gradient fast fourier transform cg fft the sed basis function is defined on the support of each single element of the periodic structure in a simplified sed ssed cg fft algorithm all elements of the periodic structure share the same sed basis function as a consequence ssed cg fft can be performed in the whole periodic structure however ssed cg fft becomes less accurate if the gap between two unit elements is very small where the single sed basis function cannot capture the strong mutual coupling in order to consider the mutual coupling an accurate sed ased cg fft algorithm is proposed in this algorithm nine types of sed basis functions are employed to distinguish interior cells edge cells and corner cells as a consequence ased cg fft can be performed in all interior cells of the periodic structure comparing with the conventional method of moments with subdomain basis functions the proposed algorithms are more efficient in both the computational complexity and the memory requirement numerical results are given to test the validity and efficiency of the proposed methods

investigation of scattering properties of large scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods this paper presents a hybrid approach for efficient analysis of electromagnetic em scattering from large scale aperiodic structures e g aperiodic penrose and danzer tilings which integrates the characteristic basis function method cbfm and the adaptive integral method aim by performing a domain decomposition a series of characteristic basis functions cbfs that are defined on a macro block and comprised of a relatively large number of sub domain basis functions facilitate a substantial reduction in the method of moments mom matrix size enabling the use of a direct solver for large problems the aim is applied to accelerate the calculation of cbfm reduced mom matrices significantly decreasing the cpu time and memory required for solving large scale problems as the size of one block becomes electrically large the original cbfm combined with the aim is employed to generate the initial cbfs by solving a large problem with multiple excitations which results in efficiently constructing the final cbfs afforded by the singular value decomposition svd procedure this methodology produces a two level cbfm aim hybrid algorithm for efficiently characterizing large scale objects the numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm then the developed solver is applied to investigate em scattering properties of large scale aperiodic tilings the numerical results show that penrose danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts

an efficient solution for cauchy likesystems of linear equations using the displacement approach and transformation of vectors the complexity ofsolving strongly nonsingular cauchy like systems of linear equations email protected email protected will be improved off a factor of log n from the known algorithms of the recursive triangular factorization where f is a field and email protected f n x 1 is a vector and c f n x n is a strongly nonsingular cauchy like matrix the efficient algorithms were presented by morf bitmead and anderson to solve strongly nonsingular toeplitz like equations of linear systems by using the recursive triangular factorization in 1980 recently this approach of the recursive triangular factorization was extended to solve cauchy like systems with the complexity of o n log 3n operations by pan et al this is the best known complexity bound by using the direct approach of recursive triangular factorization in cauchy like cases however these algorithms are still slower than the well known algorithms with the asymptotic bound of o n log 2n operations which have been proposed by the means of reducing cauchy like matrices into toeplitz like matrices in our present paper the algorithms of the recursive triangular factorization are modified so that the complexity bound of the direct recursive approach can be decreased to o n log 2n operations this matches the asymptotic bound without transforming to toeplitz like matrices our improvement of the direct recursive approach is by a factor of log n due to changing the original vectors expressed in the given cauchy like matrix into the special vectors where the entries are unit roots the applications of structured matrices include nevanlinna pick tangential interpolation problems

block size optimization of cbfm for scattering problems the characteristic basis function method cbfm was developed as an algorithm to accelerate the analysis based on direct matrix solver in cbfm the optimum block size greatly influences the overall analysis time in this paper we propose a guideline for setting the optimal block size that can be applied to every algorithm based on cbfm rough estimation of the optimal block size is l b rough approx 0 05 n 6 29 and the exact optimal block size can be determined through preprocessing based on rough estimation numerical results of electromagnetic scattering problems are shown to demonstrate the performance of the proposed method

an ie oddm mlfma scheme with dilu preconditioner for analysis of electromagnetic scattering from large complex objects for electrically large complex electromagnetic em scattering problems huge memory is often required for most em solvers which is too difficult to be handled by a personal computer pc even a workstation although the multilevel fast multipole algorithm mlfma effectively deals with electrically large problems to some extent it is still time and memory consuming for very large objects in order to further reduce the cpu time and the memory requirement a hybrid algorithm based on the overlapped domain decomposition method for integral equations ie oddm mlfma and block diagonal incomplete lower and upper triangular matrices dilu preconditioner is proposed for the analysis of electrically large problems the dominant memory requirement for plane wave expansions in the three processes of aggregation translation and disaggregation in the mlfma is drastically reduced by the first two techniques the iterative procedure for each overlapped subdomain solved by the mlfma is effectively sped up by the dilu preconditioner after integrating these techniques the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional mlfma and is more suitable for analyzing very large em scattering problems enough accurate solution can be obtained within quite a few outer iterations where an outer iteration means a complete sweep for all the subdomains some numerical examples are presented to demonstrate its validity and efficiency

error control in the perfectly matched layer based multilevel fast multipole algorithm the development of efficient algorithms to analyze complex electromagnetic structures is of topical interest application of these algorithms in commercial solvers requires rigorous error controllability in this paper we focus on the perfectly matched layer based multilevel fast multipole algorithm pml mlfma a dedicated technique constructed to efficiently analyze large planar structures more specifically the crux of the algorithm viz the pertinent layered medium green functions is under investigation therefore particular attention is paid to the plane wave decomposition for 2 d homogeneous space green functions in very lossy media as needed in the pml mlfma the result of the investigations is twofold first upper bounds expressing the required number of samples in the plane wave decomposition as a function of a preset accuracy are rigorously derived these formulas can be used in 2 d homogeneous lossy media mlfmas second a more heuristic approach to control the error of the pml mlfma s green functions is presented the theory is verified by means of several numerical experiments

discretized boundary equation method for two dimensional scattering problems a unified approach named discretized boundary equation dbe method is introduced for two dimensional 2 d scattering problems it is based on the discretization of field expressions for one or two components of the scattered field the dbes can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference fd or finite element fe mesh as termination conditions this paper describes the general theory of the dbe method and key points or limitations for its implementation a new on surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two component version of the dbe method and validated through numerical examples mesh termination conditions for the fd or fe method are derived based on the one component formulation of the dbe method and their equivalence and difference to the measured equation of invariance are discussed in particular the dbe obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results generated together with the fd method for scattering by cylinders with various material properties

fourier based fast multipole method for the helmholtz equation the fast multipole method fmm has had great success in reducing the computational complexity of solving the boundary integral form of the helmholtz equation we present a formulation of the helmholtz fmm that uses fourier basis functions rather than spherical harmonics by modifying the transfer function in the precomputation stage of the fmm time critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast fourier transforms retaining the diagonality of the transfer function and providing a simplified error analysis using fourier analysis constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance sharp error bounds are derived and verified numerically various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function

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

on the canonical grid method for two dimensional scattering problems the banded matrix iterative approach with a canonical grid expansion bmia cag has been shown by tsang et al see ibid vol 43 p 851 9 1995 to be an efficient method for the calculation of scattering for near planar two dimensional 2 d geometries such as one dimensional rough surfaces however in the article of tsang et al only the first three terms in the canonical grid series for te polarization above a perfectly conducting surface were discussed and methods for implementing only a portion of these terms were presented in this paper a general form for all terms in the canonical grid series is provided for both te and tm polarizations above an impedance surface and an efficient algorithm for calculating their contributions is described the relationship between the canonical grid and operator expansion methods is also discussed a sample surface scattering problem is shown to illustrate the utility of higher order terms in the canonical grid method

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

efficient numerical methods for multiple surfactant coated bubbles in a two dimensional stokes flow we present efficient and highly accurate numerical methods to compute the deformation of surfactant coated two dimensional bubbles in a slow viscous flow surfactant acts to locally alter the surface tension and thereby change the nature of the interface motion in this paper we restrict our attention to the case of a dilute insoluble surfactant the convection diffusion equation for the surfactant concentration on the interface is coupled with the stokes equations in the fluid domain through a boundary condition based on the laplace young condition the stokes equations are first recast as an integral equation and then solved using a fast multipole accelerated iterative procedure the computational cost per time step is only o n log n operations with n being the number of discretization points on the interface the bubble interfaces are described by a spectral mesh and is advected according to the fluid velocity in such a manner so as to preserve equal arc length spacing of marker points this equal arc length framework has the dual advantage of dynamically maintaining the spatial mesh and allowing efficient implicit treatment of the stiffest terms in the dynamics several phenomenologically different examples are presented

harmonics based inhomogeneous plane wave method hipw a formulation is presented for fast interactions between subdomains in two dimensional 2 d scattering problems the formulation combines inhomogeneous plane waves with cylindrical harmonic decompositions of fields radiated by the subdomains it is shown that the complexity of interactions naturally decays with the distance between subdomains and that very few elementary operations are involved at the lowest level an example of iterative solution for scattering by a collection of cylinders validates the proposed approach

application of multiregion model to em scattering from a dielectric rough surface with or without a target above it an efficient multiregion model is extended by the single integral equation sie method for the first time to calculate electromagnetic em scattering from a dielectric rough surface with or without a perfectly electric conducting target above it in the multiregion model the rough surface is divided into multiple regions depending on their positions along the rough surface and the energy distribution of the incident wave two intermediate regions are chosen as the dominant regions in which the method of moment is adopted if a target is located above the surface the target is also included in the dominant region hence the new model can markedly reduce the number of unknowns compared with full sie analysis mutual couplings between different regions are approximately considered based on magnetic and electric field integral equations from which closed form approximations for currents in other regions are derived

a priori bounds and global existence of solutions of the steady state sel kov model we consider the system of reaction diffusion equations known as the sel kov model this model has been applied to various problems in chemistry and biology we obtain a priori bounds on the size of the positive steady state solutions of the system defined on bounded domains in r n 1 n 3 this is the physically relevant case previously such bounds had been obtained in the case n 1 under more restrictive hypotheses we also obtain regularity results on the smoothness of such solutions and show that non trivial solutions exist for a wide range of parameter values

monte carlo simulation of electromagnetic scattering from two dimensional random rough surfaces the fast multipole method fast fourier transform fmm fft method is developed to compute the scattering of an electromagnetic wave from a two dimensional 2 d rough surface the resulting algorithm computes a matrix vector multiply in o n log n operations this algorithm is shown to be more efficient than another o n log n algorithm the multilevel fast multipole algorithm mlfma for surfaces of small height for surfaces with larger roughness the mlfma is found to be more efficient using the mlfma monte carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2 d random rough surfaces using a workstation for the rougher surface backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient for the smoother surface the monte carlo results compare well with the results of the approximate kirchhoff theory

stationary patterns created by cross diffusion for the competitor competitor mutualist model abstract in this paper we consider a competitor competitor mutualist model with cross diffusion we prove some existence and non existence results concerning non constant positive steady states patterns in particular we demonstrate that the cross diffusion can create patterns when the corresponding model without cross diffusion fails

combining kronecker product approximation with discrete wavelet transforms to solve dense function related linear systems a new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory this technique combines kronecker product approximation and wavelet sparsification for the kronecker product factors the user is only required to supply a procedure for computation of each entry of the given matrix the main sources of efficiency are the incomplete cross approximation procedure adapted from the mosaic skeleton method of the second author and data sparse preconditioners the incomplete lu decomposition with dynamic choice of the fill in structure with a prescribed threshold and the inverse kronecker product preconditioner constructed for the sum of kronecker products of sparsified finger like matrices computed by the discrete wavelet transform in some model but quite representative examples the new technique allowed us to solve dense systems with more than 1 million unknowns in a few minutes on a personal computer with 1 gbyte operative memory

stationary nonstationary and hybrid iterative method of moments solution schemes the purpose of this paper is to report on the convergence rates of two iterative matrix solution methods individually and then to combine the two methods into a hybrid scheme to achieve additional convergence rate benefits one iterative matrix solver investigated is the sparse iterative method sim which is a stationary jacobi like solver but uses a sparse and not a banded matrix with matrix elements corresponding to strong interactions rather than position in the matrix in this paper the sim is modified to include an adaptive relaxation scheme to improve its convergence speed and numerical stability another iterative scheme investigated is the nonstationary biconjugate gradient stabilized bicgstab method it is shown that the bicgstab is considerably improved when the method is preconditioned by the sparse matrix used in the sim method finally a hybrid scheme is proposed which combines both sim ar and bicgstab precon and it is shown that the hybrid gives best results on the problems considered examples giving convergence time versus accuracy are presented for two problems a wire grid plate and a wire grid partial helicopter

a recursive approach to compute normal forms normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations particularly when singularities close to a bifurcation are to be characterized however the computation of a normal form up to an arbitrary order is numerically hard this paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms a computer program to reduce the system to its normal form on a center manifold is developed using the maple symbolic language however it should be stressed that the program relies essentially on recursive numerical computations while symbolic calculations are used only for minor tasks some strategies are proposed to save computation time examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

a numerical method for electromagnetic scattering by 3 d dielectric objects buried under 2 d locally rough surfaces in this work a numerical method is developed to solve a forward scattering problem of three dimensional 3 d objects buried into two half space media with two dimensional 2 d locally rough interface the proposed method exploits the electric field integral equation efie formulation of the scattered field which involves the dyadic green s function of the background medium since the required green s function has no analytical expression in general buried object approach boa is applied to calculate it numerically method of moments mom is then used to solve the efie the presented method is numerically validated by comparing it with finite difference time domain fdtd method furthermore an elaborative numerical analysis of the proposed method is presented to show its feasibility for various roughness profiles and buried objects

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

a convergence theorem for the fast multipole method for 2 dimensional scattering problems the fast multipole method fmm designed by v rokhlin rapidly computes the field scattered from an obstacle this computation consists of solving an integral equation on the boundary of the obstacle the main result of this paper shows the convergence of the fmm for the two dimensional helmholtz equation before giving the theorem we give an overview of the main ideas of the fmm this is done following the papers of v rokhlin nevertheless the way we present the fmm is slightly different the fmm is finally applied to an acoustic problem with an impedance boundary condition the moment method is used to discretize this continuous problem

single level multipole expansions and operators for potentials of the form r lambda this paper presents the generalized multipole local and translation operators for three dimensional static potentials of the form r lambda where lambda is any real number addition theorems are developed using gegenbauer polynomials multipole expansions and error bounds are presented in a manner similar to those for truncated classical multipole expansions numerical results showing error behavior versus number of terms distance and lambda are presented

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

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

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

an eigencurrent approach to the analysis of electrically large 3 d structures using linear embedding via green s operators we present an extension of the linear embedding via green s operators lego procedure for efficiently dealing with 3 d electromagnetic composite structures in lego s notion we enclose the objects forming a structure within arbitrarily shaped domains bricks which by invoking the equivalence principle we characterize through scattering operators in the 2 d instance we then combined the bricks numerically in a cascade of successive embedding steps to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects in the 3 d case however this process becomes quite soon impracticable in that the resulting scattering matrices are too big to be stored and handled on most computers to circumvent this hurdle we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure which can be written analytically in terms of scattering operators of the bricks and transfer operators among them we then solve this equation by the method of moments combined with the eigencurrent expansion method which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures

positive steady state solutions of the noyes field model for belousov zhabotinskii reaction abstract in the paper we investigate the noyes field model for belousov zhabotinskii reaction and study positive steady state solutions of this model with the homogeneous neumann boundary condition we obtain the existence and non existence of non constant positive steady state solutions

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

the multiple sweep method of moments msmm design of wide band antennas this paper presents the use of the multiple sweep method of moments msmm in the design of electrically large wide band antennas the msmm is an o n sup 2 recursive method for solving the large matrix equations which arise in the method of moments mm analysis of electrically large bodies although the msmm is a frequency domain solution it has a time domain interpretation the main point of this paper is to show that this time domain interpretation can be used to identify the location and magnitude of points of current reflections thus making the msmm a useful tool for the analysis and design of wide band antennas the method is applied to the three dimensional 3 d problems of a long dipole antenna with a reactive load in the center of each arm and a tem horn antenna with a bend

implementation of a forward backward procedure for the fast analysis of electromagnetic radiation scattering from two dimensional large phased arrays forward backward method fbm was successfully developed for the analysis of electromagnetic radiation scattering from one dimensional 1 d phased array in an efficiency appealing fashion the fbm applications to treat 2 d array problems are developed in this paper acceleration algorithm performing better than the novel spectrum acceleration algorithm used for 1 d fbm computation is also developed for this 2 d fbm so the unique advantages of high efficiency and o n sub tot computational complexity as in the 1 d problems can be retained where n sub tot is the total number of array element numerical examples are presented to demonstrate its validity

two level tabulated interaction method for electromagnetic scattering from lossy irregular terrain profiles incorporating back scattering an efficient method is proposed for computing electromagnetic wave propagation over lossy terrain profiles using a coupled surface integral equation formulation the proposed method uses a set of basis functions which can produce a linear system with much fewer unknowns than that created using pulse basis functions in addition the matrix entries can be computed very rapidly using precomputed tabulated values the method improves upon the original tabulated interaction method tim by extending it to lossy profiles allowing for back scatter and by introducing increased accuracy for near field interactions the complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage requirement moreover the accuracy of the proposed method is demonstrated by comparing the pathloss against numerically precise solutions and measured data

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

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