application of analytical retarded time potential expressions to the solution of time domain integral equations recently exact closed form expressions of the electric and magnetic fields and potentials due to impulsively excited rao wilton glisson basis functions have been presented in this work the application of these expressions in the solution of the combined field integral equation cfie is presented solutions via analytical expressions of the electric and magnetic fields are verified and compared with the conventional marching on in time mot algorithm solutions that employ numerical basis integrations it is shown that the accuracy and stability of the solutions obtained with the proposed analytical approach are better when compared to those obtained with the conventional numerical method in addition a discussion section about the effect of the proposed approach in solving the electric field integral equation efie is added in this section it is demonstrated that the dependency of the solution via analytical expressions of the fields are less sensitive to the time step size in comparison to the conventional solution and that the increase in accuracy is a necessary but not sufficient condition for stability

a dc stable well balanced calderon preconditioned time domain electric field integral equation the marching on in time mot solution of the time domain electric field integral equation td efie has traditionally suffered from a number of problems including 1 instability 2 spurious static contributions plaguing the solution 3 low frequency breakdown and 4 dense discretization breakdown the first issue can be resolved by employing proper space time galerkin discretization schemes and accurate quadrature methods the second and the third issue have been resolved by the quasi helmholtz projected td efie qhp tdefie this contribution introduces a multiplicative preconditioner which can be applied to the qhp tdefie without further modifying the original scheme this preconditioner is based on calderon techniques and guarantees that the mot system can be solved efficiently using iterative methods not only for large time step sizes but also for dense spatial discretizations and for both simply and multiply connected geometries

multi grid methods for hamilton jacobi bellman equations in this paper we develop multi grid algorithms for the numerical solution of hamilton jacobi bellman equations the proposed schemes result from a combination of standard multi grid techniques and the iterative methods used by lions and mercier in 11 a convergence result is given and the efficiency of the algorithms is illustrated by some numerical examples

a novel scheme for the solution of the time domain integral equations of electromagnetics a new method to numerically solve time domain integral equations pertinent to electromagnetic surface scattering phenomena is presented the method uses approximate prolate spheroidal wave functions and standard rao wilton glisson basis functions to effect the temporal and spatial discretization of the integral equations respectively because the temporal basis functions are noncausal an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time domain solver

improved algorithms for economic lot size problems many problems in inventory control production planning and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by a s manne 1958 and by h m wagner and t m whitin 1958 the manne wagner whitin model and its variants have been studied widely in the operations research and management science communities and a large number of algorithms have been proposed for solving various problems expressed in terms of this model most of which assume concave costs and rely on dynamic programming in this paper we show that for many of these concave cost economic lot size problems the dynamic programming formulation of the problem gives rise to a special kind of array called a monge array we then show how the structure of monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems we focus on uncapacitated problems i e problems without bounds on production inventory or backlogging capacitated problem

an accurate scheme for the solution of the time domain integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation despite the numerous advances made in increasing the computational efficiency of time domain integral equation tdie based solvers the stability and accuracy of tdie solvers remain problematic this paper introduces a new numerical method for the accurate solution of tdies for scattering from arbitrary perfectly conducting surfaces the work described in this paper uses the higher order divergence conforming basis functions of graglia et al for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations since the basis functions used for the temporal representation are noncausal an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization

a novel td vie based on mot scheme for analysis of dispersive objects a novel time domain volume integral equation td vie is proposed to analyze the transient electromagnetic scattering from inhomogeneous dispersive objects in this td vie method the higher order nystrom method is applied in spatial domain namely the curvilinear tetrahedron elements are utilized to discretize dielectric objects and resulting unknowns are volume electric current density the lagrange interpolation polynomials are used to represent spatial basis functions in temporal domain the marching on in time mot scheme is applied and the shifted lagrange interpolation functions are used to represent temporal basis functions moreover the point matching method is applied both in spatial and temporal domain compared with the traditional spatial schaubert wilton glisson basis based on td vie this novel td vie method is more efficient several numerical examples have demonstrated that the proposed method is accurate stable and also more efficient than the traditional td vie

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

multilevel capacitated lotsizing complexity and lp based heuristics abstract this paper presents the first heuristics capable of solving multilevel lotsizing problems with capacity constraints on more than one level moreover the form of the heuristics is quite general so that they can easily be extended to solve a variety of problems if one wants to solve these problems on a routine basis in a real environment one needs to find fast and easy algorithms however we show that for certain problem classes this is a very difficult task far more difficult than has been suggested in the literature for problems with setup times we show that finding a feasible solution is np complete even without setup times testing for feasibility can be very difficult just how time consuming such heuristics must be is demonstrated this leaves little chance to build fast and easy heuristics except for the most simple cases our exploration of the complexity issues points to mathematical programming as a potential source of heuristics for these problems this paper presents a new and general approach based on rounding an lp solution for the problem without setup times the methods use different information and patterns evident in the lp solution are explored the approach is tested on a large set of problems the main contributions of this paper are the way in which we distinguish between the easy and hard lotsizing problems the lp based heuristics and the test set of capacitated multilevel lotsizing problems

a novel parallel hybrid intelligence optimization algorithm for a function approximation problem a novel parallel hybrid intelligence optimization algorithm phioa is proposed based on combining the merits of particle swarm optimization with genetic algorithms the phioa uses the ideas of selection crossover and mutation from genetic algorithms gas and the update velocity and situation of particle swarm optimization pso under the independence of pso and gas the proposed algorithm divides the individuals into two equation groups according to their fitness values the subgroup of the top fitness values is evolved by gas and the other subgroup is evolved by the pso algorithm the optimal number is selected as a global optimum at every circulation which shows better results than both pso and gas then improves the overall performance of the algorithm the phioa is used to optimize the structure and parameters of the fuzzy neural network finally the experimental results have demonstrated the superiority of the proposed phioa to search the global optimal solution the phioa can improve the error accuracy while speeding up the convergence process and effectively avoid the premature convergence to compare with the existing methods

a reduced variable neighborhood search algorithm for uncapacitated multilevel lot sizing problems multilevel lot sizing mlls problems which involve complicated product structures with interdependence among the items play an important role in the material requirement planning mrp system of modern manufacturing assembling lines in this paper we present a reduced variable neighborhood search rvns algorithm and several implemental techniques for solving uncapacitated mlls problems computational experiments are carried out on three classes of benchmark instances under different scales small medium and large compared with the existing literature rvns shows good performance and robustness on a total of 176 tested instances for the 96 small sized instances the rvns algorithm can find 100 of the optimal solutions in less computational time for the 40 medium sized and the 40 large sized instances the rvns algorithm is competitive against other methods enjoying good effectiveness as well as high computational efficiency in the calculations rvns updated 7 17 5 best known solutions for the medium sized instances and 16 40 best known solutions for the large sized instances

a new iterative method for discrete hjb equations a successive relaxation iterative algorithm for discrete hjb equations is proposed monotone convergence has been proved for the algorithm

two dimensional transverse magnetic time domain scattering using the nystro spl uml m method and bandlimited extrapolation a method is presented for the solution of the integral equations that describe the electromagnetic scattering from an infinitely long conducting cylinder in the time domain the method discretizes the integral equations spatially using a high order locally corrected nystro spl uml m method and temporally using a filtered kernel the filtering of the kernel both controls aliasing and reduces the order of its singularity on the other hand filtering also gives rise to a noncausal kernel so the time marching is accomplished with a bandlimited extrapolation scheme numerical results demonstrate the stability and accuracy of the proposed method

a novel marching on in degree solver of time domain parabolic equation for transient em scattering analysis a novel marching on in degree mod solver of 3 d time domain parabolic equation is proposed to solve the transient electromagnetic scattering from electrically large perfect electric conductor pec targets the finite difference fd scheme is applied to the spatial discretization while the weighted laguerre polynomials are used as the temporal basis functions in this way a large number of computational resources can be saved by using the fd scheme along the paraxial direction and the late time stability can be guaranteed by the mod method both the fd schemes of crank nicolson and the alternating direction implicit types are discussed in this communication numerical results are given to demonstrate the accuracy and efficiency of the proposed method

semismooth newton and newton iterative methods for hjb equation in this paper some semismooth methods are considered to solve a nonsmooth equation which can arise from a discrete version of the well known hamilton jacobi bellman equation by using the slant differentiability introduced by chen nashed and qi in 2000 a semismooth newton method is proposed the method is proved to have monotone convergence by suitably choosing the initial iterative point and local superlinear convergence rate moreover an inexact version of the proposed method is introduced which reduces the cost of computations and still preserves nice convergence properties some numerical results are also reported

integer linear programming model for multidimensional two way number partitioning problem this paper introduces a multidimensional generalization of the two way number partitioning problem as well as an integer linear programming formulation of the problem there are n binary variables and 2p constraints the numerical experiments are made on a randomly generated set in view of its integer linear programming formulation tests are run in cplex this np hard problem uses a set of vectors rather than a set of numbers the presented experimental results indicate that the generalized problem is much harder than the initial problem

smoothing methods and semismooth methods for nondifferentiable operator equations we consider superlinearly convergent analogues of newton methods for nondifferentiable operator equations in function spaces the superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally lipschitzian operator in rn is based on rademacher s theorem which does not hold in function spaces we introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework we show that a function is slantly differentiable at a point if and only if it is lipschitz continuous at that point an application to the dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed

heuristics for multilevel lot sizing with a bottleneck in this paper we present a heuristic method based on lagrangian relaxation for multilevel lot sizing when there is a single bottleneck facility a series of lagrangian relaxations one for each item in the product structure is imbedded in a branch and bound procedure the objective is to find a production schedule that fits within available capacity at minimum cost the method has two solution phases dual and primal in the dual phase of the procedure implied costs of setups and production are determined based on a tentative schedule the primal phase is repeated with these new prices and we iterate to reach a good solution the solution procedure is first tested on two special cases uncapacitated multilevel lot sizing and the capacitated single level multi item lot sizing problem the results show that the solution procedure can provide better solutions than some heuristics designed especially for those problems test results on the bottleneck problem indicate that good feasible solutions are found for problems too difficult to solve with exact methods

marching on in time solution of the time domain magnetic field integral equation using a predictor corrector scheme an explicit marching on in time mot scheme for solving the time domain magnetic field integral equation td mfie is presented the proposed mot td mfie solver uses rao wilton glisson basis functions for spatial discretization and a pe ce m type linear multistep method for time marching unlike previous explicit mot td mfie solvers the time step size can be chosen as large as that of the implicit mot td mfie solvers without adversely affecting accuracy or stability an algebraic stability analysis demonstrates the stability of the proposed explicit solver its accuracy and efficiency are established via numerical examples

an application of swarm optimization to nonlinear programming particle swarm optimization pso is an optimization technique based on population which has similarities to other evolutionary algorithms it is initialized with a population of random solutions and searches for optima by updating generations particle swarm optimization has become the hotspot of evolutionary computation because of its excellent performance and simple implementation after introducing the basic principle of the pso a particle swarm optimization algorithm embedded with constraint fitness priority based ranking method is proposed in this paper to solve nonlinear programming problem by designing the fitness function and constraints handling method the proposed pso can evolve with a dynamic neighborhood and varied inertia weighted value to find the global optimum the results from this preliminary investigation are quite promising and show that this algorithm is reliable and applicable to almost all of the problems in multiple dimensional nonlinear and complex constrained programming it is proved to be efficient and robust by testing some example and benchmarks of the constrained nonlinear programming problems

fast analysis of transient electromagnetic scattering using the taylor series expansion enhanced time domain integral equation solver this paper concentrates on an efficient fast algorithm for accelerating the marching on in time based time domain integral equation method for the analysis of the transient electromagnetic scattering from perfect electrically conducting bodies taking advantage of the approximate evaluation of the vector and scalar potential terms and the taylor series expansion of far field the computational complexity and memory requirement of the proposed algorithm scale as mathrm o n t n s log n s and mathrm o n s 1 5 respectively where n t and n s denote the number of simulation time steps and spatial basis functions respectively several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

time domain adaptive integral method for surface integral equations an efficient marching on in time mot scheme is presented for solving electric magnetic and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium the proposed scheme is the extension of the frequency domain adaptive integral pre corrected fast fourier transform fft method to the time domain fields on the scatterer that are produced by space time sources residing on its surface are computed 1 by locally projecting for each time step all sources onto a uniform auxiliary grid that encases the scatterer 2 by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global multilevel blocked space time ffts 3 by locally interpolating these fields back onto the scatterer surface as this procedure is inaccurate when source and observer points reside close to each other and 4 near fields are computed classically albeit pre corrected for errors introduced through the use of global ffts the proposed scheme has a computational complexity and memory requirement of o n sub t n sub s log sup 2 n sub s and o n sub s sup 3 2 when applied to quasiplanar structures and of o n sub t n sub s sup 3 2 log sup 2 n sub s and o n sub s sup 2 when used to analyze scattering from general surfaces here n sub s and n sub t denote the number of spatial and temporal degrees of freedom of the surface current density these computational cost and memory requirements are contrasted to those of classical mot solvers which scale as o n sub t n sub s sup 2 and o n sub s sup 2 respectively a parallel implementation of the scheme on a distributed memory computer cluster that uses the message passing interface is described simulation results demonstrate the accuracy efficiency and the parallel performance of the implementation

fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm the computational complexity of classical marching on in time mot methods for solving time domain integral equations tdies pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as o n sub t n sub s sup 2 n sub t and n sub s denote the number of temporal and spatial degrees of freedom dof of the electric current on the target this scaling law impedes the application of these schemes to the analysis of large scale scattering phenomena the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based tdie solvers previously we described a two level pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting targets the computational complexity of this algorithm scales as o n sub t n sub s sup 1 5 logn sub s here a multilevel pwtd scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described in addition a multilevel pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting scatterers using o n sub t n sub s log sup 2 n sub s cpu resources is outlined last the accuracy and cpu memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies

a fast higher order time domain finite element boundary integral method for 3 d electromagnetic scattering analysis a novel hybrid time domain finite element boundary integral method for analyzing three dimensional 3 d electromagnetic scattering phenomena is presented the method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes to accurately represent the unknown fields the scheme employs higher order vector basis functions defined on curvilinear tetrahedral elements to handle problems involving electrically large objects the multilevel plane wave time domain algorithm is used to accelerate the evaluation of the boundary integrals numerical results demonstrate the accuracy and versatility of the proposed scheme

a hybrid method combining the multitemporal resolution time domain method of moments with the time domain geometrical theory of diffraction for thin wire antenna problems in this paper a hybrid method combining a multitemporal resolution mtr enhanced time domain method of moments td mom with the td geometrical theory of diffraction gtd is presented which allows to efficiently calculate the transient fields radiated by antennas in presence of large objects the mtr scheme tailors the time step size and thus implicitly the duration of the temporal basis function on the basis of the distance between source and test element additionally the voltage induced by source elements far away from the test element is interpolated in time the hybrid method is applied to calculate the radiation properties of thin wire antennas in presence of perfectly conducting flat scatterers to demonstrate its basic features and advantages

multi level lot sizing problem evaluation of a simulated annealing heuristic abstract the multi level lot sizing problem mlp is the problem of determining production quantities in multi stage production settings such that the sum of set up and holding costs is minimized this type of problem is hard to solve to optimality thereby compelling one to use heuristic approaches in this paper we investigate heuristics based on a stochastic search method experimental results concerning the quality and efficiency of these methods for the mlp are presented and compared to the quality and efficiency of heuristic methods which are based on applying single level heuristics on a level by level basis

analysis of transient electromagnetic scattering phenomena using a two level plane wave time domain algorithm a fast algorithm is presented for solving electric magnetic and combined field time domain integral equations pertinent to the analysis of surface scattering phenomena the proposed two level plane wave time domain pwtd algorithm permits a numerically rigorous reconstruction of transient near fields from their far field expansion and augments classical marching on in time mot based solvers the computational cost of analyzing surface scattering phenomena using pwtd enhanced mot schemes scales as o n sub i n sub s sup 2 3 log n sub s as opposed to spl oscr n sub t n sub s sup 2 for classical mot methods where n sub t and n sub s are the numbers of temporal and spatial basis functions discretizing the scatterer current numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented

a semismooth newton method for a kind of hjb equation abstract in this paper we present a semismooth newton method for a kind of hjb equation by suitably choosing the initial iterative point the method is proved to have monotone convergence moreover the semismooth newton method has local superlinear convergence rate some simple numerical results are reported

incorporating a database approach into the large scale multi level lot sizing problem traditionally optimization for large scale multi level lot sizing mlls problems always encountered heavy computational burden scholars also indicated that whatever the optimal method chosen to solve the mlls problem standard optimization packages were still faced with computer memory constraints and computational limits that prevented them from solving realistic size cases therefore the main purpose of this paper is to propose an optimal method to reduce the computer memory while solving the large scale mlls problems the optimal method is designed to implement on a database entirely because the demand for computer memory can be reduced significantly by means of the utilization of database storage an example is given to illustrate the proposed method and computation capability is tested for the mlls problems with up to 1000 levels and 12 periods

lot sizing in general assembly systems with setup costs setup times and multiple constrained resources we introduce a heuristic method for finding good feasible solutions for multiproduct lot sizing problems with general assembly structures multiple constrained resources and nonzero setup costs and setup times we evaluate the performance of this heuristic by comparing its solutions to optimal solutions of small randomly generated problems and to time truncated optimization subroutine library osl solutions of medium sized randomly generated problems in the first case the heuristic locates solutions averaging 4 percent worse than optimal in less than 1 percent of time required by osl the heuristic solutions to medium sized problems are approximately 26 percent better than solutions osl finds after 10 000 cpu seconds and the heuristic finds these solutions in approximately 10 percent of osl time

explicit time marching schemes for solving the magnetic field volume integral equation a method for constructing explicit marching on in time mot schemes to solve the time domain magnetic field volume integral equation td mfvie on inhomogeneous dielectric scatterers is proposed the td mfvie is cast in the form of an ordinary differential equation ode and the unknown magnetic field is expanded using curl conforming spatial basis functions inserting this expansion into the td mfvie and spatially testing the resulting equation yield an ode system with a gram matrix this system is integrated in time for the unknown time dependent expansion coefficients using a linear multistep method the gram matrix is sparse and well conditioned for galerkin testing and consists of only four diagonal blocks for point testing the resulting explicit mot schemes which call for the solution of this matrix system at every time step are more efficient than their implicit counterparts which call for inversion of a fuller matrix system at lower frequencies numerical results compare the efficiency accuracy and stability of the explicit mot schemes and their implicit counterparts for low frequency excitations the results show that the explicit mot scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy

time domain single source integral equations for analyzing scattering from homogeneous penetrable objects single source time domain electric and magnetic field integral equations for analyzing scattering from homogeneous penetrable objects are presented their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure thus allowing for a marching on in time mot solution scheme unlike dual source formulations single source equations involve space time domain operator products for which spatial discretization techniques developed for standalone operators do not apply here the spatial discretization of the single source time domain integral equations is achieved by using the high order divergence conforming basis functions developed by graglia et al alongside the high order divergence and quasi curl conforming dqcc basis functions of valdes et al the combination of these two sets allows for a well conditioned mapping from div to curl conforming function spaces that fully respects the space mapping properties of the space time operators involved numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the mot scheme

high order calderon preconditioned time domain integral equation solvers two high order accurate calderon preconditioned time domain electric field integral equation tdefie solvers are presented in contrast to existing calderon preconditioned time domain solvers the proposed preconditioner allows for high order surface representations and current expansions by using a novel set of fully localized high order div and quasi curl conforming dqcc basis functions numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly regardless of the mesh density and of the order of the current expansion

implicit runge kutta methods for the discretization of time domain integral equations implicit runge kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory the proposed technique maps a laplace domain equation to a domain equation using the butcher tableau of the implicit runge kutta scheme a discrete time domain system is recovered by computing the inverse transform numerically the resulting technique is capable of third or fifth order accuracy in time and is stable independent of time step numerical results illustrate the accuracy and stability of the technique

embedding calderon multiplicative preconditioners in multilevel fast multipole algorithms calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation efie for perfect electric conductors at lower frequencies previous authors have shown that by using a dense matrix preconditioner based on the calderon identities the low frequency instability is removed while still maintaining the inherent accuracy of the efie it was also demonstrated that the spectral properties of the caldero n preconditioner are conserved during discretization if the efie operator is discretized with rao wilton glisson expansion functions and the preconditioner with buffa christiansen expansion functions in this article we will show how the calderon multiplicative preconditioner cmp can be combined with fast multipole methods to accelerate the numerical solution leading to an overall complexity of o n logn for the entire iterative solution at low frequencies where the cmp is most useful the traditional multilevel fast multipole algorithm mlfma is unstable and we apply the nondirectional stable plane wave mlfma nspwmlfma that resolves the low frequency breakdown of the mlfma the combined algorithm will be called the cmp nspwmlfma applying the cmp nspwmlfma at open surfaces or very low frequencies leads to certain problems which will be discussed in this article

nonuniform grid time domain ngtd algorithm for fast evaluation of transient wave fields a novel algorithm to efficiently compute transient wave fields produced by known three dimensional source constellations is proposed the algorithm uses domain decomposition concepts and comprises two steps to be repeated for each subdomain considered in the first step delay and amplitude compensated fields produced by sources residing inside each subdomain are computed at a sparse set of points surrounding the observation domain in the second step total fields in the observer domain are evaluated by interpolation delay and amplitude restoration and aggregation of subdomain fields the proposed scheme is well suited to accelerate the solution of time domain integral equations by marching on in time to carry out time domain physical optics calculations and to realize near to far field transformations of transients moreover the scheme automatically adapts to and takes advantage of special geometrical features of the source observer constellation studied a key benefit when analyzing quasi planar configurations in addition it realizes a seamless transition from the dynamic to the quasi static regime thus facilitating a unified treatment of electrically large and small problems last but not least the scheme is remarkably simple to implement

a space time discretization criterion for a stable time marching solution of the electric field integral equation numerical techniques based on a time domain recursive solution of the electric field integral equation efie may exhibit instability phenomena induced by the joint space time discretization the above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape we analyze a particular formulation of the method of moments which relies on a triangular patch geometrical model of the exterior surface of the scattering body and operates according to a marching on in time scheme whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps a heuristic stability condition is devised which allows us to define a proper time step as well as a geometrical discretization criterion ensuring convergence of the numerical procedure and therefore eliminating insurgence of late time oscillations the stability condition is discussed and validated by means of a few working examples

design of temporal basis functions for time domain integral equation methods with predefined accuracy and smoothness a key parameter in the design of integral equation methods for transient electromagnetic scattering is the definition of temporal basis functions the choice of temporal basis functions has a profound impact on the efficiency and accuracy of the numerical scheme this paper presents a framework for the design of temporal basis functions with predefined accuracy and varying smoothness properties the well known shifted lagrange basis functions naturally fit in this framework new spline basis functions will be derived that have the same interpolation accuracy as shifted lagrange basis functions and with the added advantage of being smooth numerical experiments show the positive influence of smoothness on the quadrature error in the numerical integration procedure the global accuracy in time of the numerical scheme based on shifted lagrange and spline basis functions has been experimentally analyzed for a given interpolation error the experiments confirm the expected accuracy for the shifted lagrange basis functions but remarkably show a higher order of accuracy for the spline basis functions

time dependent plane wave spectrum representations for radiation from volume source distributions a new time domain spectral theory for radiation from a time dependent source distribution is presented the full spectral representation is based on a radon transform of the source distribution in the four dimensional space time domain and consists of time dependent plane waves that propagate in all space directions and with all spectral propagation speeds v this operation termed the slant stack transform involves projection of the time dependent source distribution along planes normal to the spectral propagation direction and stacking them with a progressive delay corresponding to the spectral propagation speed v along this direction outside the source domain this three fold representation may be contracted into a two fold representation consisting of time dependent plane waves that satisfy the spectral constraint v c with c being the medium velocity in the two fold representation however the complete spectral representation involves both propagating time dependent plane waves and evanescen

time domain integral equation analysis of scattering from composite bodies via exact evaluation of radiation fields a novel marching on in time and poggio miller chang harrington wu tsai pmchwt based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented to render the marching on in time procedure stable observer and source integrals are approximated via multipoint collocation and evaluated in closed form the proposed scheme avoids the costly evaluation of five dimensional integrals required in full space time galerkin schemes and proves to be stable for all targets investigated including coated perfect electrically conducting surfaces and multiregion penetrable volumes

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

numerical stability and convergence of approximations of retarded potential integral equations stability and convergence results for approximations of retarded potential integral equations are given such integral approximations arise in time marching schemes for direct scattering problems and are both extremely complicated and computationally intensive they are often observed to have exponentially increasing unstable solutions a stability analysis is performed which is shown to provide a way of predicting whether a given scheme is stable or not the proposed test is supported by numerical experiments and requires much less computation than the scheme itself it is also shown that if an approximation for this type of integral equation is both stable and consistent then it is convergent

solving uncapacitated multilevel lot sizing problems using a particle swarm optimization with flexible inertial weight the multilevel lot sizing mlls problem is a key production planning problem in materials requirements planning mrp system the mlls problem deals with determining the production lot sizes of various items appearing in the product structure over a given finite planning horizon to minimize the production cost the inventory carrying cost the back ordering cost and etc this paper proposed a particle swarm optimization pso algorithm for solving the uncapacitated mlls problem with assembly structure all the mathematical operators in our algorithm are redefined and the inertial weight parameter can be either a negative real number or a positive one the feasibility and effectiveness of our algorithm are investigated by comparing the experimental results with those of a genetic algorithm ga

an optimization framework for solving capacitated multi level lot sizing problems with backlogging this paper proposes two new mixed integer programming models for capacitated multi level lot sizing problems with backlogging whose linear programming relaxations provide good lower bounds on the optimal solution value we show that both of these strong formulations yield the same lower bounds in addition to these theoretical results we propose a new effective optimization framework that achieves high quality solutions in reasonable computational time computational results show that the proposed optimization framework is superior to other well known approaches on several important performance dimensions

meta heuristics for dynamic lot sizing a review and comparison of solution approaches proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve because these problems are so difficult various solution techniques have been proposed to solve them in the past decade meta heuristics such as tabu search genetic algorithms and simulated annealing have become popular and efficient tools for solving hard combinatorial optimization problems we review the various meta heuristics that have been specifically developed to solve lot sizing problems discussing their main components such as representation evaluation neighborhood definition and genetic operators further we briefly review other solution approaches such as dynamic programming cutting planes dantzig wolfe decomposition lagrange relaxation and dedicated heuristics this allows us to compare these techniques understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms finally we discuss general guidelines for computational experiments and illustrate these with several examples

time domain calderon identities and their application to the integral equation analysis of scattering by pec objects part i preconditioning time domain electric field integral equations often are used to analyze transient scattering from perfect electrically conducting objects when discretized using marching on in time recipes they give rise to linear systems of equations that can be solved for the induced currents for all time steps unfortunately when the scatterer is approximated by increasingly dense meshes the condition number of these systems grows rapidly slowing down the convergence of iterative solvers here time domain calderon identities are derived and subsequently used to construct a calderon preconditioned time domain electric field integral equation that can be discretized even with dense meshes using buffa christiansen basis functions numerical results that demonstrate the effectiveness and accuracy of the proposed method are presented

robust solution of time domain integral equations using loop tree decomposition and bandlimited extrapolation a stabilization method that eradicates low frequency instabilities in the solution of the time domain integral equations of electromagnetic scattering is presented the method uses the loop tree decomposition originally suggested for the solution of low frequency scattering problems via the method of moments specifically a temporally differentiated form of the pertinent integral equation is tested using tree basis functions and the undifferentiated form is tested using solenoidal basis functions the underlying solution method uses bandlimited interpolation functions blifs and the higher order divergence conforming vector bases of graglia et al for the temporal and spatial discretization of the integral equations respectively an extrapolation technique has been implemented to overcome the noncausality introduced into the system by the blifs numerical results will demonstrate the stability and accuracy of the proposed technique

on a well conditioned electric field integral operator for multiply connected geometries all known integral equation techniques for simulating scattering and radiation from arbitrarily shaped perfect electrically conducting objects suffer from one or more of the following shortcomings i they give rise to ill conditioned systems when the frequency is low ii and or when the discretization density is high iii their applicability is limited to the quasi static regime iv they require a search for global topological loops v they suffer from numerical cancellations in the solution when the frequency is very low this work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects the new formulation is obtained starting from a helmholtz decomposition of two discretizations of the electric field integral operator obtained by using rwgs and dual bases respectively the new decomposition does not leverage loop and star tree basis functions but projectors that derive from them following the decomposition the two discretizations are combined in a calderon like fashion resulting in a new overall equation that is shown to exhibit self regularizing properties without suffering from the limitations of existing formulations numerical results show the usefulness of the proposed method both for closed and open structures

time domain bie analysis of large three dimensional electromagnetic scattering problems a time domain boundary integral equation bie solution of the magnetic field integral equation mfie for large electromagnetic scattering problems is presented it employs isoparametric curvilinear quadratic elements to model fields geometry and time dependence eliminating staircasing problems the approach is implicit which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer error dependence on discretization is investigated accurate results are obtained with as few as five nodes per wavelength the performance both on large scatterers and on low radar cross section rcs scatterers is demonstrated including the six wavelength nasa almond two spheres a thirteen wavelength missile and a high q cavity

a numerical implementation of a modified form of the electric field integral equation the details of a galerkin discretization scheme for a modified form of the electric field integral equation are outlined for smooth three dimensional perfectly conducting scatterers limitations of the divergence conforming finite element bases in preserving the self stabilizing properties of the electric field integral equation operator are indicated a numerically efficient alternative is outlined which relies on an operator based helmholtz decomposition the condition number of the resulting matrix equation is demonstrated to be frequency independent for scattering from a perfectly conducting sphere at various frequencies

a variable neighborhood search with an effective local search for uncapacitated multilevel lot sizing problems abstract in this study we improved the variable neighborhood search vns algorithm for solving uncapacitated multilevel lot sizing mlls problems the improvement is twofold first we developed an effective local search method known as the ancestors depth first traversal search adts which can be embedded in the vns to significantly improve the solution quality second we proposed a common and efficient approach for the rapid calculation of the cost change for the vns and other generate and test algorithms the new vns algorithm was tested against 176 benchmark problems of different scales small medium and large the experimental results show that the new vns algorithm outperforms all of the existing algorithms in the literature for solving uncapacitated mlls problems because it was able to find all optimal solutions 100 for 96 small sized problems and new best known solutions for 5 of 40 medium sized problems and for 30 of 40 large sized problems

electromagnetic scattering from homogeneous dielectric bodies using time domain integral equations this paper presents a stable and accurate method to compute the electromagnetic scattering from homogeneous isotropic and nondispersive bodies using time domain integral equations tdies unlike previous tdie based scattering work the formulation presented here is based on the equations of poggio miller chang harrington wu and tsai formulation the method employs the higher order divergence conforming basis functions described by graglia et al and bandlimited interpolation functions to effect the spatial and temporal discretization of the integral equations respectively as the temporal basis functions are noncausal an extrapolation mechanism is used to modify the noncausal system of equations to a form solvable by standard marching on in time procedure this work also explains the reason for late time low frequency instabilities encountered in current tdie implementations and details a stabilization technique employed to overcome them numerical results demonstrate the accuracy and stability of the proposed technique

an efficient fast algorithm for accelerating the time domain integral equation discontinuous galerkin method an efficient fast algorithm for accelerating the time domain integral equation discontinuous galerkin tdiedg method for analyzing the transient scattering from electrically large complex objects is proposed the tdiedg is discretized using the monopolar rao wilton glisson rwg function and shifted lagrange polynomial function in spatial and time domain respectively the final system of equations can be solved iteratively using the classical marching on in time scheme taking advantage of the approximate evaluation of the vector and scalar potential terms combined with the taylor series expansion of the transient far field the computational burden of the tdiedg solver has been significantly reduced in addition it is flexible and convenient to analyze object with nonconformal discretization due to the employment of the monopolar rwg functions

accelerated cartesian expansion ace based framework for the rapid evaluation of diffusion lossy wave and klein gordon potentials diffusion lossy wave and klein gordon equations find numerous applications in practical problems across a range of diverse disciplines the temporal dependence of all three green s functions are characterized by an infinite tail this implies that the cost complexity of the spatio temporal convolutions associated with evaluating the potentials scales as on s 2n t 2 where n s and n t are the number of spatial and temporal degrees of freedom respectively in this paper we discuss two new methods to rapidly evaluate these spatio temporal convolutions by exploiting their block toeplitz nature within the framework of accelerated cartesian expansions ace the first scheme identifies a convolution relation in time amongst ace harmonics and the fast fourier transform fft is used for efficient evaluation of these convolutions the second method exploits the rank deficiency of the ace translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions it is shown that the cost of both methods scales as o n sn tlog 2n t several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here

the influence of the exact evaluation of radiation fields in finite precision arithmetic on the stability of the time domain integral equation method transient electromagnetic scattering phenomena can effectively be simulated with time domain integral equation methods the stability and accuracy of the marching on in time scheme is usually established with exact evaluation of the radiation fields due to singularities in their analytical expressions straightforward evaluation in finite precision arithmetic can jeopardize the accuracy of the radiation fields computational experiments confirm this and show that it can even lead to late time instability of the numerical model hence a reformulation is necessary to remove the singular behavior and obtain the robustness required for industrial application to this end highly accurate and well behaved expressions for the quasi exact integration method in finite precision arithmetic will be derived in this paper numerical experiments confirm the robustness and stability of the improved marching on in time scheme

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

a dc stable and large time step well balanced td efie based on quasi helmholtz projectors the marching on in time mot solution of the time domain electric field integral equation td efie has traditionally suffered from a number of issues including the emergence of spurious static currents dc instability and ill conditioning at large time steps low frequencies in this contribution a space time galerkin discretization of the td efie is proposed which separates the loop and star components of both the equation and the unknown judiciously integrating or differentiating these components with respect to time leads to an equation which is free from dc instability by choosing the correct temporal basis and testing functions for each of the components a stable mot system is obtained furthermore the scaling of these basis and testing functions ensure that the system remains well conditioned for large time steps the loop star decomposition is performed using quasi helmholtz projectors to avoid the explicit transformation to the unstable bases of loops and stars or trees and to avoid the search for global loops which is a computationally expensive operation

a stable marching on in time scheme for solving the time domain electric field volume integral equation on high contrast scatterers a time domain electric field volume integral equation td efvie solver is proposed for characterizing transient electromagnetic wave interactions on high contrast dielectric scatterers the td efvie is discretized using the schaubert wilton glisson swg and approximate prolate spherical wave apsw functions in space and time respectively the resulting system of equations cannot be solved by a straightforward application of the marching on in time mot scheme since the two sided apsw interpolation functions require the knowledge of unknown future field samples during time marching causality of the mot scheme is restored using an extrapolation technique that predicts the future samples from known past ones unlike the extrapolation techniques developed for mot schemes that are used in solving time domain surface integral equations this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane this increases the stability of the mot td efvie solver significantly since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme numerical results demonstrate that the proposed mot solver maintains its stability even when applied to analyzing wave interactions on high contrast scatterers

a lagrangean based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times in this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed with the help of lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single item lotsizing problems from the solutions of these single item problems lower bounds on the minimum objective function value are derived upper bounds are generated by means of a heuristic finite scheduling procedure the quality of the approach is tested with reference to various problem groups of differing sizes

a hybrid scheme with nystrom discretization for solving transient electromagnetic scattering by conducting objects the interaction of transient electromagnetic em waves with objects can be formulated by the integral equation approach in time domain for conducting objects or homogeneous penetrable objects the time domain surface integral equations tdsies can be applied traditionally the tdsies are solved by combining the method of moments mom in spatial domain and a march on in time mot scheme in temporal domain the mom usually requires conforming meshes with a well designed basis function and the mot may suffer from a stability problem in this work we propose a hybrid scheme in which the nystrom method is used in spatial domain while the mom with laguerre function as basis and testing functions is employed with a march on in degree mod manner in the temporal domain the nystrom method does not require any basis and testing functions and can use nonconforming meshes in spatial domain whereas the mom with laguerre function as basis and testing functions can fully eliminate the stability problem in temporal domain numerical examples for em scattering by typical conducting objects are presented to demonstrate the scheme and its merits have been verified

fast transient analysis of acoustic wave scattering from rigid bodies using a two level plane wave time domain algorithm it is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size indeed performing a three dimensional scattering analysis using these methods requires o ntns2 operations where ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and nt is the number of time steps in the analysis recently novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced this paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two level setting it is shown that the resulting scheme has a computational complexity of o ntns1 5 log ns examples comparing the accuracy

a higher order nystrom scheme for a marching on in time solution of time domain integral equation a marching on in time mot solution of the time domain integral equation tdie using the higher order nystrom scheme is developed to analyze the transient electromagnetic scattering from arbitrarily shaped perfect electrically conducting pec objects in this scheme the curvilinear triangular patches are utilized to discretize the pec objects for their great ability to model geometric configuration moreover we use the lagrange interpolation polynomials to stand for the spatial basis functions and the triangle functions to represent the temporal basis functions furthermore the spatial and temporal point matching is applied numerical examples demonstrate that the proposed scheme is stable accurate and efficient

time domain weyl s identity and the causality trick based formulation of the time domain periodic green s function time domain floquet modes for analyzing scattering radiation from periodically arranged planar scatterers sources have been presented recently in a series of papers by felsen and capolino in these papers they have investigated phenomenological details of transient scattering radiation by such structures typically time domain floquet modes are derived either by fourier transforming their frequency domain counterparts or using spatial synthesis using poisson summation this paper proposes an alternative means to develop similar expressions and is motivated by the possibility of easily extending the method to the analysis of periodic structures in a layered medium as will be shown the time domain weyl s identity can be used to construct the periodic green s function using both homogeneous and inhomogeneous plane waves we will also derive expressions using the causality trick this technique involves using time symmetric non causal signals however it yields much simpler expressions that involve only homogeneous time domain plane waves and the results are identical to those obtained using the time domain weyl s identity for the time region of interest finally we will use the whittaker formulation which relies on real signals to derive time domain floquet modes this formulation is applicable for simultaneous excitation only

electromagnetic scattering from dispersive dielectric scatterers using the finite difference delay modeling method a new method for solving the time domain integral equations of electromagnetic scattering from dispersive dielectric bodies is proposed the method is based on the finite difference delay modeling scheme which accomplishes the temporal discretization by substituting a z domain finite difference approximation for the continuous time laplace domain s parameter the inverse z transform used for computing the temporal kernels is calculated numerically using the trapezoidal rule and inverse discrete fourier transform arbitrary dispersive models can be simulated without extraneous convolution using the new technique the normal field equations are augmented to the standard tangential equations to solve the low frequency instability problem

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables