new techniques for constructing t ecd edaued and t ecd eds ued codes abstract this paper presents procedures for constructing systematic t error correcting d error detecting all unidirectional error detecting t ed d ed aued codes as well as t error correcting d error detecting and s unidirectional error detecting t ec d ed aued codes the technique proposed are similar to those recently reported to construct t ec aued codes a t ec d ed code is chosen and then a tail is appended in such a way that the new code can detect all or s errors when they are unidirectional interesting tail sequences are included in this paper the efficiency of the t ec d ed aued and t ec d ed s ued codes reported in this paper compares favorably to the existing methods in addition these procedures enable simple and fast encoding and decoding algorithms many useful codes are tabulated

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

a resistive boundary condition enhanced dgtd scheme for the transient analysis of graphene in this paper the electromagnetic em features of graphene are characterized by a discontinuous galerkin time domain dgtd algorithm with a resistive boundary condition rbc the atomically thick graphene is equivalently modeled using an rbc by regarding the graphene as an infinitesimally thin conductive sheet to incorporate rbc into the dgtd analysis the surface conductivity of the graphene composed of contributions from both intraband and interband terms is first approximated by rational basis functions using the fast relaxation vector fitting frvf method in the laplace domain next through the inverse laplace transform the corresponding time domain matrix equations in integral can be obtained finally these matrix equations are solved by time domain finite integral technique fit for elements not touching the graphene sheet however the well known runge kutta rk method is employed to solve the two first order time derivative maxwell s equations the application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by courant friedrichs lewy cfl condition to validate the proposed algorithm various numerical examples are presented and compared with available references

source and boundary implementation in vector and scalar dgtd we summarize the boundary and source implementation for the several formulations of the discontinuous galerkin time domain method dgtd since dgtd with zeroth order scalar basis functions using the upwind flux coincides with the finite volume time domain fvtd many of the concepts developed for fvtd can be ported to dgtd in any of its different formulations scalar vector basis upwind centered flux numerical examples illustrate the different alternatives

transient analysis of lumped circuit networks loaded thin wires by dgtd method with the purpose of avoiding very fine mesh cells in the proximity of a thin wire the modified telegrapher s equations mtes are employed to describe the thin wire voltage and current distributions which consequently results in reduced number of unknowns and augmented courant friedrichs lewy cfl number as hyperbolic systems both the mtes and the maxwell s equations are solved by the discontinuous galerkin time domain dgtd method in realistic situations the thin wires could be either driven or loaded by circuit networks the thin wire circuit interface performs as a boundary condition for the thin wire solver where the thin wire voltage and current used for the incoming flux evaluation involved in the dgtd analyzed mtes are not available to obtain this voltage and current an auxiliary current flowing through the thin wire circuit interface is introduced at each interface corresponding auxiliary equations derived from the invariable property of characteristic variable for hyperbolic systems are developed and solved together with the circuit equations established by the modified nodal analysis mna modality furthermore in order to characterize the field and thin wire interactions a weighted electric field and a volume current density are added into the mtes and maxwell ampere s law equation respectively to validate the proposed algorithm three representative examples are presented

incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time dependent maxwell equations a scheme that discretizes exact absorbing boundary conditions eacs to incorporate them into a time domain discontinuous galerkin finite element method td dg fem is described the proposed td dg fem with eacs is used for accurately characterizing transient electromagnetic wave interactions on two dimensional waveguides numerical results demonstrate the proposed method s superiority over the td dg fem that employs approximate boundary conditions and perfectly matched layers additionally it is shown that the proposed method can produce the solution with ten eleven digit accuracy when high order spatial basis functions are used to discretize the maxwell equations as well as the eacs

observed baseline convergence rates and superconvergence in the scattering cross section obtained from numerical solutions of the mfie the scattering cross section data obtained from numerical solutions of the magnetic field integral equation mfie using a variety of basis functions and both galerkin and non galerkin testing schemes are compared to study the convergence rates of the results for the basis functions considered apparent superconvergence is observed in the mfie scattering cross section when linear tangential linear normal vector basis functions are used with galerkin testing but not with other basis functions

a discontinuous galerkin augmented electric field integral equation for multiscale electromagnetic scattering problems a discontinuous galerkin dg augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full wave solution of multiscale targets the conventional surface integral equation based dg method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low frequency breakdown by augmenting the dg efie with current continuity equation the proposed scheme can alleviate the low frequency breakdown in the augmented system the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including rao wilton glisson rwg and half rwg basis functions since the half rwg basis is not divergence conforming line charge degrees of freedom on the adjoining edges are introduced in this paper it is observed that the resulting linear system is well conditioned at low frequencies which leads to a rapid convergence over wide frequency band numerical examples demonstrate the accuracy and efficiency of the augmented system

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

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

some new constant weight codes a n d w denotes the maximum cardinality of any binary code of length n minimum distance d and constant weight w the results of a search for good constant weight codes using a combinatorial optimization algorithm are reported a brief description of the algorithm is given the problem of constructing a constant weight code of length n minimum distance d and weight w containing m codewords is mapped to an optimization problem the algorithm is used to solve the optimization problem for given parameters n d w and m the application of the algorithm has led to some new constant weight codes their parameters are given

a hybrid time domain discontinuous galerkin boundary integral method for electromagnetic scattering analysis a scheme hybridizing discontinuous galerkin time domain dgtd and time domain boundary integral tdbi methods for accurately analyzing transient electromagnetic scattering is proposed radiation condition is enforced using the numerical flux on the truncation boundary the fields required by the flux are computed using the tdbi from equivalent currents introduced on a huygens surface enclosing the scatterer the hybrid dgtdbi ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer s shape and is located very close to its surface locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain numerical examples demonstrating the accuracy and versatility of the proposed method are presented

interior penalty discontinuous galerkin time domain method based on wave equation for 3 d electromagnetic modeling built on the vector wave equation an interior penalty discontinuous galerkin time domain ipdg we method is presented for 3 d real life electromagnetic modeling in this paper we develop the interior penalty fluxes corresponding to different types of boundary conditions which are commonly used in electromagnetic modeling to construct the ipdg we system in local elements in addition to model the incident wave excitation the total field scattered field approach is incorporated into the proposed method the stability of the ipdg we method is studied analytically and demonstrated numerically we also compare the performance between wave equation based finite element time domain method the maxwell s equation based discontinuous galerkin time domain method and the proposed method both in cpu time and memory usage which demonstrates that the ipdg we method is very competitive among time domain solvers besides the presented method shows good characteristics including the energy conservation and the optimal convergence rate of o h p 1 numerical examples are presented to illustrate the validity versatility and potential of the proposed method in 3 d electromagnetic problems modeling

an efficient discontinuous galerkin finite element method for highly accurate solution of maxwell equations a discontinuous galerkin finite element method dg fem with a highly accurate time integration scheme for solving maxwell equations is presented the new time integration scheme is in the form of traditional predictor corrector algorithms pe ce m but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy numerical results demonstrate that the proposed dg fem uses larger time steps than dg fem with classical pe ce m schemes when high accuracy which could be obtained using high order spatial discretization is required

an auxiliary differential equation formulation for the complex frequency shifted pml an efficient auxiliary differential equation ade form of the complex frequency shifted perfectly matched layer cpml absorbing media derived from a stretched coordinate pml formulation is presented it is shown that a unit step response of the ade cpml equations leads to a discrete form that is identical to roden s convolutional pml method for fdtd implementations the derivation of discrete difference operators for the ade cpml equations for fdtd is also presented the ade cpml method is also extended in a compact form to a multiple pole pml formulation the advantage of the ade cpml method is that it provides a more flexible representation that can be extended to higher order methods in this paper it is applied to the discontinuous galerkin finite element time domain dgfetd method it is demonstrated that the ade cpml maintains the exponential convergence of the dgfetd method

optimal unidirectional error detecting correcting codes in this correspondence a class of t error correcting and multiple unidirectional error detecting systematic codes is presented these codes are significantly more efficient than the earlier codes the efficiency of these codes approaches the efficiency of the bch codes asymptotically furthermore it is shown that these codes can be easily decoded also in this correspondence we have presented a generalization of berger codes over zq these new codes are also shown to be optimal

a continuity preserving and divergence cleaning algorithm based on purely and damped hyperbolic maxwell equations in inhomogeneous media in the numerical solution of maxwell s equations for dynamic electromagnetic fields the two gauss s laws are usually not considered since they are a natural consequence of faraday s and maxwellampre s laws if the charge conservation law is satisfied however when the charge conservation law is not satisfied the numerical errors of gauss s laws will increase unbounded leading to numerical instability or breakdown unfortunately the charge conservation law can be easily violated in self consistent waveparticle simulations in the meantime the violation of gauss s laws will also result in an increased error in the normal flux continuity in the simulations of pure electromagnetic problems the satisfaction of tangential field continuity across a material interface is sufficient to yield accurate numerical results however in a self consistent waveparticle simulation the normal components are as important as the tangential components since they are critical in predicting the particle kinetics in this paper a divergence cleaning method is presented to enforce gauss s laws and normal flux continuity by introducing auxiliary variables and damping terms into maxwell s equations in inhomogeneous media which yield hyperbolic and mixed hyperbolicparabolic maxwell equations the numerical solution schemes of the resulting purely and damped hyperbolic maxwell equations are introduced under the framework of the discontinuous galerkin time domain method it is shown through several numerical examples that the proposed method is able to preserve the continuity conditions for both tangential field components and normal flux components and is effective in cleaning the numerical errors in both gauss s laws

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

on homogeneous radicals of semigroup rings of commutative semigroups all archimedean commutative semigroups s are described such that every s homogeneous hereditary radical is s normal it is shown that this result is in a sense unimprovable

an optimized 3 d hie fdtd method with reduced numerical dispersion fast and accurate modeling of scatters with fine structural feature in one or two directions has significant practical and scientific importance to fill such research gaps a 3 d artificial anisotropy hybrid implicit explicit finite difference time domain aa hie fdtd method is proposed the new algorithm is based on the introduction of aa parameters to the traditional hie fdtd method the iterative formulations and theoretical stability condition are given in detail the proposed method is an easy to use extension to hie fdtd with the nearly unchanged courant friedrich levy condition numerical results indicate that the proposed method has higher accuracy under the same cost of time and memory when compared with the conventional hie fdtd method in addition the proposed method allows for larger time step size than the conventional fdtd method which implies reduced time cost

a higher order multilevel fast multipole algorithm for scattering from mixed conducting dielectric bodies a higher order multilevel fast multipole algorithm mlfma is presented for computing electromagnetic scattering from three dimensional bodies comprising both conducting and dielectric objects the problem is formulated using the poggio miller chang harrington wu tsai 1973 1977 approach for multiple homogeneous dielectric objects and the combined field approach for conducting objects the resultant integral equations are discretized by the method of moments mom in which the conducting and dielectric surfaces interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling an implicit matrix filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions the resultant numerical system is then solved by mlfma which is tailored to accommodate the material properties of dielectric scatterers and the solution is accelerated using an incomplete lu decomposition preconditioner numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems

interconnect and lumped elements modeling in interior penalty discontinuous galerkin time domain methods in this paper we present an approach on how to incorporate passive lumped elements such as resistors capacitors and inductors in dgtd methods and their application to interconnect modeling starting from the voltage and current relationships we derive the equivalent relationships that describe each of the r l c in terms of the electric and magnetic fields next these field expressions are weakly enforced through the interior penalty ip dg formulation the proposed method is explicit and conditionally stable additionally a local time stepping strategy is applied to increase efficiency and reduce the computational time finally a numerical example is presented to validate the proposed approach

systematic t error correcting all unidirectional error detecting codes in this paper we give methods for the construction of systematic t random error correcting and all unidirectional error detecting codes also we give the encoding decoding algorithms and discuss their implementation

dgtd analysis of electromagnetic scattering from penetrable conductive objects with ibc to avoid straightforward volumetric discretization a discontinuous galerkin time domain dgtd method integrated with the impedance boundary condition ibc is presented in this paper to analyze the scattering from objects with finite conductivity two situations are considered 1 the skin depth is smaller than the thickness of the conductive volume 2 the skin depth is larger than the thickness of a thin conductive sheet for the first situation a surface impedance boundary condition sibc is employed wherein the surface impedance usually exhibits a complex relation with the frequency to incorporate the sibc into dgtd the surface impedance is first approximated by rational functions in the laplace domain using the fast relaxation vector fitting frvf technique via inverse laplace transform the time domain dgtd matrix equations can be obtained conveniently in integral form with respect to time t for the second situation a transmission ibc tibc is used to include the transparent effects of the fields in the tibc the tangential magnetic field jump is related with the tangential electric field via the surface conductivity in this work a specifically designed dgtd algorithm with tibc is developed to model the graphene up to the terahertz thz band in order to incorporate the tibc into dgtd without involving the time domain convolution an auxiliary surface polarization current governed by a first order differential equation is introduced over the graphene for open region scattering problems the dgtd algorithm is further hybridized with the time domain boundary integral tdbi method to rigorously truncate the computational domain to demonstrate the accuracy and applicability of the proposed algorithm several representative examples are provided

when is the jacobson radical of a semigroup ring of a commutative semigroup homogeneous abstract in this paper we determine when the jacobson radical of a semigroup ring r s of a commutative semigroup s is s homogeneous

a discontinuous galerkin finite element time domain method modeling of dispersive media a method is proposed for solving the time dependent maxwell s equations via the discontinuous galerkin finite element time domain dgfetd method with dispersive media an auxiliary differential equation ade method is used to represent the constitutive relations the method is applied to drude materials as well as to multiple pole debye and lorentz materials an efficient implementation for high order runge kutta time integration schemes is presented the method is validated and is shown to exhibit high order convergence

theory of unidirectional error correcting detecting codes in this paper we present some basic theory on unidirectional error correcting detecting codes we define symmetric asymmetric and unidirectional error classes and proceed to derive the necessary and sufficient conditions for a binary code to be unidirectional error correcting detecting

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

optimization of the artificially anisotropic parameters in wcs fdtd method for reducing numerical dispersion a 3 d artificial anisotropy weakly conditionally stable finite difference time domain aa wcs fdtd method is presented to reduce the dispersion error without introducing additional computational cost and complexity the motivation is to equal the speed of light in the numerical simulation to the physical speed through manipulating the permittivity and permeability the proposed aa wcs fdtd algorithm achieves the reduced dispersion error for the arbitrary incident angles different time step sizes and wideband frequency the analyses of the stability and dispersion indicate that the proposed algorithm is wcs and the courant friedrich levy condition is slightly changed the numerical example demonstrates that the proposed method has a reduced dispersion error and high accuracy as compared to the wcs fdtd method