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To further improve the computational efficiency of the existing wave equation-based discontinuous Galerkin time-domain (DGTD) method for modeling electrically small structures, the weighted Laguerre polynomials are incorporated to span the fields in the temporal domain, which finally results in a set of recursive linear equations related to the Laguerre polynomials to be solved. Compared with conventional time integration methods, the proposed approach requires much fewer iterations and thus shows considerable improvement in terms of computational efficiency. With respect to the first-order Maxwell’s curl equation-based DGTD method with weighted Laguerre polynomials, the proposed method reduces the unknowns by more than a half and gives a lighter linear system for solution. In addition, block iterative solvers and the block lower-diagonal-upper (LDU) direct solver can be applied to facilitating the solution at the subdomain level. Three numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. With the weighted Laguerre polynomials, the wave equation-based DGTD method is expected to be more efficient for electrically small structure modeling. [ABSTRACT FROM AUTHOR]

A number of new results aiming at facilitating the use of the $\alpha $ - $\eta $ - $\kappa $ - $\mu $ fading model are presented. These results include: 1) fast convergent, with no recursions, series representations for the envelope probability density function (PDF) and cumulative distribution function (CDF); 2) higher order moments of the envelope; 3) moment generating function (MGF) of the envelope; 4) asymptotic behavior of the envelope PDF and also of the envelope CDF; 5) a procedure for parameter estimation; 6) new closed-form expressions for particular cases of the envelope distribution; 7) new mathematical identity for the generalized Laguerre polynomial and the generalized hypergeometric function; and 8) approximate, but tight, series representation for the phase PDF. As application examples, the following are given: 1) outage probability; 2) outage capacity; 3) amount of fading; and 4) bit error rate, for which the asymptotic behavior is also presented. [ABSTRACT FROM AUTHOR]

An efficient stochastic finite-difference time-domain (S-FDTD) with weighted Laguerre polynomials algorithm is presented for calculating the standard deviation of the electromagnetic fields caused by the variability or uncertainty of the isotropic cold plasma materials in a single run. Compared with the conventional S-FDTD method, the proposed algorithm uses an implicit marching-on-in-degree scheme, which improves the computational speed significantly. The perfectly matched layer with complex-frequency-shifted factor is implemented via formulation in the stretched-coordinate system. Numerical examples demonstrate the accuracy and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The transient electromagnetic (EM) scattering from bodies of revolution (BoRs) is analyzed by the time-domain integral equation with the Silvester–Lagrange polynomials. The high-order spatial basis functions are used along the generatrix, while the weighted Laguerre polynomials are served as the temporal basis functions. In this way, the late time stability can be guaranteed by using the marching-on-in-degree scheme. In this communication, the conducting targets are simulated by the time-domain combined field integral equation while the dielectric ones are formulated in terms of the magnetic current combined field integral equation. Moreover, the multilevel adaptive cross approximation algorithm is adopted to accelerate the calculations of the well-separated groups. The numerical results demonstrate that the proposed solver is efficient to analyze the transient EM scattering from BoRs. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient higher order complex frequency shifted (CFS) perfectly matched layer (PML) derived from a stretched coordinate formulation is proposed for the unconditionally stable finite-difference time-domain method based on weighted Laguerre polynomials. The higher order CFS-PML, which is implemented with an auxiliary differential equation (ADE) approach, has apparent advantage in reducing late-time reflections compared with the standard unsplit-field PML and lower order CFS-PML. Furthermore, the parameter values of stretching functions in the higher order ADE-CFS-PML are optimized with the multiobjective genetic algorithm to improve absorbing performance. The optimal solutions can be chosen from the Pareto front for trading-off between two independent objectives. The numerical formulation is derived and its absorbing ability is validated through three numerical tests. Moreover, the proposed higher order PML can be placed very close to the objects and the simulation area can be further reduced accordingly. Numerical examples of time reversal wave propagation in a real indoor environment are included to validate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM PUBLISHER]

An efficient weighted Laguerre polynomials based spectral finite-difference time-domain scheme for 2-D periodic structures is proposed in this communication. By replacing the conventional single-angle incident wave with a constant transverse wavenumber wave, the periodic boundary condition can be directly implemented in the time domain for both oblique and normal incident waves. The huge sparse matrix is transformed into one tridiagonal matrix and one untridiagonal matrix by adding a perturbation term. Then, an iterative procedure is introduced to eliminate the error. Results from the numerical example and HFSS have verified the accuracy and efficiency of the presented method. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient Laguerre-based body of revolution finite-difference time-domain (BOR-FDTD) method is proposed. A perturbation term and the Gauss–Seidel method are introduced to get the new algorithm. The splitting error caused by the perturbation term can be reduced to a low level by using the iterative method. To be different from its counterpart in the Cartesian coordinate system, the perturbation term used for the off-axis field is not applicable to the field on the axis in the proposed method. On the axis, it is not necessary to add the perturbation term and no nonphysical intermediate variable is involved. No splitting error compensatory term is used for the field on the axis during the iteration. Another difference is that the perturbation term in the proposed method causes a pronounced splitting error on the field point which is close to the axis. Several local iterations near the axis are needed since the splitting error near the axis is especially large. To validate the proposed method, two numerical examples are given. Numerical results show that it obtains a good convergence. Meanwhile, the comparison of the computational expenditure between the proposed method and several other methods indicates its performance. [ABSTRACT FROM PUBLISHER]

Due to the finite expanding order in an actual numerical simulation, the finite-difference time-domain method based on weighted Laguerre polynomials (Laguerre-FDTD) often has a large error near $t=0$. In this communication, a new temporal basis is proposed to solve this problem, which is composed of three weighted Laguerre polynomials in adjacent orders. Based on this new temporal basis, the matrix equation for three-dimensional (3-D) FDTD method is derived in which the accumulation term is eliminated. By introducing a perturbation term and an iterative procedure to the matrix equation, an efficient 3-D FDTD method is obtained. To verify the accuracy and efficiency of the proposed FDTD method, two structures are calculated as examples. Numerical results show that the solution of the proposed method has no error at $t=0$ and the efficiency of the proposed method is superior to the conventional FDTD method, the alternating direction implicit (ADI) FDTD method, and the original efficient Laguerre-FDTD method using a single Laguerre polynomial at a comparable accuracy. [ABSTRACT FROM PUBLISHER]

An efficient marching-on-in-degree (MOD) scheme is proposed to analyze the transient EM scattering from multiple conducting bodies of revolution (MBoRs) with arbitrary axis using the equivalence principle algorithm (EPA). The self-acting of each BoR is calculated by taking advantage of the rotationally symmetrical property in its local BoR coordinate system. The interaction between any two BoRs is replaced by the one between their equivalence spheres which enclose corresponding BoR with EPA. In this way, the transient scattering properties of the randomly distributed MBoRs can be obtained with high efficiency by the use of the BOR basis functions and the weighted Laguerre polynomial. Numerical results are presented to demonstrate the accuracy and efficiency of proposed algorithm. [ABSTRACT FROM AUTHOR]

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 Nyström 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 Nyström 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. [ABSTRACT FROM PUBLISHER]

The large cost of computing resources has become a bottleneck of the marching-on-in-degree (MOD) solver of time-domain integral equation (TDIE). A set of delayed weighted Laguerre polynomials is proposed to address this problem in this paper. By incorporating the phase propagation information into itself, the proposed temporal basis function can model the phase variation of the induced current at different places of the scatterer, leading to a great reduction in the spatial unknowns. Moreover, the curvilinear Rao-Wilton-Glisson (CRWG) basis functions are adopted for the spatial discretization to improve the modeling precision of curve surfaces. Numerical results show that the proposed method can greatly reduce the mesh density of the scatterer and save the computing resources. It is both stable and efficient for the transient scattering analysis of perfect electrically conducting (PEC) objects with large smooth surfaces. [ABSTRACT FROM PUBLISHER]

We previously introduced a new efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. The new 2-D efficient algorithm is based on the use of an iterative procedure to reduce the splitting error associated with the perturbation term, and it does not involve any nonphysical intermediate variables. Numerical results indicated that the new efficient algorithm shows better performance for modeling some regions with larger spatial derivatives of the field. In this paper, we extend this approach to a full 3-D wave. Numerical formulations of the new 3-D Laguerre-based FDTD method are devised and simulation results are compared to those using the conventional 3-D FDTD method and the alternating-direction implicit (ADI) FDTD method. We numerically verify that, at the comparable accuracy, the efficiency of the proposed method with an iterative procedure is superior to the FDTD method and the ADI -FDTD method. Also, in order to verify the stability of the iterative procedure, we present a convergence analysis and a long-time simulation to it in the paper. [ABSTRACT FROM PUBLISHER]

A marching-on-in-degree solver of time domain finite element-boundary integral method is proposed for the analysis of transient electromagnetic scattering from inhomogeneous objects. Weighted Laguerre polynomials are employed as temporal basis functions and testing functions in the proposed algorithm, which leads to a recursive matrix equation without time variable and it can be solved degree by degree. Then the time domain response can be obtained by post processing. Furthermore, a hybrid algorithm using both direct method and iterative method is introduced to accelerate the convergence in the solving of matrix equation. Numerical results are presented to demonstrate the accuracy, stability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We previously introduced an efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. Numerical results indicated that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. However, the splitting error associated with the perturbation term becomes pronounced in regions with larger spatial derivatives of the field. In this paper, we present a new efficient algorithm based on the use of an iterative procedure to reduce the splitting error. The new algorithm does not involve any nonphysical intermediate variables, and its update equations are much simpler and more concise than the original ones. Instead of applying the iterative procedure uniformly to the entire computational domain, one can apply an additional number of iterations to regions with relatively large field variation. Using this approach, the overall accuracy can be improved with little computational overhead. Numerical examples are used to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient domain decomposition technique is introduced into the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials to solve two-dimensional (2-D) electromagnetic scattering problems. The whole computational space is decomposed into multiple subdomains where there is no direct field coupling between any two different subdomains. For the large sparse matrix equation generated by the implicit scheme, the domain decomposition technique transforms this large scale equation into some independent smaller equations. With the total-field/scattered-field boundary and Mur's second-order absorbing boundary condition, the radar cross sections of two 2-D structures are calculated. The numerical examples verify the accuracy and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

In marching-on-in-degree time domain method of moment, the transient responses are often expanded by a finite number of associated Laguerre functions. There is an error associated in truncating the associated Laguerre function series beyond that what is necessary in the solution process. This error is related to the scaling factor used in the argument of the associated Laguerre functions that actually approximates the unknown temporal variations. A least upper bound of this error is deduced. Based on this bound, one can obtain an optimum scaling factor to minimize this error so that it is guaranteed to be below a certain bound. [ABSTRACT FROM PUBLISHER]

A new unconditionally stable numerical method for the time domain simulation of electromagnetic problems using a combination of the Laguerre polynomials in the time domain and radial basis functions (RBF) in the spatial domain named mesh-Free Laguerre time domain (MFLTD) method is described. Unconditionally stable Laguerre based method may be computationally much more efficient than the FDTD methods and using RBFs allows computing the problems with complex-shapes in a non-uniform point's distribution. A numerical example at the final part of the communication shows the efficiency of the presented method in problems with sparse and coarse regions. Using the MFLTD method for this example, we can achieve a 96% reduction in the computation time and get an acceptable degree of accuracy in comparison to the conventional mesh-free time-domain (MFTD) method. [ABSTRACT FROM PUBLISHER]

The marching-on-in-degree (MOD) method has been presented earlier for solving time domain electric field integral equations in a stable fashion. This is accomplished by expanding the transient responses by a complete set of orthogonal entire domain associated Laguerre functions, which helps one to analytically integrate out the time variable from the final computations in a Galerkin methodology. So, the final computations are carried out using only the spatial variables. However, the existing MOD method suffers from low computational efficiency over a marching-on-in-time (MOT) method. The two main causes of the computational inefficiency in the previous MOD method are now addressed using a new form of the temporal basis functions and through a different computational arrangement for the Green's function. In this paper, it is shown that incorporating these two new concepts can speed up the computational process and make it comparable to a MOT algorithm. Sample numerical results are presented to illustrate the validity of these claims in solution of large problems using the MOD method. [ABSTRACT FROM AUTHOR]

A new unconditionally stable finite-difference time-domain (FDTD) method for periodic structures is presented, which is based on the field transformation method and the weighted Laguerre polynomials FDTD (WLP-FDTD). The proposed method uses a field transformation to remove the time gradient across the grid, and then uses the concept of the WLP-FDTD to get the implicit relationship between the transformed field variables. It holds the advantages of the WLP-FDTD, can eliminate the restriction of the Courant-Friedrich-Levy (CFL) stability condition. Compared with other field transform methods, the new method needn't to do special treatment for the additional terms. It appears to be much more efficient than the other field transformation FDTD method for solving periodic structures with fine structures and large incident angle. To verify the accuracy and the efficiency of the proposed method, we compare the results of the Split-Field FDTD method with the proposed method. [ABSTRACT FROM AUTHOR]

The time-domain radial point interpolation (RPI) meshless method has the advantage of conformal modeling of a structure with non-uniformly distributed nodes; however, the time step used is still restricted by the stability condition or distances between the nodes. The time step has to be small and computational time can be long when the distances between nodes are small. In this paper, an unconditionally stable scheme using the weighted Laguerre Polynomials is introduced into the (RPI) meshless method. The result is an always-stable RPI meshless method; it retains the advantages of both the node-based meshless method and the unconditionally stable scheme with the weighted Laguerre Polynomials. The unconditional stability, numerical accuracy and efficiency of the proposed method are verified and confirmed through numerical examples. In the case of the numerical examples computed, CPU time saving can be more than 99% in comparisons with the CPU time used with the conventional conditionally stable meshless method. [ABSTRACT FROM AUTHOR]

A marching-on-in-degree (MOD)-based scheme for analyzing transient electromagnetic scattering from three-dimensional dispersive dielectric objects is proposed. A time-domain volume integral equation (TDVIE) for the electric flux density throughout the object is first formulated and then solved using the MOD scheme. With the use of weighted Laguerre polynomials as entire-domain temporal basis functions, the convolution of the electric flux density and the medium susceptibility and its derivatives can be handled analytically. By employing the Galerkin temporal testing procedure, the time variable is eliminated in the resultant recursive matrix equation so that the proposed algorithm overcomes the late-time instability problem that may occur in the conventional marching-on-in-time (MOT) approach. Some complex dispersive media, such as the Debye, Lorentz, and Drude media, are simulated to illustrate the validity of the TDVIE-MOD algorithm. [ABSTRACT FROM AUTHOR]

the Laguerre-based bodies of revolution finite-difference time-domain (BOR-FDTD) method, the plane wave excitation takes a major part of the total computation time. This time is mainly consumed in evaluating the expansion coefficient of incident field which involves integral of the weighted Laguerre polynomial with respect to time. In this work, an efficient one-dimensional auxiliary Laguerre-based FDTD algorithm combined with correlation operation is presented to speed up the plane wave excitation. Numerical results indicate that the proposed method is valid and highly efficient. [ABSTRACT FROM AUTHOR]

Many finite-difference-based time-domain methods have been developed in the past three decades. Typical among them are the finite-difference time-domain method of Yee's scheme, the transmission-line-matrix method, the multiresolution time-domain method, the pseudospectral time-domain method, and the unconditionally stable finite-difference time-domain methods. All these methods have become powerful tools in solving electromagnetic structure problems, yet their formulations appear to be unrelated. The concept of the method of moments (MoM) is applied in this paper to generalize all these different finite-difference-based methods. It is shown theoretically that differences among various finite-difference-based methods lie in different choices of basis functions used in solution expansions and weighting functions in error testing, in both time and space. The significance of this paper is twofold: 1) all the finite-difference time-domain-based methods can now be unified under the framework of MoM and 2) any other new finite-difference-based time-domain methods, including hybrid techniques, may now be developed with MoM procedure. [ABSTRACT FROM AUTHOR]

An improved testing procedure using the marching-on-in-order method to solve the time-domain electric field integral equation (TD-EFIE) for conducting objects using the Laguerre polynomials is presented. Exact temporal testing is performed before the spatial testing, therefore the retarded terms composed of the spatial and the temporal variables can be analytically separated. The uniqueness of this testing procedure is that the time variable can be analytically integrated out and the accuracy can be improved. This paper is then an improvement over the earlier marching-on-in-order method. In addition, this methodology is quite different from the conventional marching-on-in-time algorithm as the present method leads to a set of final equations which need to be numerically solved containing only the spatial variables. Therefore, there is no requirement to have a Courant stability condition in this procedure. How the singular, integrals are treated is also discussed. Several examples are simulated both for radiation and scattering problem. The results are compared with the inverse discrete Fourier transform of the frequency domain data and they agree well. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other wave shapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared. [ABSTRACT FROM AUTHOR]