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The matrix enhancement and matrix pencil (MEMP) has been used to reduce the number of array elements in the planar array with a shaped-beam pattern. This work extends the MEMP-based synthesis method to the synthesis of pattern reconfigurable sparse planar arrays in wide angle scanning and wide-band, which exploits a necessary restriction on finding the common element positions and individual element excitations for multiple patterns. Moreover, a unitary transformation is exploited into the multiple-composite equivalent Hankel matrix, which converts the complex computations of singular value decomposition (SVD) and eigenvalue decomposition (EVD) courses into real ones and effectively reduces the computation complexity. A new tactic is also restricted on avoiding too small element spacing with the consideration of the size of array antenna element. A set of numerical experiments is provided to validate the effectiveness and advantages of the proposed method.

This paper addresses a novel rotationally symmetric technique with multiple constraints for sparse conformal array synthesis. The purpose is to synthesis a sparse optimal common element positions on the conformal surface varying multiple patterns of wide angle scanning with the behavior of low sidelobe levels (SLL). The conformal surface aperture is partitioned into several rotationally symmetric sections. The element positions and element numbers of only one section need to be optimized, which contribute to the reduction of optimizing variables and computation resources. We formulate the synthesis problem as a constrained optimization problem, which takes the peak sidelobe level (PSLL) as the fitness function, and sets the total number of array elements, the minimum spacing between two adjacent elements to form multiple constraints. The Brain Storm Optimization (BSO) is further exploited into the synthesis problem with multiple constraints. A set of representative numerical examples are presented to assess the advantages and effectiveness of the proposed method.

An equivalent fractional order orbital angular momentum (OAM) mode based on concentric uniform circular array (CUCA) is proposed in this paper. It is known that the azimuthal resolution of electromagnetic vortex imaging is closely related to the number of OAM modes. Although the multiple-in-multiple-out (MIMO) scheme gives better azimuthal resolution than the multiple-in-single-out (MISO) scheme, it suffers aliasing problem, which means the scattering points with their azimuthal difference larger than 180 degree can not be separated correctly. One possible way to solve this is adding fractional modes in MIMO scheme, but unfortunately, fractional modes are unstable and can not transmit to far field. In this paper, an equivalent fractional order OAM mode is introduced to deal with the problem to achieve higher azimuthal resolution by MIMO scheme. The transmitted and received modes are set to be two adjacent integer modes to realize an equivalent fractional mode. Since the radiation patterns generated by uniform circular array (UCA) for different modes are not aligned, concentric uniform circular array (CUCA) is applied and optimized to overcome this shortage. Simulation results demonstrate the validity of the proposed method.

An innovative noniterative approach based on the matrix enhancement and matrix pencil (MEMP) is proposed for the synthesis of arbitrary sparse planar arrays. In this study, the estimation of array parameters is recast as a 2-D pole extraction problem, and the number of array elements is minimized by the reduced rank processing. Subsequently, the Hankel matrix decomposition algorithm is exploited to accelerate the singular value decomposition (SVD) of the Hankel matrix constructed by the desired pattern samples, which conquers the restriction on the matrix dimension of the sampled Hankel matrix with the increasing of the number of array elements. The MEMP approach is further extended to the synthesis of shaped-beam patterns by using the forward–backward matrix enhancement and matrix pencil method (FBMEMP). A set of representative numerical experiments is provided to validate the effectiveness and advantages of the proposed method.

This paper concentrates on harmonic analysis in gaseous helium, including microscopic generation, selective filtration and macroscopic propagation. A coherent method is proposed, with time-dependent Schrodinger equation for harmonic generation and Maxwell's wave equation for harmonic propagation. By introducing the polarization source based on the microscopic single-atom response, the macroscopic nonlinear propagation can be efficiently solved by a set of linear equations at each harmonic frequency. Using the proposed method, we numerically investigate the propagation effects of selective harmonics in gaseous helium. Our results reveal that specific harmonics allow the synthesis of an isolated attosecond pulse, which presents a high beam quality and an excellent spatial profile with Gaussian-like distribution. Moreover, the generated pulse provides a promising potential on high power defense, quantum radar and communication.

We propose a flat retroreflector that can efficiently reflect the electromagnetic waves back along its incident direction in a wide continuous range of angles. This retroreflector consists of a quadratic metalens and a flat metallic reflector at the focal plane of the former. The quadratic metalens is a dielectric pillar array encoded with a quadratic phase profile and it is embedded in the top side of the substrate. The flat reflector is on the bottom side of the substrate. The designed retroreflector has a diameter of 40 mm, a thickness of 15 mm, and a working frequency of 77 GHz. Through meta-units optimization, a retroreflection efficiency of 38.51% at ± 60° incidence and an average retroreflection efficiency of 46.39% for the incident angles from 0° to 60° can be numerically demonstrated. This flat retroreflector is easy for integration, which is promising for potential applications in the miniature wireless communication systems.

In this paper, a mixed inner–outer iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as outer iteration and the electric-magnetic current combined-field integral equation as inner iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.

A novel technique incorporating the unitary matrix pencil (UMP) method is extended to the case of sparse linear arrays with wideband frequency invariant (FI) patterns. Multiple pattern data at different frequencies are formulated with the same poles corresponding to the FI element positions by a new sampling strategy. The unitary transform converts the complex computations for block Hankel matrices into real ones, which contributes to the reduction of the computation complexity for the singular value decomposition and the eigenvalue decomposition procedures. Taking advantage of the equivalent matrix pencil obtained by the unitary transformation, a new relation between the element positions and generalised eigenvalues can be built by the UMP method, which contributes to the real solutions for all element positions win wideband. A new tactics is exploited to avoid small element spacing with the consideration of the size of array antennas. Multiple FI patterns are reconstructed with a higher matching accuracy by only varying the excitation distributions. A set of representative numerical examples demonstrate the efficiency and advantages of the proposed method.

An efficient high order plane wave time domain algorithm is presented for analyzing the transient scattering from three dimensional electrically large conducting objects. This method uses a set of hierarchical divergence-conforming vector basis functions to accurately represent the current distribution on the perfect electrically conducting (PEC) surface. The higher order functions can significantly reduce the number of unknowns without compromise on the accuracy. The time domain combined field integral equation (TD-CFIE) is then discretized using the hierarchical divergence-conforming vector basis functions and shifted Lagrange polynomial functions in spatial and time domain, respectively. The final matrix equation can be accelerated using the plane wave time domain (PWTD) algorithm. Finally, a parallel algorithm that can execute on a distributed-memory parallel cluster is developed, which provides an appealing avenue for analyzing the transient scattering from three-dimensional electrically large complex PEC objects. Numerical examples are given to demonstrate the accuracy and efficiency of the method.

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.

A nested complex source beam (NCSB) method based on octree structure is proposed to accelerate the method-of-moments (MoM) solution for three-dimensional (3-D) electromagnetic scattering analysis. At the finest level, the far-field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed on the equivalent sphere surface for every group. Furthermore, the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level. Similarly, the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level group. An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method, and only the CSBs at the finest level have the direct association with the basis functions in their group. The NCSB method is shown to be O(NlogN) computational complexity for both matrix–vector product (MVP) time and memory storage by numerical examples with appropriate parameters, and numerical results demonstrate the better efficiency of the proposed method than the current multilevel CSB method.

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.

The transient EM scattering from a homogeneous dielectric body of revolution (BOR) is formulated in terms of the time-domain PMCHW (TD-PMCHW) integral equation. Triangular functions along the generatrix of the BOR and weighted Laguerre polynomials are used as the spatial and temporal basis functions, respectively, to expand the unknown equivalent surface electric/magnetic current densities. In this way, both the memory requirement and the CPU time can be reduced largely since the matrix equation for each Fourier mode can be solved independently. Numerical results are presented to demonstrate the feasibility of the proposed method. Moreover, the convergence is discussed for both the weighted Laguerre polynomials and the Fourier mode.

As a powerful variant of the dual-primal finite-element tearing and interconnecting (FETI-DP) method in electromagnetics (EM), the FETI-DPEM method shows excellent convergence properties and numerical scalability. A key factor affecting the performance of the FETI-DPEM is the direct solution of sub-domain FE systems. An efficient direct solver based on hierarchical (ℋ-) matrix technique is proposed to solve the sub-domain FE systems. ℋ-matrix formatted lower-upper (LU) decomposition with subsequent forward and backward substitution (FBS) can significantly reduce the computational costs of the direct solution with sufficient accuracy. The nested dissection technique is employed to further accelerate the ℋ-LU decomposition and the ℋ-FBS. Numerical examples demonstrate that the proposed method is very robust for the three-dimensional EM simulation.

This communication presents a new numerical method for the efficient solution of marching on in time (MOT)-based time domain integral equations (TDIE) for electromagnetic scattering from perfect electrically conducting (PEC) object with large smooth surfaces. A set of space-delayed temporal basis functions is proposed for the temporal discretization, and the curvilinear Rao-Wilson-Glisson (CRWG) basis functions for the spatial discretization. The space-delayed temporal basis functions are firstly extended to the time domain electric field integral equations (TDEFIE), then easily to the time domain combined field integral equations (TDCFIE). Numerical results demonstrate that the new method is stable and effective for the transient scattering problems from PEC objects with large smooth surfaces and a single plane wave incidence. A significant reduction of the number of spatial unknowns is achieved by using the space-delayed temporal basis functions.

This paper proposes a multigrid preconditioner for integral equation fast analysis of electromagnetic scattering problems. The multigrid model is constructed by recursively dividing every triangular element on the coarse level into 4 small ones. The Rao–Wilton–Glisson (RWG) basis functions defined on the coarse level are expressed with linear combinations of those on the fine level, and the expansion coefficients of which are used to construct the restriction and interpolation operator. To further accelerate the convergence of iterative solution, a set of solenoidal basis functions on the coarse level are constructed additionally, which are also expressed with linear combinations of RWG basis functions on the fine level and adopted to construct the second restriction and interpolation operator. The two sets of coarsening techniques are then combined together to remove the low-frequency components of the iterative error. Numerical results show that the proposed method can reduce both the steps of iteration and CPU time compared with the iterative solver without preconditioning.

The alternating direction implicit (ADI) scheme is used for the parabolic equation (PE) method to analyse electromagnetic scattering problems. The three-dimensional (3D) electromagnetic scattering problem can be reduced to a series of 1D problems to be solved by the ADI-PE method, which is more efficient than the traditional Crank-Nicolson scheme. In this way, both the memory requirement and the central processing unit time can be saved substantially even for electrically large targets with encouraging accuracy. The full bistatic scattering pattern can be obtained by decoupling the marching direction from the direction of the incidence wave. Numerical results are provided to demonstrate the efficiency of the proposed method.

We present a new multilevel fast Fourier transform (MLFFT) method and its application for the 3-D structures capacitance extraction. The multilevel octree structure, multilevel interpolation/projection, and subdomain FFTs techniques are employed in the MLFFT. Distinctions between the MLFFT and the conventional FFT-based methods are discussed carefully. Numerical results demonstrate that the MLFFT is more efficient than conventional FFT based methods, especially when analyzing inhomogeneous problems.

In order to efficiently solve the large sparse complex linear system arising from the vector finite element method (vector FEM) in electromagnetic scattering problems, the factorized sparse approximate inverse (FSAI) algorithm and the programmable graphics processing unit (GPU) are employed in the context of the conjugate gradient (CG) iterative method. The combination of the FSAI with the GPU technique has two advantages. Firstly, the convergence rate of the CG algorithm is significantly accelerated. Secondly, the calculation of the sparse matrix vector product (SMVP) in the FSAI preconditioned CG algorithm is accelerated by harnessing the tremendous parallel processing capacity of the GPU. Numerical experiments indicate that the FSAI preconditioned CG algorithm enhanced by the GPU technique is very effective and can reduce both the number of iterations and the computational time significantly.

In this communication, the adaptive cross approximation (ACA) algorithm is utilized to analyze the scattering from arbitrary metallic bodies of revolution (BoRs) that is formulated by the electric field integral equation approach. For a given mode, a multilevel partitioning is used to group the basis functions of the BoRs along the longitudinal dimension. The interactions of the adjacent groups are calculated directly by the method of moments (MoM), and the interactions of well-separated groups are compressed by the ACA algorithm. The memory requirement and CPU time consumption are reduced drastically.

A hybrid interpolation method is proposed for the fast analysis of the radar cross-section (RCS) over a broad frequency band by use of the matrix interpolation method. In order to efficiently compute electromagnetic scattering, the general minimal residual (GMRES) iterative solver is applied to compute the coefficients of Rao-Wilton-Glisson (RWG) basis functions and the sparse approximate inversion (SAI) preconditioning technique is used to accelerate the iterative solver. Moreover, both the near field impedance and SAI preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, a lot of time can be saved for the calculation of both the near field impedance and preconditioning matrices. Numerical results demonstrate that this hybrid method is efficient for wideband RCS calculation with high accuracy.

The programmable graphics processing unit (GPU) is employed to accelerate the unconditionally stable Crank-Nicolson flnite-difierence time-domain (CN-FDTD) method for the analysis of microwave circuits. In order to e-ciently solve the linear system from the CN-FDTD method at each time step, both the sparse matrix vector product (SMVP) and the arithmetic operations on vectors in the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm are performed with multiple processors of the GPU. Therefore, the GPU based BI-CGSTAB algorithm can signiflcantly speed up the CN-FDTD simulation due to parallel computing capability of modern GPUs. Numerical results demonstrate that this method is very efiective and a speedup factor of 10 can be achieved.

A new set of multiresolution curvilinear Rao-Wilton-Glisson (MR-CRWG) basis functions is proposed for the method of moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. The MR-CRWG basis functions are constructed as linear combinations of curvilinear Rao-Wilton-Glisson (CRWG) basis functions which are defined over curvilinear triangular patches, thus allowing direct application on the existing MoM codes that using CRWG basis. The multiresolution property of the MR-CRWG basis can lead to the fast convergence of iterative solvers merely by a simple diagonal preconditioning to the corresponding MoM matrices. Moreover, the convergence of iterative solvers can be further improved by introducing a perturbation from the principle value term of the magnetic field integral equation (MFIE) operator to construct diagonal preconditioners for efficient iterative solution of the electric field integral equation (EFIE). Another important property of the MR-CRWG basis is that the MoM matrices using the MR-CRWG basis can be highly sparsified without loss of accuracy. The MR-CRWG basis has been applied to the 3-D electromagnetic scattering problems and the numerical results indicate that the MR-CRWG basis performs much better than the CRWG basis.

To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations. The inner-outer flexible generalized minimum residual method (FGMRES) is combined with the symmetric successive over- relaxation (SSOR) preconditioner based on the near-part matrix of the EFIE in the inner iteration of FGMRES to speed up the convergence rate of iterative methods. Numerical experiments with a few electromagnetic scattering problems for open structures are given to demonstrate the efficiency of the proposed method.

Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moment’s discretization to the hypersingular volume integral equation in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green’s function and the contrast source over the domain of interest. For electrically large problems, the direct solution of the resulting linear system is expensive, both computationally and in memory use. Conventionally, the fast Fourier transform method (FFT) combined Krylov subspace iterative approaches are adopted. However, the uniform discretization required by FFT is not ideal for those problems involving inhomogeneous scatterers and sharp discontinuities. In this paper, a nonuniform FFT method combined weak form integral equation technique is presented. The method performs better in terms of speed and memory use than FFT on the configuration involving both the electrically large and fine structures. This is illustrated by a representative numerical test case.

In this paper, frequency selective surfaces (FSSs) are analyzed and designed. The analytical procedure is based on method of moments (MoM). The generalized minimal residual recursive method combined with fast Fourier transform (GMRESR-FFT) is utilized to accelerate the solution of the matrix equation. Our numerical results show that the GMRESR-FFT method can converge at least 3 times faster than the generalized minimal residual fast Fourier transform method (GMRES-FFT). In this paper, the cross dipoles are first used to design the FSS filter with a passband at 300 GHz and a stopband at 450 GHz, and then the Jerusalem cross slots are utilized to avoid grating lobes and improve the bandwidth of FSS. Numerical results demonstrate the validity and efficiency of the presented method.

A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations solved by method of moments. The hierarchical two-level spectral preconditioning technique is developed for the generalized minimal residual iterative method, in which the multilevel fast multipole method is used to accelerate matrix-vector product. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basis functions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. Numerical experiments indicate that the new preconditioner can significantly reduce both the iteration number and computational time.

A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations (EFIE) solved by method of moments (MoM). The multilevel fast multipole method (MLFMM) is used to accelerate matrix-vector product. An improved sparse approximate inverse (SAI) preconditioner in the higher order hierarchical MLFMM context is constructed based on the near- field matrix of the EFIE. The quality of the SAI preconditioner can be greatly improved by use of information from higher order hierarchical MLFMM implementation. Numerical experiments with a few electromagnetic scattering problems for open structures are given to show the validity and efficiency of the proposed SAI preconditioner.

The efficient algorithm is presented for the analysis of electromagnetic scattering from composite structures with coexisting open and closed conductors. A hybrid combined-field integral equation-the improved electric-field integral equation (CFIE-IEFIE) formulation with the incomplete LU factorization (ILU) preconditioner is proposed. Numerical results are given to demonstrate that the efficiency of our algorithm can be significantly improved when compared with the conventional EFIE formulation and the hybrid CFIE-EFIE formulation.

The problem of electromagnetic scattering by three-dimensional dielectric bodies is formulated in terms of a weak formulation of the domain-integral equation. Applying Galerkin's method with rooftop functions as basis and testing functions, the integral equation can be solved by the Krylov-subspace iterative fast Fourier transform (FFT) methods. However, poor convergence is observed when the relative permittivity of the scatterer becomes large. In order to relieve this trouble, an augmented generalized minimum residual method (AGMRES) is presented. Comparisons between several typical iterative methods are made to show the efficiency of our proposed method.

A frequency-domain method based surface integral equation of the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai formulation is presented as a full wave analysis to evaluate surface second-harmonic generation from noble metal nanoparticles of virtually arbitrary shape. According to the similar solution of fields and boundary conditions at fundamental and second-harmonic frequency, we get the derivation of surface integral equation formulations with only half unknowns compared with the conventional surface integral equation method. Simultaneously, the condition number of impedance matrix has been sharply declined. Numerical examples of gold nanospheres of different radius are presented to demonstrate the accuracy and efficiency of the proposed method. To further research the distribution of surface nonlinear polarization and properties of the second-harmonic radiation, we apply our method to a noncentrosymmetric L-shaped gold nanoparticle studied experimentally. This method provides an efficient and promising approach for evaluation of nonlinear optical radiation generated from metal nanoparticles array and optimization design of nonlinear nanoantennas.

We propose a novel doubly hierarchical method of moments for the analysis of large and multiscale structures. A reciprocal multilevel matrix compression method (rMLMCM) is combined with the multilevel fast multipole algorithm (MLFMA), and they are used for the small-scale and large-scale cluster interactions, respectively. The resulting system is preconditioned following the hierarchical multiresolution-incomplete LU approach, which has proven successful for solving multiscale complex structures. The proposed method is applied to electromagnetic compatibility analysis of the real life, complex structures. Numerical results demonstrate the proposed preconditioned rMLMCM/MLFMA is effective also for large structures with strongly nonuniform discretization.

This paper explores tests of the hypothesis that the tail thickness of a distribution is constant over time. Using Hill's conditional maximum likelihood estimator for the tail index of a distribution, tests of tail shape constancy are constructed that allow for an unknown breakpoint. The recursive test is shown to be inconsistent in one direction, and only a one-sided test is recommended. Specifically, the test can be used when the alternative hypothesis is that the tail index decreases over time. A rolling and sequential version of the test is consistent in both directions. The methods are illustrated on recent stock price data for Thailand, Malaysia and Indonesia. The period covers the recent Asian financial crisis and enables us to assess whether breakpoints in domestic asset return distributions are related to known changes in institutional arrangements in the foreign currency markets of these countries.

A doubly hierarchical method of moments (MoM) is proposed for the analysis of large scale multiscale structures. The separate handling of the high and low frequency interactions of the MLMCM/MLFMA is exploited to efficiently analyze multi-scale structures; the resulting system is further preconditioned following the MR-ILU approach, which has proven successful for solving multi-scale complex structures. Numerical results are shown to prove the effectiveness of the proposed approach.

This work investigates the feasibility of utilising the multilevel compressed block decomposition algorithm (MLCBD) to increase the efficiency of solving the matrix equation obtained from the finite-element method in the electromagnetic analysis. The MLCBD takes advantage of the low-rank approximation of each sub-matrix of the inverse matrix by truncating the information relative to the minor singular values. The choice of truncating tolerance will affect the accuracy and efficiency of the solution. Original MLCBD requires a small truncating threshold and uses a large amount of memory to yield a satisfying result. A novel technique is proposed to improve the solving efficiency by combining a less accurate truncating threshold in MLCBD with a rapid and cheap iterative refinement process. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed technique.

In this study, the finite-element boundary integral (FE-BI) method is applied to analyse the electromagnetic scattering from arbitrary objects in the half-space environment. Combined with the real image method to approximate the half-space Green's function, the half-space FE-BI can be extended for electrically large problems by the fast multipole method. An efficient preconditioner is constructed with both the finite-element matrix and the near-field part of the boundary integral equation operator for the FE-BI analysis. The numerical examples demonstrate that this preconditioner is efficient for electromagnetic scattering in the half space.

Several preconditioning techniques, such as Jacobi, SSOR and ILU0, are used to accelerate the convergence of iterative methods, such as CG and GMRES, which are used to solve the large system of linear equations resulted from the time-domain finite-element methods (TDFEM). Convergence properties of these conventional preconditioning techniques are compared. The cylindrical cavity partially filled with dielectric rod and the perfectly matched layer terminated waveguides are simulated. Numerical results show that the ILU0 preconditioned method converges fastest in TDFEM compared with other preconditioning techniques when computing the same number of time steps.

To efficiently solve large, dense, complex linear systems that arise in the electric field integral equation (EFIE) formulation of electromagnetic scattering problems, a new modified incomplete LU (ILU) preconditioner is developed and used in the context of the generalised minimal residual iterative method accelerated with the multilevel fast multipole method. The key idea is to perturb the near-field impedance matrix of EFIE with the principle value term of the magnetic field integral equation operator before constructing ILU preconditioners. Numerical experiments indicate that this new perturbation technique is very effective with the ILU preconditioner and the resulted ILU preconditioner can reduce both the iteration number and the computational time substantially.

A multi-step preconditioning technique suitable for the solution of a sequence of linear systems arising in monostatic radar cross-section (RCS) calculation is presented. This technique is a combination of a prescribed preconditioner and a low-rank update spectral preconditioner in a successive multi-step manner that computes on the fly approximation of the eigenvectors associated with the smallest eigenvalues. Numerical results show that this technique is very effective in monostatic RCS calculation and can reduce simulation time significantly.