Huanhuan Zhang

Parallel Marching-on-in-Degree Solver of Time-Domain Combined Field Integral Equation for Bodies of Revolution Accelerated by MLACA

Time-domain combined field integral equation (TD-CFIE) for bodies of revolution (BORs) is solved by marching-on-in-degree (MOD) method. A multilevel partitioning is adopted to group the spatial basis functions along the longitudinal dimension. The interactions of the adjacent groups are calculated directly in the traditional manner, while the impedance matrices associated with the well-separated groups at each level are computed by the multilevel adaptive cross approximation (MLACA) algorithm. The hybrid MPI and OpenMP parallel programming technique is utilized to further accelerate the solving process on a shared-memory computer system. Two numerical results demonstrate that the proposed method can greatly reduce the memory requirement and CPU time, thus enhance the capability of MOD method.

Acceleration of the Impedance Matrix Filling for Marching-on-in-Degree Method by Equivalent Dipole Moment

Abstract In this article, the equivalent dipole moment method is employed to accelerate the marching-on-in-degree method for the time-domain combined field integral equation. Each element can be viewed as a dipole model when the distance between the source and the testing basis functions is beyond a threshold distance. In this way, the impedance matrix elements of each order can be easily computed by a simple procedure, and the computational time is reduced significantly for transient electromagnetic scattering. Numerical results are presented to demonstrate the efficiency of the proposed method for electromagnetic scattering from perfect electric conductor objects.

Radar Target Recognition Based on Multi-Directional E-Pulse Technique

In the implementation of E-pulse technique based radar target recognition system, only one E-pulse is constructed for each target and it is considered to be aspect-independent, which is grounded in the knowledge that E-pulse synthesis is based on the poles of targets and they are aspect-independent. But our recent study suggests that the poles obtained by pole extraction algorithm are aspect-dependent although theoretically poles of targets are aspect-independent. This is because the residues of the poles are aspect-dependent. The residues represent the contributions of the poles to the late-time transient scattered field and they may be so small at some aspect angles that the corresponding poles can not be extracted by pole extraction algorithm. Consequently, different poles may be extracted at different aspect angles. If only one E-pulse is constructed using the poles extracted at one aspect angle, it may not work for the transient scattered fields at other aspect angles. In order to solve this problem, we propose a multi-directional E-pulse technique which constructs multiple E-pulses for different angle regions of a target. Numerical results show that the proposed method is very robust and can dramatically improve the recognition rate of E-pulse technique.

Efficient Generation of Aggregative Basis Functions in the Marching-on-in-Degree Time-Domain Integral Equation Solver

Abstract The aggregative basis function method for a marching-on-in-degree time-domain integral equation solver can significantly reduce the matrix size and storage and make the reduced system easily manageable and solvable. In the conventional generation of an aggregative basis function, a repeated solution of the matrix equation is required with various excitations, and hence, an efficient approach to generate the aggregative basis function is proposed in this article. The singular value decomposition is performed on multiple right-hand sides, which are linearly dependent or rank deficient, and after the singular value decomposition truncation, fewer matrix equation solutions are necessary with the retained excitation to generate the aggregative basis function. The size-reduced system is then constructed in the marching-on-in-degree time-domain integral equation solver with the aggregative basis function method to analyze transient electromagnetic scattering of conducting objects. Several numerical examples are included to demonstrate the performance of the proposed method.

Marching-on-in-Degree Method With Delayed Weighted Laguerre Polynomials for Transient Electromagnetic Scattering Analysis

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.

Fast Wideband Scattering Analysis Based on Taylor Expansion and Higher-Order Hierarchical Vector Basis Functions

A fast wideband electromagnetic scattering analysis method based on Taylor expansion and higher order hierarchical vector basis functions is proposed. By extracting a phase term from the green function, the remaining exponent term can be approximated by its Taylor expansion. After that, some computationally intensive matrices related to the geometry of the object can be computed in advance. During the frequency sweeping process, the impedance matrix is generated efficiently by combining the precomputed matrices and some frequency dependent terms. By using higher order hierarchical vector basis functions, only one coarse mesh corresponding to the lowest frequency of the given frequency band is generated. The order of the basis functions increases with the rising of frequency. Moreover, only the precomputed matrices corresponding to the highest order basis need to be computed. All impedance matrices at different frequencies can be generated by these precomputed matrices due to the hierarchical property of the basis functions. The proposed method is implemented in the platform of the multilevel fast multipole algorithm (MLFMA). Numerical results show that the proposed method can efficiently accelerate the wide-band scattering analysis.

Incomplete LU factorization preconditioner for the efficient solution of improved electric field integral equations

This paper is a study on the numerical solution of linear systems arising from the discretization of the improved electric field integral equation (IEFIE) for electromagnetic scattering problems. Using incomplete LU factorization preconditioner, the IEFIE is solved by generalized minimal residual iterative method in the context of the multilevel fast multipole algorithm (MLFMA). Numerical results show that the efficiency and robustness of the solution can be significantly improved by contrast with the conventional EFIE formulation.

Adaptive Neighborhood-Preserving Discriminant Projection Method for HRRP-Based Radar Target Recognition

A new manifold learning algorithm named adaptive neighborhood preserving discriminant projection method is proposed for the feature extraction of high-range resolution profile (HRRP)-based radar target recognition. By utilizing the objective functions of both neighborhood-preserving projection (NPP) and adaptive maximum margin criterion (AMMC), the proposed method can not only preserve the neighborhood structure of original data in the dimensionality reduced space, but also exhibit good classification performance. The proposed method is applied to the feature extraction of HRRP-based radar target recognition. Numerical experiments show that the proposed method can effectively reduce the dimensionality of HRRP and give satisfactory recognition rate.

Marching-on-in-degree solver of time domain integral equation based on near-orthogonal higher order hierarchical basis functions

In this paper, the time domain integral equation is solved by marching-on-in-degree method with near-orthogonal higher order hierarchical Legendre basis as spatial basis functions and causal weighted Laguerre polynomials as temporal basis functions. In the traditional marching-on-in-degree solver of time domain integral equation, RWG basis functions are used as spatial basis functions. The memory requirement and time consuming is very large, which becomes a bottleneck of marching-on-in-degree method. In order to solve this problem, the object is meshed with second-order nine-node curved quadrilateral elements and near-orthogonal higher order hierarchical Legendre basis functions are adopted as spatial basis functions. Numerical results show that this method can greatly reduce the unknowns of the problem, by which it can save memory and CPU time.

Marching-on-in-degree solver of time domain finite element-boundary integral method

A marching-on-in-degree solver of time domain finite element-boundary integral method is proposed for the analysis of transient electromagnetic scattering from complex materials and fine detail structures. Unlike the marching-on-in-time solver of time domain finite element-boundary integral method, the proposed algorithm uses weighted Laguerre polynomials as temporal basis functions and testing functions, which leads to a recursive matrix equation solved degree by degree. Due to the property of weighted Laguerre polynomials, the proposed method does not involve late-time instability. Numerical results demonstrate that the proposed method is both stable and accurate.