X. Q. Hu

Multilevel Complex Source Beam Method for Electromagnetic Scattering Problems

This letter proposes a multilevel complex source beam (MLCSB) method for electromagnetic (EM) scattering problems. The multilevel structure is obtained with the octree grouping technique. Each basis function in the nonempty group is expanded with CSBs that tightly surround the group. The interactions between far groups are expressed with interactions of these CSBs. To accelerate the computation, the symmetry and shift invariance of the Greens function is employed. The adaptive cross approximation (ACA) algorithm is then applied to accelerate the computation of interactions of CSBs. Due to the directionality of the radiation pattern of the CSBs, the interactions of CSBs are truncated with an angle threshold. Numerical examples demonstrate the efficiency of this method.

An H-matrix direct method with improved solution for finite element analysis of scattering problems

An efficient direct method based on hierarchical matrices (H-matrices) was developed for the solution of large sparse finite element systems. H-matrix technique provides a data-sparse way to approximate the inverse of a finite element matrix which is dense originally. The approximate inverse can be computed and stored in the algebra of hierarchical matrices with almost linear complexity. The accuracy of this approximation is controllable with different choices of the related parameters. A modification algorithm was introduced to iteratively improve the accuracy of an approximate solution generated from H-matrix inversion. Some numerical examples are provided to illustrate the accuracy and efficiency of this method.

Augmented MLFMM for solving the electromagnetic scattering problems with fine structures

MLFMM augmented with a Greens function interpolation method is proposed to efficiently solve the electromagnetic scattering problems. One well-known shortcoming of the traditional mid-frequency MLFMM method is that the finest box size must be at least 0.25 wavelength to ensure the accuracy. However, there exists a myriad of real targets having fine structure, and it usually produces a large number of unknowns in each finest box when discretizing these targets in the MLFMM implemetation, which leads to a large mount of storage of near-field interactions. In this article, a Greens function interpolation method (MLGFIM) is proposed to attack this kind of problem, the MLGFIM can make the finest box size reduced to as small as 0.1 wavelength or even smaller, and it enables a significant reduction in memory and complexity against the MLFMM. Numerical examples are presented to validate the proposed scheme.

Combined MDA-SVD-MLFMA for analysis of the EM scattering from complex objects

The multilevel fast multipole algorithm (MLFMA) is very efficient for solving the three-dimensional problems, but for the small size of the complex objects, the memory usage of the multilevel fast multipole algorithm is very large. To overcome this problem, the matrix decomposition algorithm — singular value decomposition (MDA-SVD) is used to alleviate the pressure of the “strong” interaction portion of the impedance matrix of the MLFMA. So a new hybrid method named combined MDA-SVD-MLFMA is proposed. It also overcomes the problem that the matrix filling time of the far field of MDA-SVD is a little long. The numerical results demonstrate the efficiency of this method.

A modified spectral shift preconditiner for electromagnetic scattering of complex objects

In order to efficiently solve large dense complex linear systems arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector product operations. This paper presents a modified spectral shift preconditioner, which is combined with other preconditioner can greatly improve the convergence of restart GMRES iterative method for large dense complex linear systems. Numerical experiments demonstrate that the modified spectral shift preconditioner combined with other preconditioner is very effective and can reduce the iteration number and the computational time significantly