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We propose the recent progress in fast integral multiscale simulations in our group in this contribution. Firstly, a wideband fast kernel independent fast solver is proposed. The equivalence sources on designed equivalence surface are introduced to obtain the nested low rank approximation. At the low to mid frequency, thanks to the nested low rank approximation, the computation complexity of the proposed...
A marching-on-in-degree (MOD) solution of the time-domain combined field integral equation (TD-CFIE) with Nystrom scheme is proposed to analyze transient electromagnetic scattering from arbitrarily shaped perfect electrically conducting (PEC) objects. In this scheme, the Lagrange interpolation polynomials and weighted Laguerre polynomials are used to represent the spatial and temporal basis functions,...
A nested complex source beam (NCSB) method based on the method of moment (MoM) solution is proposed for electromagnetic scattering analysis. In the finest level, the far field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed evenly on the equivalent surface for every group. Furthermore, the far-field coupling of CSBs in the son level group also...
A marching-on-in-time (MOT) based non-conformal time domain volume surface integral equation (TD-VSIE) method is proposed to analyze transient electromagnetic scattering from the composite object comprising perfect electrically conducting (PEC) bodies and inhomogeneous dielectric materials. Half RWG and SWG functions are chosen for the trail and test spatial functions, and triangular basis functions...
We introduce a kernel-independent wideband nested equivalent source approximation method. The nested equivalent source approximation (NESA), proposed by these authors to solve low frequency problems with linear complexity, is extended here to electrically large multiscale structures. The low frequency algorithm is directly employed at the bottom levels of an Octree clustering; in the high frequency...
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...
An efficient method for analysis of the ultra-wide band (UWB) antenna is proposed, the UWB microstrip antennas are analyzed by the mixed potential integral equation (MPIE). The produced dense impedance matrix is partitioned and compressed hierarchically by the multilevel UV method. And the linear systems are solved by the generalized minimal residual method (GMRES) iterative solver, the required matrix-vector...
In this paper, the matching-on-in-order time-domain volume-surface integral equation (MOO TD-VSIE) method is utilized to analyze electromagnetic scattering from objects composed of both conductor and dielectric material. SWG and RWG basis functions are used as the spatial basis functions in volume and surface discretization respectively. Different orders of weighted Laguerre polynomials are used as...
In this paper, interpolatory vector basis functions for a new combined-field surface integral equation (JMCFIE) solved with the method of moments has been presented. This method applied to solve complex electromagnetic scattering problems, like perfect electric conductors, homogeneous dielectric objects, and conductor-dielectric combined structure. New combined-field surface integral equation (JMCFIE)...
In this paper, a novel solution to marching-on-in-order (MOO) time-domain integral equations (TDIE) are introduced using order-independent temporal (OIT) basis functions to analyze transient electromagnetic scattering from perfect electrically conducting (PEC) structures. The OIT basis function is based on the Laguerre polynomials and generated via a singular value decomposition (SVD). It can considerably...
A numerical scheme of computing the reflection coefficient and transmission coefficient of the finite and arbitraried shaped frequency selective surfaces (FSS) is proposed. The volume-surface integral equation (VSIE) sovler in conjunction with the parallel multilevel fast multipole method (MLFMM) is applied to calculate the transmission and reflection coefficient of two typical finite size frequency...
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...
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...
A numerically efficient technique for the evaluation of transmission coefficients of the finite planar Frequency - Selective Surfaces (FSSs) embedded in stratified medium is presented in this letter. The numerical analysis involves the solution of a mixed potential integral equation (MPIE) with the layered media Green's function. The layered media Green's function is derived by using discrete complex...
In this paper, the UV method is utilized to reduce both the memory requirement and computational complexity in time-domain combined field integral equation (TD-CFIE) method to analyze scattering from arbitrarily shaped conducting structures. The UV method takes advantage of the rank-deficiency feature and it is kernel-independent. Different orders of weighted Laguerre polynomials are used as temporal...
In this paper, a new method called fast directional multilevel algorithm is preconditioned by an efficient Calderon multiplicative preconditioner (CMP) for three-dimensional (3-D) electromagnetic problems. The new algorithm does not require the implementation of multipole expansions of the Green's function but based only on kernel evaluations. Combined with the Caldron identities of the CMP, the new...
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