A Wavelet-Enhanced PWTD-Accelerated Time-Domain Integral Equation Solver for Analysis of Transient Scattering From Electrically Large Conducting Objects

Abstract

A wavelet-enhanced plane-wave time-domain (PWTD) algorithm for efficiently and accurately solving time-domain surface integral equations (TD-SIEs) on electrically large conducting objects is presented. The proposed scheme reduces the memory requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD-accelerated TD-SIE solver, when applied to the analysis of transient scattering from smooth quasi-planar objects with near-normal incident pulses, scale nearly as (log) s s O N N and 1.5 () s O N , respectively. Here, s N denotes the number of spatial unknowns. The efficiency and accuracy of the proposed scheme are demonstrated through its applications to the analysis of transient scattering from a 185 wavelength-long NASA almond and a 123-wavelength long Airbus-A320 model. Index Terms-Fast algorithms, marching-on-in-time (MOT), wavelet, local cosine basis (LCB), plane-wave time-domain algorithm (PWTD), time-domain surface integral equation (TD-SIE), transient scattering, very large-scale problems, complexity analysis.

An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

“…The memory required to store the matrices used in the computation of f e/h during time marching [i.e., matrices arising from the discretization of ( 10)] scales with O(N 2 S K 2 ). that the computational cost and the memory requirement of TDBI can be reduced using the FFT-based schemes [26], [27] or the plane wave time domain (PWTD) algorithm [28], [29]. For example, if the multilevel PWTD is used for accelerating TDBI, its computational cost and memory requirements would reduce to O(NBINSKlog 2 [NSK]) and O([NSK] 1.5 NG), respectively.…”

Integral equation modelling of unmanned aerial vehicle radar scattering characteristics in VHF to S frequency bands

“…Therefore, for mathematical modelling of their radar scattering, it is reasonable to use methods based on the boundary IE. Note that IEs of EM scattering are usually solved using method of moments (MoM) [3,8,14,16,[19][20][21][22][23][24][25][26][27][28][29][30][31][32], which belongs to the class of projection methods.…”

“…However, their application requires a large amount of computer memory and careful selection of the basis and test functions, the form of which significantly depends on the complexity of the object's shape. Recently, the method of boundary IEs has also been used to calculate the scattering characteristics of electrically large objects [28][29][30][31][32]. At the same time, the use of AHFMs [13][14][15][16][17][18], devoid of the complexity associated with solving IEs, is preferable in the case of large scatterers.…”

Analytical Improvement on the Electromagnetic Scattering From Deformed Spherical Conducting Objects

“…N ONSPHERICAL objects are of great importance and taken into consideration in many areas of study, e.g., elasticity [1], fluid dynamics [2], neuroscience [3], astrophysics [4], and acoustics [5]- [7], including electromagnetic scattering [8], [9]. The interest in the scattering properties of conducting objects for real-life problems [10]- [13] never decreases for researchers in many different fields [14]- [16]. The studies on PEC bodies maintain their importance because they either find direct applications [17], [18] or allow one to examine and understand more complex materials, such as dielectrics and others [7], [19]- [22].…”