Matrix decomposition and novel singular value decomposition combined method for complex layered medium structures

Abstract

The invention discloses a method capable of implementing quick electromagnetic simulation of complex layered medium structures, wherein the method is used for efficient simulation of the complex layered medium structures on basis of combination of matrix decomposition and novel singular value decomposition. The method includes: using triangular meshes to precisely simulate a model, and subjecting far-field groups to low-order compact according to the principle of fine low-order characteristics of far-field groups in tree structures to obtain a sparse matrix representation form. The method which is a pure mathematic analytical method is independent of an expansion form of the green function, internal memory and computing time are reduced by the novel singular value compact method based on MDA (matrix decomposition algorithm), the computing complexity can be lowered to O (NlogN), and memory consumption can be lowered to O (NlogN). The method is especially suitable for electromagnetic simulation analysis of complex layered medium structures and can be also used for providing effective means for layered medium structure simulation with the complex green function.

Description

a technical field [0001] The invention relates to an electromagnetic simulation technology, in particular to a new singular value decomposition method based on matrix decomposition, which can provide an important analysis approach for the analysis of electromagnetic characteristics of complex layered medium structures. 2. Background technology [0002] With the development of science and technology, the working frequency of the existing layered media structure is continuously increasing rapidly, which can be doubled in a few years, but then, the distortion caused by the layered media structure due to dispersion, discontinuity and packaging Problems such as time delay and crosstalk noise due to coupling also become very serious. The traditional quasi-static design method can no longer meet the design requirements, but the accurate electromagnetic field full-wave simulation analysis method can better solve these problems. At present, complex layers such as microwave integrated...

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Problems solved by technology

[0002] With the development of science and technology, the working frequency of the existing layered media structure is continuously increasing rapidly, which can be doubled in a few years, but then, the distortion caused by the layered media structure due to dispersion, discontinuity and packaging Problems such as time delay and crosstalk noise due to coupling also become very serious

The traditional quasi-static design method can no longer meet the design requirements, but the accurate electromagnetic field full-wave simulation analysis method can better solve these problems. At present, complex layers such as microwave integrated circuits, microstrip antennas, and microstrip scatterers The full-wave analysis of the medium structure can be divided into two categories: one is the analysis method based on the differential equation model, and the other is the analysis method based on the integral equation model

The analysis method of differential equation model is mainly based on volume division, therefore, this method will lead to very large unknowns and require a lot of computing resources, so it is difficult to apply

Based on the analysis method of the integral equation model, a variety of integral methods are disclosed in the existing literature for the analysis of complex layered media structures, such as W.C.Chew, J.M.Jin, E.Michielssen, and J.Song, Fast efficient algorithms in computational electromagnetics , Boston, MA: Artech House, 2001 disclosed a multi-layer fast multipole algorithm (MLFMA), which mainly uses the addition theorem to expand the Green's function, and its memory and computational complexity are very low, but this method Excessive reliance on the expression of Green's function has led to great limitations in the application of this method to problems with complex layered media structures

Literature Michielssen E. and Boag A, "A multilevel matrix decomposition algorithm for analyzing scattering from large structures," IEEE Trans.Antennas Propag, Vol.44, No.8, pp.1086-1093, Aug.1996. and literature Fang- Shun Deng; Si-Yuan He; Hai-Tao Chen; Wei-Dong Hu; Wen-Xian Yu; Guo-Qiang Zhu, "Numerical Simulation of Vector Wave Scattering From the Target and Rough Surface Composite Model With 3-D Multilevel UV Method , "IEEE Trans.Antennas Propagat., Vol.AP-58, pp.1625-16348, 2010. A purely mathematical method based on matrix compression is proposed. These methods have nothing to do with the expansion of the Green's function. They are multi-layer fast multipole The computational complexity and storage capacity of the sub-algorithm are significantly reduced, but the memory and calculation time are still relatively large, so the problem is still not fundamentally solved

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