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Piecewise linear cyclic convolution-based one-dimensional left-handed material Crank-Nicolson perfectly matched layer realizing algorithm

A technology of complete matching layer and circular convolution, which is applied in the field of one-dimensional left-handed material Crank-Nicolson complete matching layer to realize the algorithm, which can solve the problems of large algorithm error, increased numerical dispersion, and low calculation accuracy of the algorithm.

Inactive Publication Date: 2016-06-01
TIANJIN POLYTECHNIC UNIV
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Problems solved by technology

[0006] Although the ADI-FDTD algorithm and the LOD-FDTD algorithm have overcome the limitation of stability conditions to a certain extent, the calculation accuracy of the algorithm is too low and the performance is not ideal. The reason is that when the time step increases, the numerical value The dispersion increases, which leads to a larger error in the algorithm

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  • Piecewise linear cyclic convolution-based one-dimensional left-handed material Crank-Nicolson perfectly matched layer realizing algorithm
  • Piecewise linear cyclic convolution-based one-dimensional left-handed material Crank-Nicolson perfectly matched layer realizing algorithm
  • Piecewise linear cyclic convolution-based one-dimensional left-handed material Crank-Nicolson perfectly matched layer realizing algorithm

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[0019] The gist of the present invention is to propose a one-dimensional left-handed material Crank-Nicolson complete matching layer realization algorithm based on piecewise linear circular convolution, which uses convolution operation to reduce the calculation amount and optimize the calculation process, thereby increasing the electromagnetic field calculation speed.

[0020] The embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0021] figure 1 It is a flowchart of the present invention, and the specific implementation steps are as follows:

[0022] Step 1: Modify Maxwell’s equations in the frequency domain to Maxwell’s equations with a stretched coordinate operator, and express the modified Maxwell’s equations in the frequency domain in a Cartesian coordinate system. The TEM (transverse electromagnetic) wave is along the left-hand material The z-direction propagation can be described as

[0023] ...

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Abstract

The invention relates to a piecewise linear cyclic convolution-based one-dimensional left-handed material Crank-Nicolson perfectly matched layer realizing algorithm, belongs to the technical field of numerical simulation, and aims at shortening the left-handed material FDTD computational domain and simulating the finite memory spaces of computers into infinite spaces. The algorithm is technically characterized by comprising the following steps: in the process of transforming plural stretching coordinate variables from a frequency domain to a time domain, eliminating the second-order differential in the stretching variables by utilizing a piecewise linear cyclic convolution method so as to remarkably decrease the number of imported auxiliary variables and optimize the memory; dispersing a time domain Maxwell equation by utilizing a Crank-Nicolson time domain finite difference method so as to derive an explicit iterative equation of an electric field; and finally solving the value of an electromagnetic field component. The algorithm has the advantages of providing unconditional stability, improving the electromagnetic field calculation speed and saving the memory.

Description

technical field [0001] The invention relates to the technical field of numerical simulation, in particular to a realization algorithm of a one-dimensional left-handed material Crank-Nicolson complete matching layer based on piecewise linear circular convolution. Background technique [0002] Finite Difference Time Domain (FDTD), as a computational electromagnetic method, is widely used in various time-domain electromagnetic simulation calculations, such as antennas, radio frequency circuits, optical devices and semiconductors. FDTD has the characteristics of wide applicability, suitable for parallel computing, and universality of computing programs. [0003] However, with the deepening of scientific research and the needs of more and more extensive applications, the defect that the algorithm itself is limited by the numerical stability conditions of Courant Friedrichs Lewy (CFL) becomes more and more obvious. The algorithm itself is limited by numerical stability conditions...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 李建雄陈明省闫必行蒋昊林宋战伟
Owner TIANJIN POLYTECHNIC UNIV
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