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Two-dimensional vacuum Crank-Nicolson complete matching layer implementation algorithm based on auxiliary differential equation

A technology of perfect matching layer and differential equation, which is applied in the field of two-dimensional vacuum Crank-Nicolson perfect matching layer realization algorithm, which can solve the problems of increased numerical dispersion, large algorithm error, and unsatisfactory performance, etc.

Inactive Publication Date: 2016-07-13
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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  • Two-dimensional vacuum Crank-Nicolson complete matching layer implementation algorithm based on auxiliary differential equation
  • Two-dimensional vacuum Crank-Nicolson complete matching layer implementation algorithm based on auxiliary differential equation
  • Two-dimensional vacuum Crank-Nicolson complete matching layer implementation algorithm based on auxiliary differential equation

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Embodiment Construction

[0020] The gist of the present invention is to propose a two-dimensional vacuum Crank-Nicolson complete matching layer realization algorithm based on auxiliary differential equations, and use the Douglas-Gunn solution idea to greatly improve the electromagnetic field calculation speed.

[0021] The embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0022] figure 1 It is a flowchart of the present invention, and the specific implementation steps are as follows:

[0023] 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 propagation behavior of TM waves in vacuum can be described as

[0024] - jωH x = c 0 · S ...

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Abstract

The invention relates to a two-dimensional vacuum Crank-Nicolson complete matching layer implementation algorithm based on an auxiliary differential equation and belongs to the technical field of numerical simulation.The method aims at reducing a vacuum FDTD computational domain and simulating limited memory space of a computer into infinite space.The implementation algorithm is technically characterized in that in the process that a two-dimensional modified Maxwell equation with plural stretching coordinate variables is converted into the time domain finite difference from the frequency domain, a Douglas-Gunn (DG) algorithm is utilized, an iteration equation with coefficients being block tridiagonal matrixes is approximately decomposed into two iteration equations with coefficients being tridiagonal matrixes, wherein the two iteration equations can be efficiently solved, and computational efficiency is obviously improved.The implementation algorithm has the advantages of achieving unconditional stability, increasing the electromagnetic field computational speed and saving memory.

Description

technical field [0001] The invention relates to the technical field of numerical simulation, in particular to a two-dimensional vacuum Crank-Nicolson complete matching layer realization algorithm based on auxiliary differential equations. 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: the time step and spac...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 李建雄陈明省刘鹏雪蒋昊林闫必行
Owner TIANJIN POLYTECHNIC UNIV
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