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One-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on auxiliary differential equation

A technology of fully matching layers and left-handed materials, applied in computing, special data processing applications, instruments, etc., can solve problems such as low algorithm calculation accuracy, large algorithm error, and increased numerical dispersion

Inactive Publication Date: 2016-05-04
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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  • One-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on auxiliary differential equation
  • One-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on auxiliary differential equation
  • One-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on auxiliary differential equation

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Embodiment Construction

[0020] The gist of the present invention is to propose a one-dimensional left-handed material Crank-Nicolson complete matching layer realization algorithm based on auxiliary differential equations, use auxiliary equations to reduce calculation amount, optimize calculation process, thereby increasing 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 TEM (transverse electromagnetic) wave is along the left-hand material The z-direction propagation can be described as

[0024] jωϵ ...

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Abstract

The invention relates to a one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on an auxiliary differential equation, and belongs to the technical field of numerical simulation. The method aims at reducing the left-handed material FDTD (Finite-Different Time-Domain) computational domain, and simulating a computer finite memory space into an infinite space. The one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm has the technical characteristics that in a process of converting a plurality of stretched coordinate variables from the frequency domain to the time domain, the second-order differential in the stretched variables is eliminated by an improved auxiliary differential equation method, so that the number of the introduced auxiliary variables is obviously lowered, and a memory is optimized; then, a time domain Maxwell equation is subjected to discretization by a Crank-Nicolson time domain finite differential method; an explicit iteration equation of an electric field is deduced out; and finally, a value of an electromagnetic field component is obtained. The one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm has the advantages that the unconditional stability is realized; the electromagnetic calculation is accelerated; and the memory is saved.

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 an auxiliary differential equation. 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: t...

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/20
Inventor 李建雄陈明省刘鹏雪蒋昊林韩晓迪
Owner TIANJIN POLYTECHNIC UNIV
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