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Unconditionally Stable FDTD Method Based on Orthogonal Functions of Associated Hermite

An orthogonal function and basis function technology, applied in complex mathematical operations and other directions, can solve problems such as unacceptable, long simulation time, and large number of time steps, and achieve the effect of efficient calculation

Inactive Publication Date: 2017-03-22
PLA UNIV OF SCI & TECH
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Problems solved by technology

In order to ensure the stability of the calculation, the value of the time step is also very small, and the number of time steps required is very large, which makes the simulation time of the traditional FDTD method very long or even unacceptable

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  • Unconditionally Stable FDTD Method Based on Orthogonal Functions of Associated Hermite
  • Unconditionally Stable FDTD Method Based on Orthogonal Functions of Associated Hermite
  • Unconditionally Stable FDTD Method Based on Orthogonal Functions of Associated Hermite

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Embodiment Construction

[0053] The specific implementation process of the present invention can be divided into the following steps (such as figure 1 shown).

[0054] ①. According to the needs of practical problems, discrete spatial grids, selected basis function translation and scale factors, produce time-domain AH basis functions.

[0055] ②. The five-diagonal coefficient matrix on the left side of the implicit equation (13) and the non-zero items on the right side are composed of space grid division, medium parameters, initial conditions and excitation sources.

[0056] ③. The coefficient matrix is ​​decomposed by LU, and the magnetic field coefficient in the AH domain is solved by the chasing method.

[0057] ④. Substitute the magnetic field coefficient into equations (10)-(11) to solve the electric field coefficient in the AH domain.

[0058] ⑤. Reconstruction of time domain electromagnetic field results using AH domain coefficients and basis functions.

[0059] The present invention wil...

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Abstract

The invention relates to an unconditional stability finite-different time-domain (FDTD) algorithm. The unconditional stability FDTD algorithm expands a differential-form Maxwell equation set through an Associated Hermite (AH) orthogonal function, eliminates a time variable through the Galerkin principle, obtains a finite-dimension AH domain implicit equation for solution, and finally obtains the electromagnetic field time domain result through AH domain inverse transformation. According to the unconditional stability FDTD algorithm based on the AH orthogonal function, through the conversion from the time domain to the AH domain, the solution number of an unknown quantity is largely reduced, and the calculation efficiency is obviously improved. The whole calculation process has nothing to do with the time variable and is not limited by a traditional FDTD stability condition, and the calculation result is unconditionally stable. Through the characteristics, a new resolution method is provided for the problem of efficiently and rapidly calculating a complex electromagnetic field with a multi-scale characteristic.

Description

technical field [0001] The invention relates to an unconditionally stable electromagnetic field finite difference time domain (FDTD) method. Background technique [0002] With the development of computer technology and the application and promotion of electromagnetic theory, the time-domain method of computational electromagnetics has been greatly developed, and it complements the frequency-domain method. The advantage of the time-domain method is that it can give rich transient information and simulate physical phenomena more intuitively. By directly doing Fourier transform (Fourier) to the time domain information, the frequency domain information of the problem can be obtained. Based on these good properties, time-domain methods have been widely used and deeply researched in communication, radar, electromagnetic protection, electromagnetic compatibility, medical diagnosis and so on. In addition, in some specific fields, such as transient pulse phenomena such as electroma...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/14
Inventor 石立华黄正宇陈彬周颖慧
Owner PLA UNIV OF SCI & TECH
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