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Three-dimensional alternate iteration unconditional stability FDTD algorithm

An alternate iterative, three-dimensional technology, applied in the field of FDTD algorithm, can solve the problems of inappropriate FDTD algorithm and memory resources affecting computing efficiency, and achieve the effect of reducing computing time, improving computing efficiency and high precision.

Pending Publication Date: 2020-06-09
ARMY ENG UNIV OF PLA
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Problems solved by technology

[0005] Aiming at the deficiencies of the prior art, the object of the present invention is to provide a three-dimensional alternating iterative unconditional stable FDTD algorithm to solve the problem that the FDTD algorithm in the prior art is not suitable for calculations with fine grids due to the limitation of CFL stability conditions, A technical problem that affects computing efficiency due to the large amount of memory resources required

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  • Three-dimensional alternate iteration unconditional stability FDTD algorithm
  • Three-dimensional alternate iteration unconditional stability FDTD algorithm
  • Three-dimensional alternate iteration unconditional stability FDTD algorithm

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Embodiment Construction

[0052] The specific embodiment of the present invention provides a three-dimensional alternating iterative unconditional stable FDTD algorithm, comprising the following steps:

[0053] Step 1, use the Laguerre orthogonal basis to expand the three-dimensional Maxwell equations to the Laguerre domain, and use the method of constructing variables to write the six Maxwell equations in the Laguerre domain into a matrix equation.

[0054] In a lossless, homogeneous, isotropic medium, the Maxwell equations in the three-dimensional time domain are:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] In the formula, ε is the permittivity, μ is the magnetic permeability, E x ,E y ,E z are the components of the electric field along the x, y, and z directions, H x 、H y 、H z is the component of the magnetic field along the three directions of x, y, and z, J x 、J y 、J z are the components of the current source along the x, y, and z directions.

[0062] ...

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Abstract

The invention discloses a three-dimensional alternate iteration unconditional stability FDTD algorithm in the technical field of FDTD algorithms. The method aims to solve the technical problems that an FDTD algorithm in the prior art is not suitable for calculation with fine grids due to limitation of CFL stability conditions, and calculation efficiency is affected due to the fact that a large number of memory resources need to be occupied. According to the algorithm, an ADI algorithm is combined with an idea of utilizing Laguerre-based expansion; writing the Maxwell equation set of the Laguerre domain into a matrix form; through a method of actively adding error terms, calculation of electric and magnetic field components is decoupled, unknown field quantities in the constructed linear equation set are all located on the same straight line, the dimensionality of the linear equation set is geometrically reduced in series, the calculation efficiency is greatly improved, and memory consumption is reduced. And finally, the size of an error term is enabled to tend to zero through an alternating direction iteration method to obtain an accurate solution of the electromagnetic field component.

Description

technical field [0001] The invention relates to a three-dimensional alternating iterative unconditional stable FDTD algorithm, which belongs to the technical field of FDTD algorithms. Background technique [0002] Finite-Difference Time-Domain (FDTD) is an intuitive time-domain electromagnetic field calculation method, which has been widely used in numerical simulations in fields such as electromagnetic compatibility, antenna characteristics, integrated circuits, and absorbing materials. . [0003] The traditional FDTD algorithm was proposed by K.S.Yee in 1966. It adopts the method of alternate grid calculation of electric and magnetic field components, and skillfully describes the propagation of Maxwell equations in space. However, the traditional FDTD algorithm must meet the requirements of Courant-Friedrich-Lewy (CFL) stability conditions. When the value of the space step is small, the time step must be correspondingly small, which greatly increases the numerical simulat...

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Application Information

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IPC IPC(8): G06F30/23G06F111/10
Inventor 张波刘亚文段力群代晓青熊自明卢浩潘明司卿李治中马超岳松林蒋海明徐畅
Owner ARMY ENG UNIV OF PLA
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