CN111191392B - Rapid method for calculating electromagnetic scattering problem of electrically large target - Google Patents

Rapid method for calculating electromagnetic scattering problem of electrically large target Download PDF

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CN111191392B
CN111191392B CN201911304102.1A CN201911304102A CN111191392B CN 111191392 B CN111191392 B CN 111191392B CN 201911304102 A CN201911304102 A CN 201911304102A CN 111191392 B CN111191392 B CN 111191392B
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章幻
盛亦军
陈如山
张天成
李兆龙
王贵
叶晓东
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Nanjing University of Science and Technology
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Abstract

The invention discloses a rapid method for calculating electromagnetic scattering problem of an electric large target, which uses a discontinuous Galerkin time domain finite element method based on an electric field wave equation as a basic algorithm and uses an anisotropic perfect matching layer (UPML) as an absorption boundary, so that the limitation of the original algorithm that an impedance matching condition is used as the absorption boundary is changed, the electromagnetic wave absorption performance is improved, the calculation airspace is greatly reduced, and the calculation efficiency is improved. Meanwhile, compared with the traditional discontinuous Galerkin time domain finite element method based on the first-order Maxwell equation, the novel algorithm adopts the internal punishment discontinuous Galerkin technology to realize independent solution of the electric field, so that the unknown quantity is reduced by more than 50%.

Description

Rapid method for calculating electromagnetic scattering problem of electrically large target
Technical Field
The invention belongs to the technical field of electromagnetic simulation, in particular to a discontinuous Galerkin time domain finite element algorithm numerical calculation method, which is a high-efficiency algorithm for electromagnetic scattering analysis in an electric large size.
Background
The problem of electrically large-size scattering occurs in a plurality of practical electronic engineering fields, such as electromagnetic interference, electromagnetic compatibility and the like of complex systems. The traditional electric large-size target scattering problem calculation is to use a first order Maxwell equation based on a UPML boundary as a control equation, solve by using a discontinuous Galerkin technique, and additionally introduce a secondary working variable solution. The invention adopts a second-order vector electric field wave equation based on a UPML boundary as a control equation, changes the limitation of taking an impedance matching condition as an absorption boundary in the original algorithm, adopts an internal punishment discontinuous Galerkin method to solve, reserves the natural parallelism of the discontinuous Galerkin finite element method, reduces the simulation area, reduces the unknown quantity by half, reduces the occupied memory, and greatly shortens the system simulation time, thereby having significance in researching the rapid method for calculating the electromagnetic scattering problem of the electric large target.
Disclosure of Invention
The invention aims to provide a rapid method for calculating electromagnetic scattering problems of an electrically large target.
The technical solution for realizing the purpose of the invention is as follows: a rapid method for calculating electromagnetic scattering problem of electrically large target comprises the following steps:
firstly, establishing an electromagnetic simulation model containing a UPML absorption layer, and dispersing the model by using tetrahedral units to obtain structural information of the model;
and secondly, establishing a discontinuous Galerkin time domain electric field iterative formula containing a UPML absorption layer, and applying structural information of an electromagnetic simulation model to the formula to form an iterative solution which only contains an electric field unknown quantity and has an explicit solving format.
Thirdly, performing iterative solution for the specified steps of the electric field according to time steps, and calculating a radar scattering section (RCS) of the electromagnetic target according to the near-far field conversion relation.
Compared with the prior art, the invention has the remarkable advantages that: (1) Memory consumption can be reduced in the calculation of the electric large object RCS. (2) The time required for calculation can be reduced in the calculation of the electric large object RCS. (3) The method is particularly suitable for solving the electromagnetic scattering problem of the electrically large target, and the memory consumption of a computer can be greatly reduced by using the algorithm, so that the calculation time is saved.
Drawings
Fig. 1 is a schematic view of a metal scattering model.
Fig. 2 is a graph showing a comparison of scattering cross-sectional areas.
Detailed Description
The invention is further described below with reference to fig. 1 and 2.
The invention relates to a rapid method for calculating electromagnetic scattering problem of an electrically large target, which comprises the following steps:
firstly, establishing an electromagnetic simulation model containing a UPML absorption layer, and dispersing the model by using tetrahedral units to obtain structural information of the model;
step two, a discontinuous Galerkin time domain electric field iterative formula containing a UPML absorption layer is established, and the method starts from a second-order vector electric field wave equation based on UPML boundary:
Figure GDA0004184550920000021
Figure GDA0004184550920000022
where ε and ε represent the permittivity and permeability of the discrete units, respectively, and E and q represent the electric field strength and the curl of the electric field strength, respectively. Wherein, UPML related parameters:
Figure GDA0004184550920000023
Figure GDA0004184550920000024
ξ＝x,y,z。
the Galerkin test is carried out on the equations (1) and (2), and the Galerkin test is obtained by using the divergence theorem:
Figure GDA0004184550920000025
Figure GDA0004184550920000026
substituting formula (4) into formula (3):
Figure GDA0004184550920000027
two operators are defined:
Figure GDA0004184550920000028
Figure GDA0004184550920000031
introducing penalty flux in the formula (5) area score:
an inner face:
Figure GDA0004184550920000032
PEC：
Figure GDA0004184550920000033
Figure GDA0004184550920000034
Γ I is an inner surface Γ b Is a boundary surface, h f,- Is the radius of the outer ball of the body, h f,+ Is the radius of the adjacent external ball. The method comprises the following steps: />
Figure GDA0004184550920000035
Both sides multiply with S x S y S z The inverse fourier transform yields a time domain solution matrix equation:
Figure GDA0004184550920000036
performing central differential format dispersion on the equation (7) in time to obtain a final discontinuous Galerkin time domain electric field iterative equation containing the UPML absorption layer:
Figure GDA0004184550920000037
e represents the electric field value in the process unit and the adjacent solving unit, e 'is the electric field one-time integral value in the process unit and the adjacent solving unit, and e' is the electric field two-time integral value in the process unit and the adjacent solving unit. T, T q 、P、T p 、S e 、S se 、T 1 、P 1 、S e1 、Ss e1 、T th 、P th 、S eth 、Ss eth Respectively, the matrix formed.
Wherein each matrix block is as follows:
T＝∫∫∫εN i ·N j dV
Figure GDA0004184550920000041
Figure GDA0004184550920000042
Figure GDA0004184550920000043
Figure GDA0004184550920000044
Figure GDA0004184550920000045
Figure GDA0004184550920000046
Figure GDA0004184550920000047
Figure GDA0004184550920000048
/>
Figure GDA0004184550920000049
Figure GDA00041845509200000410
Figure GDA00041845509200000411
Figure GDA00041845509200000412
Figure GDA0004184550920000051
thirdly, performing iterative solution for the specified steps of the electric field according to time steps, and calculating a radar scattering section (RCS) of the electromagnetic target according to the near-far field conversion relation.
In order to verify the correctness and effectiveness of the present invention, the electromagnetic scattering properties of a metal model are analyzed as follows.
Calculating: a metal cube with a side length of 1m×1m×1m is calculated, and the center point of the cube is taken as the origin of coordinates. The center frequency of the modulated Gaussian source is 300MHz, the frequency range is 10MHz to 600MHz, the pulse width correlation quantity is 2.3ns, plane waves are incident along the positive direction of the Z axis, and the X direction of the electric field is polarized. The metal cubes in the model can be modeled by hollowing out according to PEC properties, with ambient air and PML split by 0.05m, c·Δt=0.02 m, where c is the speed of light in vacuum. The 300MHz dual station RCS was observed in comparison with CST simulation results. The problem is solved by two methods, the first method is a traditional discontinuous Galerkin time domain finite element algorithm based on Maxwell, the second method is a second-order vector electric field wave equation internal punishment discontinuous Galerkin time domain finite element algorithm based on UPML boundary, and the accuracy of the method is verified by comparing the two-station RCS calculated by the two methods in FIG. 2. Table 1 shows the comparison of the calculation resources of the method proposed by the patent and the traditional discontinuous Galerkin time domain finite element method, and the table shows that the IPDG-WE-UPML algorithm does not introduce additional secondary working variable solution because the control equation is a second-order vector electric field wave equation, the unknown quantity is saved by more than half, the memory consumption is reduced by 26%, and the iteration time is reduced by 51.6%.
TABLE 1 comparison of computing resources
Unknown quantity Memory Iteration time (64 processes)
DGTD-ME-UPML 33073408 390GB 4526.06s
IPDG-WE-UPML 16525888 288GB 2188.47s

Claims (1)

1. A rapid method for calculating electromagnetic scattering problems of electrically large objects, comprising the steps of:
firstly, establishing an electromagnetic simulation model containing a UPML absorption layer, and dispersing the model by using tetrahedral units to obtain structural information of the model;
secondly, establishing a discontinuous Galerkin time domain electric field iterative formula containing a UPML absorption layer, and applying structural information of an electromagnetic simulation model to the formula to form an iterative solution which only contains an electric field unknown quantity and has an explicit solving format;
thirdly, performing iterative solution of a specified step number on the electric field according to time steps, and calculating a radar scattering cross section RCS of the electromagnetic target according to a near-far field conversion relation; in the second step, a discontinuous Galerkin time domain electric field iterative formula containing a UPML absorption layer is as follows:
(T e +0.5ΔtT q )e n+1 ＝(2T e -Δt 2 (P+T p +S e +S se ))e n +(0.5ΔtT q e n-1 -T e e n-1 )-Δt 2 (T 1 +P 1 +S e1 +Ss e1 )e' n -Δt 2 (T th +P th +S eth +Ss eth )e” n
wherein:
T＝∫∫∫εN i ·N j dV
Figure FDA0004184550910000011
Figure FDA0004184550910000012
Figure FDA0004184550910000013
Figure FDA0004184550910000014
Figure FDA0004184550910000015
Figure FDA0004184550910000016
Figure FDA0004184550910000017
Figure FDA0004184550910000018
Figure FDA0004184550910000021
Figure FDA0004184550910000022
Figure FDA0004184550910000023
/>
Figure FDA0004184550910000024
Figure FDA0004184550910000025
wherein epsilon and mu respectively represent the dielectric constant and the magnetic permeability of the discrete units, and sigma x 、σ y 、σ z Is UPML related parameter, N i 、N j Testing and developing basis functions for finite element tetrahedral edges, N j + Representing neighbor test basis functions, τ f Is an internal penalty factor;
Figure FDA0004184550910000026
Γ I is an inner surface Γ b Is a boundary surface, h f,- Is outside the bodyBall catching radius, h f,+ For the external ball-receiving radius of adjacent bodies, u f,- For the magnetic permeability of the body, u f,+ Magnetic permeability for adjacent bodies; e represents the electric field value in the process unit and the adjacent solving unit, e 'is the electric field one-time integral value in the process unit and the adjacent solving unit, and e' is the electric field two-time integral value in the process unit and the adjacent solving unit; t, T q 、P、T p 、S e 、S se 、T 1 、P 1 、S e1 、Ss e1 、T th 、P th 、S eth 、Ss eth Respectively, the matrix formed. />
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CN104636553A (en) * 2015-02-06 2015-05-20 南京理工大学 Time domain spectral element simulation method for microwave ferrite component
CN107688680A (en) * 2016-08-05 2018-02-13 南京理工大学 A kind of efficient time-Domain FEM domain decomposition parallel method

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CN104636553A (en) * 2015-02-06 2015-05-20 南京理工大学 Time domain spectral element simulation method for microwave ferrite component
CN107688680A (en) * 2016-08-05 2018-02-13 南京理工大学 A kind of efficient time-Domain FEM domain decomposition parallel method

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不连续伽辽金时域有限元p自适应电磁分析技术研究;刘阳;《中国优秀硕士学位论文全文数据库》;20190315;第1-52页 *

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