CN113705044B - Finite element symmetric boundary implementation method for electromagnetic symmetric antenna - Google Patents

Finite element symmetric boundary implementation method for electromagnetic symmetric antenna Download PDF

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CN113705044B
CN113705044B CN202110958666.8A CN202110958666A CN113705044B CN 113705044 B CN113705044 B CN 113705044B CN 202110958666 A CN202110958666 A CN 202110958666A CN 113705044 B CN113705044 B CN 113705044B
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赵勋旺
王泽松
左胜
张玉
林中朝
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Abstract

The invention provides a finite element symmetric boundary implementation method for an electromagnetic symmetric antenna, aiming at simplifying the modeling process of the electromagnetic symmetric antenna and reducing the consumption of computing resources. The method comprises the following implementation steps: (1) subdividing an electromagnetic symmetrical antenna; (2) setting symmetric boundary attributes; (3) generating a tetrahedral mesh of the calculation region; (4) solving the electromagnetic field of each grid unit in the calculation area; (5) calculating the electromagnetic field of each mirror image area; (6) and calculating the overall electromagnetic property of the electromagnetic symmetric antenna. The finite element symmetric boundary method is applied to the electromagnetic characteristic solving of the electromagnetic symmetric antenna, so that the modeling process of the electromagnetic symmetric antenna is simplified, the calculation memory is reduced, and the solving time is shortened.

Description

Finite element symmetric boundary implementation method for electromagnetic symmetric antenna
Technical Field
The invention belongs to the technical field of electromagnetic simulation, and further relates to a finite element symmetric boundary implementation method for an electromagnetic symmetric antenna in the technical field of electromagnetic radiation. The invention solves the electromagnetic parameters of the antenna with a symmetrical structure by utilizing the boundary conditions of the electromagnetic symmetrical antenna and analyzes the electromagnetic radiation characteristic of the electromagnetic symmetrical antenna.
Background
The finite element algorithm is an electromagnetic simulation method for calculating the electromagnetic radiation characteristic of the antenna, obtains the electromagnetic field distribution of the antenna by solving Maxwell differential equations, and can analyze the electromagnetic radiation characteristic of the antenna by utilizing the obtained electric field. Finite element algorithms require boundary condition constraints to obtain the determined electric field distribution when solving Maxwell differential equations, and the boundary conditions comprise radiation boundary conditions and impedance boundary conditions. The antennas with symmetric structures, such as array antennas and horn antennas, have wide application in the field of electromagnetic field in the microwave technology, and as the application requirements continue to increase, the antennas with symmetric structures have the characteristic of larger and larger electrical size, so that the calculation resources required for solving the electromagnetic parameters of the antennas with symmetric structures are larger and larger, which brings great difficulty to the numerical analysis of the electromagnetic properties of the antennas with symmetric structures.
The patent document "waveguide port excitation method for electromagnetic finite element solution" (application No. 201911174059.1, application publication No. CN 110866361 a) applied by the research and design center of naval ships of china discloses an electromagnetic finite element solution method for waveguide port excitation. The method comprises the steps of 1) establishing a target model to be solved; 2): solving a huygens source on an excitation end face of the waveguide port; 3): and (3) substituting the Huygens source obtained in the step (2) into a three-dimensional finite element solving formula, and solving the electromagnetic field distribution of the electromagnetic finite element calculation area and the far-field radiation excited by the waveguide port. The method can effectively avoid disturbance to a calculation region and the placement position of the waveguide port is not limited. However, the method still has the disadvantages that the method does not consider the symmetry of the port, and the calculation and storage resources required for carrying out the electromagnetic characteristic analysis of the port are large. Therefore, when the computing resources are limited, the method is only suitable for solving the electromagnetic characteristics of the antenna with a smaller scale.
The patent document "a rapid electromagnetic field analysis method and system of OAM perimeter antenna array" applied by Nanjing university of science and engineering "(application No. 202110461169.7, application publication No. CN 113221340A) discloses a rapid electromagnetic field analysis method using axial symmetry. The method comprises the steps of 1) establishing a loop antenna array model; 2) decomposing the annular antenna array into a plurality of small areas, wherein each small area only comprises a target array element to be calculated and other array elements adjacent to the target array element; 3) solving the corresponding target array element in each cell to obtain a spatial electromagnetic field of the array element; 4) and mapping the calculated array element electromagnetic field according to the axial symmetry to obtain an electromagnetic field of another array element symmetrical to the array element, thereby obtaining the space electromagnetic fields of all the array elements. The method can obviously reduce the calculation time and the memory. However, the method still has the defects that the electromagnetic characteristics of the antenna are analyzed by using the axial symmetry characteristics, and the electromagnetic characteristics of the antenna with the plane symmetry structure cannot be solved.
Disclosure of Invention
The invention aims to provide a finite element symmetric boundary implementation method for an electromagnetic symmetric antenna aiming at the defects in the prior art, and the finite element symmetric boundary implementation method is used for solving the problem of high calculation resource consumption when the electromagnetic characteristics of the electromagnetic symmetric antenna are solved.
The technical idea for realizing the purpose of the invention is that only the electromagnetic field of the symmetrical part of the electromagnetic symmetrical antenna is calculated by utilizing the symmetrical boundary conditions of the finite element algorithm, and the electromagnetic field of the symmetrical part of the electromagnetic symmetrical antenna is converted into the overall electromagnetic radiation characteristic of the electromagnetic symmetrical antenna, compared with the prior art, the characteristic is that the calculation scale of the electromagnetic characteristic solving of the electromagnetic symmetrical antenna is at least reduced to 1/2 of the original problem, even 1/8 of the original problem, thereby greatly reducing the unknown quantity of the solved problem, and reducing the memory occupation and the solving time.
The specific steps for realizing the purpose of the invention comprise the following steps:
step 1, subdividing an electromagnetic symmetrical antenna:
subdividing the electromagnetic symmetric antenna by using the symmetric surface of the electromagnetic symmetric antenna to obtain 2 N -areas, N representing the total number of symmetry planes of the electromagnetically symmetric antenna; selecting any one of the areas as a calculation area, and taking each of the rest areas as a mirror image area;
step 2, setting symmetric boundary attributes:
if the direction of an electric field for exciting the electromagnetic symmetrical antenna is vertical to the splitting surface, taking the splitting surface as an ideal electric wall symmetrical boundary; if the magnetic field direction of the excitation electromagnetic symmetric antenna is vertical to the splitting surface, taking the splitting surface as an ideal magnetic wall symmetric boundary;
step 3, generating a tetrahedral mesh of the calculation area;
carrying out tetrahedral mesh dispersion on the calculation region, and marking corresponding symmetric boundary attributes on the mesh unit surface on each subdivision surface;
step 4, solving the electromagnetic field distribution of each grid unit in the calculation area:
generating a solving equation set for solving the electric field distribution of each grid unit by using a finite element electromagnetic solver, setting the electric field of a grid unit surface for calculating and marking the symmetric boundary attribute of the ideal electric wall to be zero to obtain the electric field of each grid unit in a calculation area, and obtaining the magnetic field of each grid unit in the calculation area through the mutual transformation relation of the electromagnetic fields;
step 5, calculating the electromagnetic field of the mirror image area of the electromagnetic symmetric antenna:
(5a) establishing a local coordinate system corresponding to each subdivision surface to obtain the local coordinate of the global coordinate of each grid unit relative to each subdivision surface in the calculation area;
(5b) calculating the electromagnetic field of each mirror image area;
and 6, calculating the overall electromagnetic characteristic of the electromagnetic symmetric antenna.
Compared with the prior art, the invention has the following advantages:
firstly, because only the electromagnetic field of the symmetrical part of the electromagnetic symmetrical antenna is solved, the electromagnetic symmetrical antenna modeling is carried out only by establishing the model of the symmetrical part of the electromagnetic symmetrical antenna, and the problem of complex process of establishing the electromagnetic symmetrical model in the prior art is solved, so that the electromagnetic symmetrical antenna modeling method has the advantage of simple process of establishing the electromagnetic symmetrical model.
Secondly, the invention utilizes the symmetric boundary conditions of the finite element algorithm to convert the electromagnetic field of the symmetric part of the electromagnetic symmetric antenna into the overall electromagnetic radiation characteristic of the electromagnetic symmetric antenna, thereby overcoming the problem of high consumption of computing resources in the prior art and having the advantages of obviously reducing computing memory and reducing solving time.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of 1/4 geometric modeling of the feedhorn according to the present invention followed by symmetrical boundary setting;
FIG. 3 is a schematic diagram of a complete model of the horn antenna of the present invention;
FIG. 4 is a schematic diagram illustrating specific dimensions of 1/4 horn antenna of the present invention;
FIG. 5 is a graph of the electromagnetic characteristics of the 1/4 horn antenna of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The specific steps implemented by the present invention are further described with reference to fig. 1.
Step 1, subdividing the electromagnetic symmetrical antenna.
Subdividing the electromagnetic symmetric antenna by using the symmetric surface of the electromagnetic symmetric antenna to obtain 2 N The number of regions, N, represents the total number of planes of symmetry of the electromagnetically symmetric antenna. Any one of the areas is selected as a calculation area, and each of the rest areas is used as a mirror image area.
The following describes the specific steps of splitting the electromagnetically symmetric antenna with reference to the 1/4 geometric modeling schematic diagram of the feedhorn of the embodiment in fig. 2 and the complete model schematic diagram of the feedhorn of the embodiment in fig. 3.
The region inside the rectangular parallelepiped box in fig. 2 represents the calculation region, the black part inside the rectangular parallelepiped box represents 1/4 in the feedhorn, the face on the rectangular parallelepiped located on the plane xoz represents the ideal electrical wall symmetry plane, and the face on the rectangular parallelepiped located on the plane yoz represents the ideal electrical wall symmetry plane.
The black parts in fig. 3 represent the complete feedhorn. As can be seen from fig. 3, the feedhorn is symmetrical about the xoz planes and the yoz plane respectively, so that the feedhorn can be split by the xoz planes and the yoz plane when the overall electromagnetic characteristic analysis of the feedhorn is performed, and finally, the part of the feedhorn in the first quadrant is the calculation area.
And 2, setting a symmetric boundary attribute.
If the direction of the electric field of the excitation electromagnetic symmetrical antenna is vertical to the splitting surface, taking the splitting surface as an ideal electric wall symmetrical boundary; if the magnetic field direction for exciting the electromagnetically symmetric antenna is perpendicular to the splitting plane, the splitting plane is taken as an ideal magnetic wall symmetry boundary.
And 3, generating a tetrahedral mesh of the calculation region.
And carrying out tetrahedral mesh dispersion on the calculation region, and marking corresponding symmetric boundary attributes on the mesh unit surface on each split surface.
And 4, solving the electromagnetic field of each grid unit in the calculation area.
And generating a solving equation set for solving the electric field distribution of each grid unit by using a finite element electromagnetic solver, setting the electric field of the grid unit surface for calculating and marking the symmetric boundary attribute of the ideal electric wall to be zero to obtain the electric field of each grid unit in the calculating area, and obtaining the magnetic field of each grid unit in the calculating area through the mutual transformation relation of the electromagnetic fields.
The following illustrates a specific procedure for solving the electric field of each grid cell in the calculation area.
And generating a solving equation set for solving the electric field of each grid unit by using a finite element electromagnetic solver as follows: the system of equations contains three matrices, where [ K ] represents the finite element system matrix, [ E ] represents the matrix composed of the electric fields of the elements to be solved, [ b ] represents the matrix composed of the excitations, and n represents the total number of unknowns determined by the computation of the area tetrahedral mesh.
Figure BDA0003221311820000051
When solving the equation system, the electric field of the grid cell surface for marking the symmetric boundary attribute of the ideal electric wall is subjected to the processing of imposing the symmetric boundary condition of the ideal electric wall:
e in the equation set is solved correspondingly for the electric field of the grid cell surface if the symmetric boundary attribute of the ideal electric wall is marked i Then let K ij ＝0,j≠i，K ji ＝0,j≠i，K ii ＝1，b i 0, wherein, K ij Is represented by [ K]And (3) obtaining the modified solving equation set by the elements of the ith row and the jth column in the matrix as follows:
Figure BDA0003221311820000052
and calculating the modified solution equation set to obtain the electric field E of each grid unit in the calculation area.
And 5, calculating the electromagnetic field of the mirror image area of the electromagnetic symmetric antenna.
And establishing a local coordinate system corresponding to each subdivision surface to obtain the local coordinate of the global coordinate of each grid unit relative to each subdivision surface in the calculation area.
The electromagnetic field of each mirror region is calculated according to the following procedure.
First, the electric field E of each grid unit in the calculation area is decomposed into a horizontal polarization field E parallel to the splitting plane || And a vertical polarization field E perpendicular to the splitting plane ⊥ . If the splitting plane is an ideal magnetic wall symmetry plane, the horizontal polarization field at the symmetrical position of each grid cell with respect to the splitting plane is-E || And the vertical polarization field is E ⊥ . If the splitting plane is an ideal plane of electrical wall symmetry, the horizontal polarization field about the symmetric position of the splitting plane is E || With a vertical polarization field of-E ⊥ . Decomposing the magnetic field H of each grid cell in the calculation region into a horizontally polarized magnetic field H parallel to the splitting plane || And a vertical polarization magnetic field H perpendicular to the splitting plane ⊥ If the splitting plane is an ideal magnetic wall symmetry plane, the horizontal polarization field at the symmetrical position of each grid cell with respect to the splitting plane is H || The vertical polarization field is-H ⊥ (ii) a If the splitting plane is an ideal plane of electrical wall symmetry, the horizontal polarization field at the symmetric position about the splitting plane is-H || Vertical polarization field of H ⊥ 。
And secondly, forming an electric field E 'at the position by using the horizontal polarization electric field and the vertical polarization electric field at the symmetrical positions of the grid units relative to the splitting plane, forming a magnetic field H' at the position by using the horizontal polarization magnetic field and the vertical polarization magnetic field at the symmetrical positions of the grid units relative to the splitting plane, converting the local coordinates of each mirror image area into global coordinates, and obtaining a complete electromagnetic field of the electromagnetic symmetrical antenna.
And 6, calculating the overall electromagnetic characteristic of the electromagnetic symmetric antenna. And converting the electromagnetic field of the electromagnetic symmetrical antenna into the electromagnetic characteristic of the electromagnetic symmetrical antenna by utilizing an electromagnetic characteristic post-processing calculator.
The effect of the present invention is further explained by combining the simulation experiment as follows:
1. simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the cloud platform virtual machine comprises 1 processor of 16-core Intel (R) Xeon (R) Gold 6240CPU, a main frequency of 2.60GHz and a memory of 32 GB.
The software platform of the simulation experiment of the invention is as follows: windows10 operating system and Fortran 90.
2. Simulation content and result analysis thereof:
the simulation experiment of the present invention was conducted by using the method of the present invention to calculate 1/4 horn antenna shown in fig. 2, which represents the electromagnetic properties of the complete horn antenna shown in fig. 3.
The 1/4 feedhorn configuration is further described in conjunction with the 1/4 feedhorn detailed dimension schematic of fig. 4. The dimension AB of the tail of the 1/4 horn antenna is 11.93mm, BE is 5.66mm, AC is 2mm, the dimension CD of the middle of the 1/4 horn antenna is 21.99mm, FG is 41.05mm, the dimension HI of the 1/4 horn antenna mouth is 16mm, IJ is 27.6mm, and the thickness KJ of the 1/4 horn antenna is 0.6 mm. The working frequency of the horn antenna is 8.43GHz, and the electric field exciting the horn antenna is along the y-axis direction.
The simulation experiment of the present invention selects the electromagnetic characteristic result for explaining the analysis as the gain, and the calculation of the electromagnetic characteristic of the feedhorn will result in the gain curve of the feedhorn on the xoz plane shown in fig. 3, as shown in fig. 5.
The abscissa in fig. 5 represents the angle θ in the counterclockwise direction from the z-axis in degrees, and the ordinate represents the gain of the horn antenna in the xoz plane in dBi.
The results of the electromagnetic characteristic calculation for the 1/4 feedhorn are further described below in conjunction with the 1/4 feedhorn electromagnetic characteristic calculation results diagram of fig. 5.
Fig. 5 shows the calculation results of the electromagnetic characteristics of the horn antenna shown in fig. 3, which are calculated by the method for calculating the overall electromagnetic characteristics of the electromagnetically symmetric antenna using the finite element symmetric boundaries and the method for calculating the overall electromagnetic characteristics of the electromagnetically symmetric antenna without using the finite element symmetric boundaries according to the present invention. The solid line in fig. 5 represents the calculation result obtained by the method for calculating the electromagnetic characteristics of the electromagnetic symmetric antenna using the finite element symmetric boundary according to the present invention, and the dotted line represents the calculation result obtained by the method for calculating the electromagnetic characteristics of the electromagnetic symmetric antenna without using the finite element symmetric boundary. As can be seen from FIG. 5, the calculation results of the method of the present invention are well matched with those of the prior art method, and the calculation accuracy of the present invention is verified.
Table 1 is a comparison table of memory and calculation time used in the method for calculating the overall electromagnetic property of the electromagnetic symmetric antenna using the finite element symmetric boundary according to the present invention and the method for calculating the overall electromagnetic property of the electromagnetic symmetric antenna without using the finite element symmetric boundary according to the present invention.
TABLE 1
Figure BDA0003221311820000071
As can be seen from the data in Table 1, the present invention greatly reduces the memory usage and computation time in solving the electromagnetic characteristics of the electromagnetically symmetric antenna.
The finite element symmetric boundary implementation method for the electromagnetic symmetric antenna converts the electromagnetic field of the symmetric part of the electromagnetic symmetric antenna into the overall electromagnetic radiation characteristic of the electromagnetic symmetric antenna, overcomes the problem of high consumption of computing resources in the prior art, and has the advantages of remarkably reducing computing memory and reducing solving time.
The foregoing description of the embodiments is provided to enable one of ordinary skill in the art to understand and apply the techniques herein, and it is to be understood that various modifications may be readily made to the embodiments, and that the general principles defined herein may be applied to other embodiments without the use of inventive faculty. Therefore, the present disclosure is not limited to the above embodiments, and those skilled in the art should make improvements and modifications within the scope of the present disclosure.

Claims (3)

1. A finite element symmetric boundary implementation method for an electromagnetic symmetric antenna is characterized in that a finite element algorithm is used for calculating electromagnetic field distribution of a symmetric part of the electromagnetic symmetric antenna, and symmetric boundary conditions are used for converting the electromagnetic field distribution of the symmetric part into overall electromagnetic characteristics of the electromagnetic symmetric antenna; the method comprises the following steps:
step 1, subdividing an electromagnetic symmetric antenna:
subdividing the electromagnetic symmetric antenna by using the symmetric surface of the electromagnetic symmetric antenna to obtain 2 N -areas, N representing the total number of symmetry planes of the electromagnetically symmetric antenna; selecting any one of the areas as a calculation area, and taking each of the rest areas as a mirror image area;
step 2, setting symmetric boundary attributes:
if the direction of the electric field of the excitation electromagnetic symmetrical antenna is vertical to the splitting surface, taking the splitting surface as an ideal electric wall symmetrical boundary; if the magnetic field direction of the excitation electromagnetic symmetric antenna is vertical to the splitting surface, taking the splitting surface as an ideal magnetic wall symmetric boundary;
step 3, generating a tetrahedral mesh of the calculation area;
carrying out tetrahedral mesh dispersion on the calculation region, and marking corresponding symmetric boundary attributes on the mesh unit surface on each subdivision surface;
step 4, solving the electromagnetic field of each grid unit in the calculation area:
generating a solving equation set for solving the electric field of each grid unit by using a finite element electromagnetic solver, setting the electric field of the grid unit surface for calculating and marking the symmetric boundary attribute of the ideal electric wall to be zero to obtain the electric field of each grid unit in the calculating area, and obtaining the magnetic field of each grid unit in the calculating area through the mutual transformation relation of the electromagnetic fields;
step 5, calculating the electromagnetic field of the mirror image area of the electromagnetic symmetric antenna:
(5a) establishing a local coordinate system corresponding to each subdivision surface to obtain the local coordinate of the global coordinate of each grid unit relative to each subdivision surface in the calculation area;
(5b) calculating the electromagnetic field of each mirror image area;
and 6, calculating the overall electromagnetic characteristic of the electromagnetic symmetric antenna.
2. The finite element symmetric boundary implementation method for electromagnetically symmetric antennas of claim 1, wherein the step of calculating the electromagnetic field of each mirror region in step (5b) is as follows:
first, the electric field E of each grid unit in the calculation area is decomposed into a horizontal polarization electric field E parallel to the splitting plane || And a vertically polarized electric field E perpendicular to the splitting plane ⊥ If the splitting plane is an ideal magnetic wall symmetry plane, the horizontal polarization electric field at the symmetrical position of each grid cell with respect to the splitting plane is-E || Vertical polarization electric field of E ⊥ (ii) a If the splitting plane is an ideal plane of electric wall symmetry, the horizontal polarization electric field at the symmetrical position about the splitting plane is E || The vertically polarized electric field is-E ⊥ (ii) a Decomposing the magnetic field H of each grid cell in the calculation region into a horizontally polarized magnetic field H parallel to the splitting plane || And a vertical polarization magnetic field H perpendicular to the splitting plane ⊥ If the splitting plane is an ideal magnetic wall symmetry plane, the horizontal polarization field at the symmetrical position of each grid cell with respect to the splitting plane is H || Vertical polarization field of-H ⊥ (ii) a If the splitting plane is an ideal plane of electrical wall symmetry, the horizontal polarization field at the symmetric position about the splitting plane is-H || Vertical polarization field of H ⊥ ；
And secondly, forming an electric field E 'at the position by using the horizontal polarization electric field and the vertical polarization electric field at the symmetrical positions of the grid units relative to the splitting plane, forming a magnetic field H' at the position by using the horizontal polarization magnetic field and the vertical polarization magnetic field at the symmetrical positions of the grid units relative to the splitting plane, converting the local coordinates of each mirror image area into global coordinates, and obtaining a complete electromagnetic field of the electromagnetic symmetrical antenna.
3. The method for realizing finite element symmetric boundaries of electromagnetically symmetric antennas as claimed in claim 1, wherein said calculating the overall electromagnetic characteristics of the electromagnetically symmetric antennas in step 6 is: and converting the electromagnetic field of the electromagnetic symmetrical antenna into the electromagnetic characteristic of the electromagnetic symmetrical antenna by utilizing an electromagnetic characteristic post-processing calculator.
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