CN113792257B - Electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption - Google Patents
Electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption Download PDFInfo
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Abstract
The invention discloses an electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption, which comprises the steps of firstly subdividing all triangles of an initial grid, secondly projecting current coefficients of the initial grid onto the subdivision grid, obtaining voltage vectors of the subdivision grid through gamma detection and calculation, then directly irradiating the voltage vectors obtained by the subdivision grid with the voltage vectors and plane waves obtained by the projection calculation, comparing the voltage vectors and marking the triangle grid with larger voltage vector errors, and finally carrying out local grid encryption on the part with larger errors according to a marking graph, and processing non-conformal grids by using a plurality of RWG (MBRWG) basis functions. The method can well balance the grid quantity and the calculation precision when being applied to solving the electromagnetic scattering problem of the multi-scale target.
Description
Technical Field
The invention relates to an electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption, which is suitable for analyzing a multi-scale problem.
Background
Grid quality is critical to accurately solving many problems. In general, the accuracy of the solution is proportional to the density of the grid, but the grid is too dense resulting in reduced solution efficiency, thus requiring us to trade off between grid density and computational cost. It is a challenge to achieve the desired accuracy for multi-scale targets. The adaptive partial encryption has two key steps: 1. error detection, 2, local encryption.
For the surface area partial equation approach, local posterior error estimation techniques have been applied to identify regions of high error in the case of simple geometries. In addition, ubeda et al propose a geometry-based mesh encryption method, mainly used to encrypt sharp edges to improve the resolution accuracy. Recently, vasquez et al have proposed an adaptive encryption method for complex three-dimensional surface equations. The method improves the overall accuracy by encrypting the grid with larger residual errors.
To solve for the adaptively encrypted non-conformal mesh (including the mesh with different sizes and non-matching nodes), the Vasquez method uses a discontinuous gamma technique based on Half RWG (Half RWG, HRWG) basis functions. However, the introduction of the discontinuous gamma technique can cause the increase of the iteration steps of the iterative solution of the impedance matrix, and the iterative solution efficiency is affected. In addition, the penalty term and its coefficient in the discontinuous gamma technique need to be selected empirically, which is inconvenient to use.
Disclosure of Invention
The invention aims to: by using a Multi-Branch RWG (MBRWG) basis function and a grid with a large local encryption residual, a good balance of accuracy and efficiency can be achieved. The method can reduce the number of grids as much as possible under the condition of ensuring the precision, and is suitable for solving the multi-scale problem. When the non-conformal grid part is processed, the invention replaces HRWG with MBRWG, thereby avoiding the selection of penalty items and reducing the number of unknowns. Compared with HRWG, MBRWG does not break the continuity of current and has better iterative convergence characteristic.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows:
an electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption is characterized by comprising the following steps:
step 1: establishing a surface area component equation for scattering calculation aiming at an electromagnetic scattering problem of a conductor target, dispersing the surface of the conductor by triangular grids, defining RWG basis functions on each adjacent triangular grid pair, dispersing a surface integral equation by utilizing the defined RWG basis functions and a moment method, calculating by a traditional moment method to obtain an impedance matrix, and solving the impedance matrix by iteration to obtain an initial current coefficient;
step 2: performing multi-layer binary grid subdivision on the initial grid to obtain multi-layer fully-encrypted grids, and calculating the inclusion relation and projection coefficient of RWG basis functions between every two adjacent layers of grids;
step 3: projecting the initial current coefficient obtained in the step 1 downwards layer by layer until the lowest layer of all-encryption grids by using the projection coefficient of the RWG basis function between every two adjacent layers of grids obtained in the step 2; the voltage vector obtained by multiplying the current coefficient and the impedance matrix of the bottom full-encrypted grid is subtracted from the voltage vector obtained by the plane wave irradiating the bottom full-encrypted grid to obtain an error vector; normalizing the error on the bottommost full-encryption grid to obtain a relative error;
step 4: comparing the absolute value of the relative error obtained in the step 3 with a set error threshold, when the absolute value of the relative error is larger than the set error threshold, marking two triangular grids of the related bottommost RWG to obtain a grid marking graph of the bottommost full-encrypted grid, and then subdividing a parent triangular grid into four sub-triangular grids according to the grid marking graph of the bottommost full-encrypted grid and a father-son grid relation caused by a binary subdivision grid method, namely, projecting upwards layer by layer until the initial grid to obtain a triangular grid marking graph of each full-encrypted grid;
step 5: according to the triangle mesh marking graph of each layer of full-encryption mesh obtained in the step 4, starting from an initial mesh, carrying out layer-by-layer downward local encryption, namely carrying out binary mesh subdivision on the triangle mesh marked by each layer of mesh to obtain a final local encryption mesh graph; defining a plurality of basis functions, namely MBRWG processing local encryption-caused non-conformal grids, calculating to obtain an impedance matrix by utilizing a mixed basis function based on RWG and MBRWG and a moment method, obtaining a current coefficient of the encryption grid by iteratively solving the impedance matrix, and obtaining an RCS result by current calculation.
The invention has the following beneficial effects:
1. the numerical precision is controllable: the invention can adaptively encrypt the grid with larger residual error, so that even if the initial grid quality is not as good as the intention, the grid quality can be improved through codes in the follow-up process. By locally adaptive encryption, the number of grids and the calculation accuracy can be well balanced by reducing the unknown quantity as much as possible while guaranteeing the numerical accuracy.
2. Is suitable for processing multi-scale problems: when the object is a multi-scale structure, the fine structure of the object can be encrypted to thereby improve the overall accuracy.
3. Good convergence: non-conformal grids can appear in the local encryption process, and current continuity at the non-conformal position can be ensured by adopting MBRWG (m-ary-random-g) basis functions to replace traditional HRWG (high-rate-g-basis functions). Relative to a regular triangle mesh of a conventional RWG corresponding to a negative triangle mesh, MBRWG is a regular triangle mesh corresponding to a plurality of negative triangle meshes. MBRWG connects areas of non-uniform mesh size while ensuring that there is no charge build-up at non-conformals. The use of MBRWGs can both reduce the number of unknowns and increase the iterative solution speed compared to using Half RWGs (HRWGs) to process non-conformal meshes.
Drawings
FIG. 1 is a schematic diagram of a grid subdivision process in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of a marking process according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an encryption process according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an embodiment of the invention with RWG internally subdivided into eight new RWGs;
FIG. 5 is a representation of the MBRWG basis functions that occur naturally during partial encryption in accordance with an embodiment of the present invention;
FIG. 6 is a process of two-layer full encryption of a cube in an embodiment of the invention;
FIG. 7 is a diagram of triangles marking a subdivision grid of a cube based on an error map in accordance with an embodiment of the present invention;
FIG. 8 is a process of projecting markers layer by layer up a subdivision grid marker graph in accordance with an embodiment of the present invention;
FIG. 9 is a cube two-layer partial encryption process in accordance with an embodiment of the present invention;
FIG. 10 is a result of local encryption of a boat according to an embodiment of the present invention;
FIG. 11 is a comparison of RCS results before and after partial encryption with FEKO results for a boat of an embodiment of the present invention.
Detailed description of the preferred embodiments
Taking two layers of local encryption as an example, the implementation of the technical scheme is further described in detail with reference to the accompanying drawings:
the first step: establishing a surface area component equation for scattering calculation aiming at an electromagnetic scattering problem of a conductor target, dispersing the surface of the conductor by triangular grids, defining RWG basis functions on each adjacent triangular grid pair, dispersing a surface integral equation by utilizing the defined RWG basis functions and a moment method, calculating by a traditional moment method to obtain an impedance matrix, and solving the impedance matrix by iteration to obtain an initial current coefficient I;
and a second step of: binary mesh subdivision is carried out on each triangle of the initial mesh to obtain two layers of fully encrypted meshes, and the inclusion relation and projection coefficients of RWG basis functions between two adjacent layers of meshes (namely coefficients of RWG basis functions between two adjacent layers of meshes) are calculated.
The binary mesh subdivision process is shown in fig. 1, wherein the midpoints of three sides of a triangle of the initial mesh are taken, and the original triangle is subdivided into four small triangles through two-by-two connection. At this point, the RWG areas originally defined on the initial grid are redefined after the first encryption to eight new RWGs, as shown in FIG. 4. From the same divergence of the basis functions of the same region, we can get equation (4).
Wherein A is + And A - Is the area of the positive and negative triangular meshes of RWG, A i Is the area of the i-th small triangle after subdivision, a i Is the projection coefficient of the ith RWG, l i Is the length of the RWG common edge. The solution for solving equation (4) to get the coefficients is as follows:
wherein α=a 2 l 2 a 3 l 3 Since the coefficient is an unknown quantity, the value of α is calculated by the following formula
Wherein the method comprises the steps ofIs the unit normal vector of the RWG common edge, R j Is the jth layer RWG basis function.
The RWG basis function RWG defined on the j-th layer full encryption grid is calculated by the formula (5) j Eight RWG basis functions RWG projected to the j+1th layer j+1 Applying;
wherein the method comprises the steps ofIs the mth RWG basis function defined on the jth layer full encryption grid, a i Is the projection factor, +.>Is the RWG basis function defined on the j+1-th layer encryption grid of the same region.
The same operation is performed on the first layer full-encryption grid, so that the second layer full-encryption grid and the projection relation of the RWG basis function between the first layer and the second layer can be obtained, and the lowest layer full-encryption grid is called a subdivision grid, as shown in fig. 6.
And a third step of: and (3) projecting the initial current coefficient obtained in the first step downwards layer by layer until the lowest layer of the fully-encrypted grid by utilizing the inclusion relation and the projection coefficient of the RWG basis function between every two adjacent layers of grids obtained in the second step.
Notably, each RWG j+1 Belonging to three RWGs j So each RWG j+1 Is passed through three RWGs j Is provided for the summation of the current coefficient projections. By recording each RWG j Is of eight RWGs of (2) j+1 And coefficients thereof, the projection relationship between two layers of fully encrypted grids can be obtained.
In obtaining the current coefficient I of the subdivision grid R Then, the impedance matrix Z of the subdivision grid is calculated by using the formula (1) R And compares it with the projected current coefficient I R Multiplying to obtain electricityPressure vector V R ；
Z R I R ＝V R (1)
Then the plane wave irradiates the bottommost layer full-encryption grid to obtain another group of voltage vectors V i Subtracting the two groups of voltage vectors according to the formula (2) to obtain an error vector E R ；
E R ＝V R -V i (2)
Normalizing the error by the RWG basis function relative error calculation formula (3) to obtain a relative error element
Wherein,the mth RWG basis function representing the first layer (i.e., the lowest fully encrypted mesh, subdivision mesh), based on the relative error +.>Obtaining a relative voltage error map of the subdivision grid +.>As shown in fig. 7 (a).
Fourth step: setting an error threshold (e.g., 0.1), based on the relative errorAnd (b) find out the RWG basis functions larger than the error threshold on the subdivision grid, and mark the two triangle grids of the corresponding RWG basis functions, and finally obtain the mark graph as shown in fig. 7 (b).
After the marking map of the subdivision grid is obtained, the relationship of father and son triangles between two layers of grids is utilized (one father triangle grid can obtain four son triangle grids after binary subdivision), then the father triangle grid of the upper layer is marked according to the son triangle grid marked by the current layer (as long as one of the four son triangles of the father triangle grid is marked, the father triangle grid needs to be marked), the triangle grid of the same area of the upper layer is marked layer by layer until the initial grid is reached, and the triangle grid marking map of each layer of full-encryption grid is obtained, as shown in fig. 8.
Taking two layers as an example, fig. 2 shows the labeling process (where white is labeled network, the same applies below). Each layer of triangle mesh corresponds to the next four relatively small triangles, so long as the four small triangles have been marked, the large triangles to which they belong need to be marked as well.
Fifth step: and (3) according to the triangle mesh mark graph of each layer of full-encryption mesh obtained in the fourth step, starting from the initial mesh, carrying out layer-by-layer downward local encryption, namely carrying out binary mesh subdivision on the triangle mesh marked by each layer of mesh, and obtaining a final local encryption mesh graph. The encryption process is schematically shown in fig. 3, the marking diagram of the initial grid is shown in fig. 9 (a), the partial encryption is performed layer by layer downwards, and binary grid subdivision is performed on the triangles marked by the initial grid to realize the first layer of partial encryption, as shown in fig. 9 (b). And performing binary subdivision on the triangles marked by the first layer of local encryption grids according to the first layer of marking graphs to obtain a final graph (c) of the local encryption grids 9.
The present invention utilizes MBRWG basis functions to handle non-conformal meshes that appear during partial encryption. As shown in fig. 5, a non-conformal mesh may appear during subdivision, and the non-conformal mesh resulting from binary mesh subdivision is naturally suitable for defining MBRWG basis functions. MBRWG, as opposed to HRWG, requires penalty terms to address the charge accumulation problem at grid non-conformality, naturally guarantees current continuity as does RWG basis functions. The MBRWG basis function is defined as follows:
wherein the method comprises the steps ofIs the regular triangle of MBRWG, +.>Is the i-th negative triangle, the number N of the negative triangles n With the exception of the non-conformal mesh details, the RWG basis function definition is the same as that of the conventional: l represents the length of the common edge of the RWG basis function, A represents the area of the triangle, and r represents the point on the triangle.
And calculating to obtain an impedance matrix by using a mixed basis function and a moment method based on RWG and MBRWG, obtaining a current coefficient of the local encryption grid by iteratively solving the impedance matrix, and finally obtaining an RCS result by current calculation.
The invention further verifies the improvement of the local encryption grid on the precision through the small ship model with the grid size of 0.2 wavelength. As shown in fig. 10, this method is basically encrypted at the edge with larger error, and fig. 11 also shows improvement of accuracy. Finally, the data of table 1 demonstrate the advantages of using MBRWG versus using the traditional discontinuous gamma method in terms of unknowns and iteration speed. The solving time refers to the solving time after the local encryption grid is generated.
TABLE 1 advantages of MBRWG versus HRWG at unknown quantity, memory, time and iteration step
| Basis functions | Unknown quantity | Impedance matrix Memory (MB) | Solving time(s) | Number of iteration steps |
| RWG+HRWG | 7762+2023 | 731 | 235 | 363 |
| RWG+MBRWG | 7762+626 | 536 | 116 | 97 |
Claims (3)
1. An electromagnetic scattering solving method based on MBRWG and grid self-adaptive encryption is characterized by comprising the following steps:
step 1: establishing a surface area component equation for scattering calculation aiming at an electromagnetic scattering problem of a conductor target, dispersing the surface of the conductor by triangular grids, defining RWG basis functions on each adjacent triangular grid pair, dispersing a surface integral equation by utilizing the defined RWG basis functions and a moment method, calculating by a traditional moment method to obtain an impedance matrix, and solving the impedance matrix by iteration to obtain an initial current coefficient;
step 2: performing multi-layer binary grid subdivision on the initial grid to obtain multi-layer fully-encrypted grids, and calculating the inclusion relation and projection coefficient of RWG basis functions between every two adjacent layers of grids;
step 3: projecting the initial current coefficient obtained in the step 1 downwards layer by layer until the lowest layer of all-encryption grids by using the projection coefficient of the RWG basis function between every two adjacent layers of grids obtained in the step 2; the voltage vector obtained by multiplying the current coefficient and the impedance matrix of the bottom full-encrypted grid is subtracted from the voltage vector obtained by the plane wave irradiating the bottom full-encrypted grid to obtain an error; normalizing the error on the bottommost full-encryption grid to obtain a relative error;
step 4: comparing the absolute value of the relative error obtained in the step 3 with a set error threshold, when the absolute value of the relative error is larger than the set error threshold, marking two triangular grids of the related bottommost RWG to obtain a grid marking graph of the bottommost full-encrypted grid, and then subdividing a parent triangular grid into four sub-triangular grids according to the grid marking graph of the bottommost full-encrypted grid and a father-son grid relation caused by a binary subdivision grid method, namely, projecting upwards layer by layer until the initial grid to obtain a triangular grid marking graph of each full-encrypted grid;
step 5: according to the triangle mesh marking graph of each layer of full-encryption mesh obtained in the step 4, starting from an initial mesh, carrying out layer-by-layer downward local encryption, namely carrying out binary mesh subdivision on the triangle mesh marked by each layer of mesh to obtain a final local encryption mesh graph; defining a plurality of basis functions, namely MBRWG processing local encryption-caused non-conformal grids, calculating to obtain an impedance matrix by utilizing a mixed basis function based on RWG and MBRWG and a moment method, obtaining a current coefficient of the encryption grid by iteratively solving the impedance matrix, and obtaining an RCS result by current calculation.
2. The MBRWG-based locally adaptive encryption method of claim 1, wherein the step 2 includes the steps of:
step 2-1: taking the midpoints of three sides of the triangle of the previous layer of grid, and subdividing the triangle into four small triangles through the connection of the midpoints to form the current layer of grid;
step 2-2: after the multi-layer full encryption is completed, RWG basis functions are defined on grids, and the inclusion relation and projection coefficients of the RWG basis functions between every two adjacent layers of grids are obtained.
3. The MBRWG-based locally adaptive encryption method of claim 1, wherein the 3 rd step comprises the steps of:
step 3-1: the initial current coefficient obtained in step 1 is obtained according to step 2The projection coefficients of RWG basis functions between every two adjacent layers of grids are projected downwards layer by layer to obtain the current coefficient I of the bottommost layer fully-encrypted grid R ；
Step 3-2: calculating the impedance matrix Z of the bottommost layer full-encryption grid R And the current coefficient I of the bottom layer full-encryption grid obtained by projection R Multiplying to obtain a voltage vector V R ；
Z R I R ＝V R (1)
Step 3-3: irradiating the bottommost layer full-encryption grid with plane waves to obtain another set of voltage vectors V i Subtracting the two groups of voltage vectors to obtain an error vector E R ；
E R ＝V R -V i (2)
Step 3-4: pair E R Each element of the vectorNormalization processing to obtain relative error->The calculation formula is as follows:
wherein the method comprises the steps ofRepresenting the mth RWG basis function defined on the lowest fully encrypted mesh.
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| CN103279612A (en) * | 2013-05-30 | 2013-09-04 | 南京理工大学 | Multi-grid precondition method for fast acquiring complex target radar echoes |
| CN106295120A (en) * | 2016-07-26 | 2017-01-04 | 上海无线电设备研究所 | A kind of electromagnetic characteristic of scattering quick calculation method |
| CN111046603A (en) * | 2019-12-03 | 2020-04-21 | 南京理工大学 | Electromagnetic scattering characteristic analysis method based on GPU parallel acceleration characteristic basis function algorithm |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103279612A (en) * | 2013-05-30 | 2013-09-04 | 南京理工大学 | Multi-grid precondition method for fast acquiring complex target radar echoes |
| CN106295120A (en) * | 2016-07-26 | 2017-01-04 | 上海无线电设备研究所 | A kind of electromagnetic characteristic of scattering quick calculation method |
| CN111046603A (en) * | 2019-12-03 | 2020-04-21 | 南京理工大学 | Electromagnetic scattering characteristic analysis method based on GPU parallel acceleration characteristic basis function algorithm |
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