A fast analysis method for local variation electromagnetic scattering problems based on grid modification and IEDG

Abstract

The present invention discloses a method for rapid analysis of local change electromagnetic scattering problems based on grid modification and IEDG, firstly calculating the impedance matrix of the parent structure, then using the grid modification to improve the edge of the structure so that the jagged boundary becomes smooth and then subsequently adding the structure, and introducing the IEDG process to add the mismatch problem of the nodes at the boundary between the structure and the remaining structure. The present invention can only perform modeling and partitioning once, and only calculate the impedance matrix and its inverse matrix of the original target once when the target undergoes multiple local changes, thereby reducing the complexity of the calculation, improving the calculation efficiency, reducing the grid error, and enabling the changed parent structure to be properly connected with the subsequently added structure, without considering whether the grid is conformal, thereby improving the flexibility of the traditional local change algorithm and expanding its application range.

Description

Technical Field

[0001] The present invention relates to a method for analyzing electromagnetic scattering characteristics of a target, and in particular to a method for rapid electromagnetic scattering analysis in which a grid discrete target undergoes local changes in a program and requires a grid modification algorithm and a discontinuous Galerkin method to process errors and grid mismatches in the changed grid. Background Art

[0002] The analysis of electromagnetic scattering characteristics of electrically large targets has always been a hot topic of concern for scholars at home and abroad, especially the electromagnetic scattering problem of electrically large targets with local changes. In actual electromagnetic engineering problems, it is often necessary to make multiple local modifications to the model in order to find the optimal structure. For example, in order to reduce the radar cross section (RCS) of the target or obtain better performance parameters of antenna radiation, the structure needs to be changed continuously. The traditional method of moments is not only very time-consuming to deal with such problems, but also requires re-modeling, segmentation and re-calculation after each change.

[0003] In order to solve this kind of problem, some local change methods have been proposed. Among them, the traditional local change algorithm can effectively handle the local change problems of subtracting, adding, subtracting and adding structures. However, they all solve the situation where the changed structure and the parent structure are independent and separated and not in contact with each other or the situation where the mesh matching is conformal. Since a large mesh error will be generated when the subtracted structure and the parent structure are connected, it cannot handle the situation where a structure is subtracted from the parent mesh itself when the target is already meshed discretized, nor can it handle the situation where the local change position is randomly set in the program. Since the current continuity cannot be guaranteed when the boundary mesh does not match, it cannot handle the situation where the added structure and the parent structure contact boundary mesh do not match. When the subtracted structure is on the surface of the parent structure, the boundary of the remaining structure after the change will be jagged, resulting in mesh errors that are not completely consistent with the expected target structure, which also affects the subsequent local changes. Summary of the invention

[0004] Purpose of the invention:

[0005] In view of the mesh error and mesh non-conformality problems encountered in the above-mentioned local changes, the present invention proposes a local change algorithm based on mesh modification and discontinuous Galerkin integral equation method (IEDG). By using IEDG, the change structure and the parent structure can be divided independently without maintaining strict conformality; by using mesh modification, the mesh error generated when the structure is subtracted from the parent structure mesh can be reduced. The use of mesh modification and IEDG expands the application scope of the traditional local change algorithm and improves its flexibility.

[0006] Technical solution:

[0007] In order to achieve the object of the present invention, the present invention provides a method for rapid analysis of local variation electromagnetic scattering problems based on grid modification and IEDG, which is characterized by comprising the following steps:

[0008] Step 1: Calculate the impedance matrix and voltage vector of the original matrix structure, and perform LU decomposition on the impedance matrix of the original matrix structure;

[0009] Step 2: Perform local changes on the original parent structure, subtract a structure and modify the mesh of the remaining structure edge, so that the jagged edge of the remaining structure left by subtracting a structure becomes smooth;

[0010] Step 3: Add local changes on the boundary of the remaining structure, add a structure and use IEDG to handle the mismatch problem of the nodes at the boundary between the added structure and the remaining structure, add RWG basis functions to the inside of the structure, and add HRWG basis functions to the connection boundary between the remaining structure and the added structure;

[0011] Step 4: Use the impedance matrix and voltage vector of the original parent structure to solve the induced current I on the remaining structure and the added structure after the local change r and I a ;

[0012] Step 5: Use the solved induced current I r and I a Solve for the far-field radar cross section of the remaining targets.

[0013] Beneficial effects:

[0014] 1. High computational efficiency: The present invention can perform modeling and segmentation only once and calculate the impedance matrix and its inverse matrix of the original target only once when the target undergoes multiple local changes, thus avoiding the need for repeated calculations when local changes occur, thereby reducing the complexity of the calculation, shortening the calculation time, and improving the calculation efficiency.

[0015] 2. Improved the function of the local change algorithm: The addition of grid modification makes the location of local changes in the target more arbitrary. The location of the local change can be set arbitrarily and the grid after the change can be repaired, reducing the grid error between the local change and the expected ideal target.

[0016] 3. No need to consider the grid conformality problem during local changes: The introduction of IEDG makes it unnecessary to consider whether the changed structure and the parent structure are independently separated and whether the grid matches conformality when the target undergoes local changes. The two can be independently segmented and current continuity can be guaranteed when the contact boundary nodes do not match.

[0017] 4. Wide range of applications: The local change solution method with grid modification and IEDG proposed in the present invention can be applied to a variety of electromagnetic simulation problems with local changes. On the one hand, it reduces the grid error of the model, and on the other hand, it enables the changed parent structure to be properly connected with the subsequent added structure without considering whether the grid is conformal. For example, it can solve the electromagnetic scattering problem before and after the antenna is loaded on the aircraft, and the electromagnetic simulation of different launch positions of aircraft missiles, etc. It improves the flexibility of the traditional local change algorithm and expands its application range. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the local change problem to be solved by the present invention;

[0019] Figure 2(a)-Figure 2(e) is a schematic diagram of the mesh modification principle; Figure 2(a) is a schematic diagram of the original matrix structure; Figure 2(b) is a schematic diagram of the local change on the original matrix structure minus a circular structure; Figure 2(c) is a schematic diagram of the point set P; Figure 2(d) is a schematic diagram of the set S 3 Schematic diagram; Figure 2(e) is S a Schematic diagram;

[0020] Figure 3 It is a schematic diagram of mesh non-conformality;

[0021] Figure 4 is a schematic diagram of the computational model;

[0022] Figure 5 It is the RCS calculation result diagram of the calculation model. DETAILED DESCRIPTION

[0023] The present invention will be further explained below in conjunction with the accompanying drawings.

[0024] In traditional local variation methods, any local variation can be divided into two processes: first subtracting a structure and then adding a structure. However, when the parent structure, the subtracted structure, and the added structure are connected or the mesh is non-conformal, i.e., when processing Figure 1 The present invention aims at the situation that the traditional local change algorithm based on the moment method cannot solve, and proposes a fast electromagnetic scattering analysis method with grid modification and IEDG local change problem, thereby reducing repeated calculations and improving calculation efficiency, reducing the grid error caused by subtracting local changes and solving the grid mismatch problem caused by adding local changes, and expanding the flexibility of the local change algorithm.

[0025] The method of the present invention first calculates the impedance matrix of the parent structure, which accounts for a large proportion of the overall structure and only needs to be calculated once, and then calculates the self-impedance matrix of the changed structure and the mutual impedance matrix between them and the unchanged structure. The changed structure and the unchanged structure here refer to whether the basis function level has changed or not. Macroscopically, a structure is subtracted from the surface of the parent structure, and then the mesh is modified to improve the edge of the structure so that the jagged boundary becomes smooth and then the structure is added. When a structure is subtracted from the surface of the parent mesh, a reduction in basis functions is generated. The basis functions that have changed after the mesh modification should be added again as a new part of the basis functions, and the basis functions of the added structures should also be added as the added part, so as to complete the local changes in the theoretical sense.

[0026] The present invention solves the problem that local changes occur on the surface of a grid discrete target and each structure is independently divided. The edges of the remaining structure are processed well by grid modification to reduce grid errors and add structures in the subsequent process. The current continuity problem is solved before subsequent local changes can be made at the grid mismatch boundary. In the calculation process, repeated calculations of unchanged structures in the matrix are also avoided, so that the calculation information of the unchanged structure can be used multiple times in subsequent local changes, thereby improving calculation efficiency. Secondly, the change position can be set in the calculation, so that each structure can be divided independently, which is more flexible.

[0027] For example, when installing antennas on ships, Figure 4 As shown, in order to obtain better radiation characteristics, we need to modify the position and shape of the antenna many times and perform calculations. Each time we place the antenna, we need to subtract a structure from the original target grid surface in the program before we can place the antenna in the corresponding position. At this time, we need to process the grid of the remaining boundary after subtracting the structure in order to place the antenna on it with a better and more fitting connection.

[0028] The method for rapid analysis of local variation electromagnetic scattering problems based on grid modification and IEDG of the present invention specifically comprises the following steps:

[0029] Step 1: Calculate the impedance matrix Z and voltage vector of the original matrix structure, and perform LU decomposition on the impedance matrix of the original matrix structure. LU decomposition is a type of matrix decomposition, which can decompose the matrix Z into a lower triangular matrix L and an upper triangular matrix U.

[0030] Step 2: Make local changes to the original parent structure as shown in Figure 2(a), such as subtracting a circular structure. Ideally, the resulting target structure should be as shown in Figure 2(b). However, since the target is discretized by the grid, the edge is not smooth after subtracting the structure. The grid needs to be modified to make the jagged edges left by subtracting the circular structure smooth, so that the model can be as similar to Figure 2(b) as possible to reduce the error caused by the grid. The specific process is as follows:

[0031] A. Mark and classify the mesh triangles. Divide the mesh triangles into two sets according to whether the discrete mesh triangles have common areas with the ideal subtracted structure: S 1 and S 2 , where the mesh triangles that have no common area with the subtracted structure belong to the set S 1 , otherwise it belongs to the set S 2 . It can be seen from this that the set S 2 The area formed by the mesh triangles in contains the subtracted structure area.

[0032] B. Find the nodes that need to be moved and assign them to a point set P; if the set S 2 If there is a node in the mesh triangle outside the ideal subtracted structure area, the node is defined as belonging to the point set P, as shown in Figure 2(c), and the node that needs to be moved is marked in white.

[0033] C. Move nodes; according to the ideal structural boundary equation, move the nodes in the set P that need to be moved to the boundary line minus the structure, and update the coordinate information of these moved nodes.

[0034] D. Define the subtracted, remaining, and added triangle sets; since the nodes move, the basis function information related to the moved nodes will also change, so the triangle set S 1 The mesh triangles associated with the mobile nodes (white) in the figure also need to be marked, and these mesh triangles are defined as belonging to the set S 3 , which is marked as medium gray in Figure 2(d). Define the triangle set S s , S r and S a . Set S s represents the set of mesh triangles that need to be subtracted in a local change and S s =S 2 ∪S 3 ; Set S r represents the set of mesh triangles remaining in a local change and S r =S 1 -S 3 ; Set S a It represents the set of mesh triangles that need to be added back after the mesh nodes are modified due to the extra mesh triangles that were subtracted in the local change, that is, the set S 3 The part of the mesh triangle in is marked in dark gray in Figure 2(e).

[0035] E. Divide the basis functions on the target structure and define the set of basis functions R that need to be subtracted, remaining, and added in the local changes , R r and R a ; The specific division rule is: traverse all basis functions, if the mesh triangles corresponding to a basis function belong to the set S r , then define the basis function to belong to the set R r ; If the mesh triangle corresponding to the basis function exists in the set S s , then the basis function is defined to belong to the set R s ; If the mesh triangle corresponding to the basis function exists in the set S a , then the basis function is defined to belong to the set R a .

[0036] Through the above process, the target structure has completed the reduction of local changes. In this process, not only some RWG basis functions need to be subtracted, but also some RWG basis functions need to be added. Due to the introduction of mesh modification, the jagged edges of the target structure formed when the structure is subtracted are also smoothed.

[0037] Step 3: Add local changes on the boundary of the remaining structure. Since the nodes of the added structure and the remaining structure at the boundary do not necessarily match, such as Figure 3 As shown, IEDG is introduced for processing, the RWG basis function is applied inside the structure, and the HRWG is applied to the connection boundary between the remaining structure and the added structure.

[0038] In the process of adding structure changes, some RWG basis functions and HRWG basis functions are also added to the set R a In , the added RWG basis function exists inside the added structure, and the added HRWG basis function exists at the connection boundary between the remaining structure and the added structure. So far, the subtracted, remaining, and added basis functions have been determined.

[0039] Step 4: After the above changes are processed through mesh modification and IEDG, the impedance matrix information and voltage vector information of the original parent structure are used to calculate the remaining structure after the local changes and the induced current I added to the structure r and I a .

[0040] After defining the subtracted, residual, and added RWG basis functions, the MoM impedance matrix equation before and after the local change can be written as follows:

[0041]

[0042] Among them, Z rr , Z ss and Z aa are the self-impedance matrices of the residual structure, the subtracted structure, and the added structure, respectively, Z rs, Z sr , Z ra and Z ar are the mutual impedance matrices between the remaining structure and the subtracted structure, the subtracted structure and the remaining structure, the remaining structure and the added structure, and the added structure and the remaining structure; J r and J s is the current coefficient of the remaining structure and the subtracted structure before the local change, V r and V s is the voltage vector of the remaining structure and the subtracted structure before the local change, V r and V s The collection of is the voltage vector of the original parent structure; I r and I a is the current coefficient of the remaining structure and the added structure after the local change, V a is the voltage vector after the local changes plus the structure.

[0043] For electromagnetic scattering problems based on the electric field integral equation (EFIE), the voltage element calculation formula is:

[0044]

[0045] Among them, E i is the incident wave, f m represents the mth basis function, T m Yes m Scope.

[0046] In order to ensure the current continuity across the boundary mismatched grid, the impedance element form of the electric field integral equation (EFIE) in IEDG is:

[0047]

[0048] Where I is the identity matrix; k, η, and G are the wave number, impedance, and Green's function in free space; f n 、f m Respectively represent the nth and mth RWG or HRWG basis functions, T n , T m They are f n 、f m The scope of C n , C m T n , T m The contour boundary of C n , C m The unit normal of ; and Corresponding to the contour boundary C n The potential penalty and charge penalty generated by the charge at:

[0049]

[0050] In formula (4), the dual gradient Green's function is reduced to produce surface line integral (SLI), line surface integral (LSI), and line line integral (LLI) terms. The line line integral term can be Item offset.

[0051] After using the block matrix inversion formula and the Sherman-Morrison-Woodbury formula, the solution of equation (2) is:

[0052]

[0053] in:

[0054]

[0055] In formula (10), I is the identity matrix, X rr , X rs It is a matrix composed of the elements corresponding to the rows and columns where the corresponding structural basis function numbers are located in the inverse matrix of the parent structure impedance matrix before the local change.

[0056] The information of the original impedance matrix is ​​used to calculate the residual structure after the local change and the induced current I added to the structure r and I a , that is, the local change algorithm formulas (7)-(10) can be used for effective calculation.

[0057] Step 5: Use the solved induced current I r and I a Solve the far-field radar cross section of the remaining targets. The radar cross section (RCS) is defined as:

[0058]

[0059] Among them, E s is the scattered electric field in the far field.

[0060] In the calculation of multiple local changes, the parent impedance matrix and its LU decomposition are calculated only once. The data information used in the later local change solution only requires a small amount of calculation, and the parent data information can be extracted from the original information, which reduces a lot of repeated calculations and speeds up the solution. In the case of mesh modification and IEDG, we can independently divide each structure, set the change position directly in the program, and then make local changes at that position for calculation. This method not only reduces the boundary mesh error caused by subtracting the structure, making the calculation closer to the ideal expected goal, but also realizes the function that the change position can be set in the program without considering whether the added structure is conformal with the remaining structure mesh. It is no longer necessary to consider all possible change positions when modeling. Only one modeling division is required with the parent structure and the added structure model.

[0061] The method of the present invention is further described below with a specific example:

[0062] As attached Figure 4 As shown in , the present invention discusses the algorithm in detail by analyzing the problem of locally changing electromagnetic scattering characteristics of installing antennas at different positions on a ship as a research object: the bow of the ship points to the positive x-axis, the length, width and height of the ship are 15 meters, 4 meters and 6 meters respectively, and the deck is on the xoy plane and the bow is at the origin, the radius of the cylinder at the lower end of the antenna is 0.2 meters and the height is 0.7 meters, the radius of the middle cylinder is 0.5 meters and the height is 0.5 meters, the radius of the upper hemisphere is 0.5 meters, and the ship and the antenna are discretized into 64143 and 1440 basis functions respectively. In this example, the hull is the parent structure, and the center coordinates of the three installed antennas are (3m, 0, 0), (4m, 0, 0), and (5m, 0, 0), respectively. The single-station RCS is calculated, the incident angle is φ=90°, θ=0°-180°, and the step size is 1°. The frequency of the incident electromagnetic wave is 300MHz, the parent section size is 0.1 meter, and the antenna section size is 0.075 meter.

[0063] Figure 5 The single-station RCS result of the ship and a local change thereof is shown in Table 1. The comparison of the RCS calculation results and the calculation time of this embodiment and the prior art are shown in Table 1.

[0064] Table 1 Comparison of RCS calculation results and calculation time

[0065]

[0066] As shown in Table 1, the calculation results obtained by the method of the present invention are in good agreement with the results of the traditional method of moments, and the calculation time is significantly shortened.

[0067] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A fast analysis method for local variation electromagnetic scattering problems based on grid modification and IEDG, characterized by The steps include: Step 1: Calculate the impedance matrix and voltage vector of the original matrix structure, and perform LU decomposition on the impedance matrix of the original matrix structure; Step 2: Perform local changes on the original parent structure, subtract a structure and modify the mesh of the remaining structure edge, so that the jagged edge of the remaining structure left by subtracting a structure becomes smooth; Step 3: Add local changes on the boundary of the remaining structure, add a structure and use IEDG to handle the mismatch problem of the nodes at the boundary between the added structure and the remaining structure, add RWG basis functions to the inside of the structure, and add HRWG basis functions to the connection boundary between the remaining structure and the added structure; Step 4: Use the impedance matrix and voltage vector of the original parent structure to solve the induced current I on the remaining structure and the added structure after the local change r and I a ; Step 5: Use the solved induced current I r and I a Solve the far-field radar cross section of the remaining targets; In step 2, mesh modification of the remaining structure edges includes the following steps: A. Mark and classify mesh triangles: Divide the mesh triangles into two sets: S1 and S2 according to whether the discrete mesh triangles have common areas with the subtracted structure. Mesh triangles that do not have common areas with the subtracted structure belong to set S1, otherwise they belong to set S2. B. Find the nodes that need to be moved and assign them to a point set P: If there is a node in the mesh triangles of the set S2 that is outside the subtracted structure area, then define the node as belonging to the point set P; C. Move nodes: According to the structural boundary equation, move the nodes in the point set P that need to be moved to the boundary line minus the structure, and update the coordinate information of the moved nodes at the same time; D. Define the subtracted, remaining, and added mesh triangle sets: assign the mesh triangles associated with the mobile node in triangle set S1 to set S3, and define set S s , S r and S a , where the set S s represents the set of mesh triangles that need to be subtracted in a local change and S s =S2∪S3; set S r represents the set of mesh triangles remaining in a local change and S r =S1-S3; Set S a Represents the set of mesh triangles that are subtracted due to local changes and need to be added back after the mesh nodes are modified; E. Divide the basis functions on the target structure: define the set of basis functions R that need to be subtracted, remaining, and added in the local change s , R r and R a The specific method is: traverse all basis functions, if the mesh triangles corresponding to a basis function belong to the set S r , then define the basis function to belong to the set R r ; If the mesh triangle corresponding to a basis function belongs to the set S s , then the basis function is defined to belong to the set R s ; If the mesh triangle corresponding to a basis function belongs to the set S a , then the basis function is defined to belong to the set R a .

2. The method for rapid analysis of local variation electromagnetic scattering problems based on grid modification and IEDG as claimed in claim 1, characterized in that: The MoM impedance matrix equation before and after local changes is written as follows: Among them, Z rr , Z ss and Z aa are the self-impedance matrices of the residual structure, the subtracted structure, and the added structure, respectively, Z rs , Z sr , Z ra and Z ar are the mutual impedance matrices between the remaining structure and the subtracted structure, the subtracted structure and the remaining structure, the remaining structure and the added structure, and the added structure and the remaining structure; J r and J s are the current coefficients of the remaining structure and the subtracted structure before the local change, V r and V s are the voltage vectors of the remaining structure and the subtracted structure before local change; V a is the voltage vector after the local change plus the structure; Use the block matrix inversion formula and the Sherman-Morrison-Woodbury formula to solve formula (2): in: I is the identity matrix, X rr , X rs They are matrices composed of the elements corresponding to the rows and columns where the corresponding structural basis function numbers are located in the inverse matrix of the parent structure impedance matrix before the local change.

3. The method for rapid analysis of local variation electromagnetic scattering problems based on grid modification and IEDG as claimed in claim 1, characterized in that: In order to ensure the current continuity across the boundary mismatched grid, the impedance element form of the electric field integral equation in IEDG is: Where I is the identity matrix; k, η, and G are the wave number, impedance, and Green's function in free space, respectively; f n 、f m Respectively represent the nth and mth RWG or HRWG basis functions, T n , T m They are f n 、f m The scope of C n , C m T n , T m The contour boundary, C n , C m The unit normal of ; and Corresponding to the contour boundaries C n The potential penalty and charge penalty generated by the charge at: In formula (4), the dual gradient Green's function is reduced to produce surface-line integral, line-surface integral, and line-line integral terms; the line-line integral term can be Item offset.

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