An electromagnetic scattering simulation method for coated aircraft based on multi-resolution preprocessing

Abstract

The present invention belongs to the field of electromagnetic simulation technology, and specifically provides an electromagnetic scattering simulation method for coated aircraft based on multi-resolution preconditioning, which is used to complete the electromagnetic scattering simulation calculation of coated targets, accelerate iterative convergence while ensuring the simulation calculation accuracy, and effectively reduce the memory requirement. The present invention introduces multi-resolution (MR) preconditioning on the basis of the locally coupled multiple unknowns domain decomposition method. First, new Robin transmission conditions are set, and the LCMT-DDM equation is constructed based on them; then symmetry is carried out, and the MR-LCMT-DDM equation is further constructed; finally, the equation is solved to obtain the unknown coefficient vector, and then the electromagnetic scattering of the coated target is calculated. The symmetry method proposed by the present invention can reduce the memory requirement by nearly half, and the matrix property can be further improved through multi-resolution preconditioning, significantly accelerating the iterative convergence without affecting the numerical accuracy.

Description

Technical Field

[0001] The invention belongs to electromagnetic simulation technology, and specifically provides a coated aircraft electromagnetic scattering simulation method based on multi-resolution preprocessing. Background Art

[0002] The electromagnetic scattering characteristics of composite targets of layered dielectrics or metal dielectrics such as coated aircraft have important research value in the stealth and anti-stealth aspects of the military field. Computational electromagnetics provides a powerful electromagnetic simulation technology for this purpose. Among them, the local coupling multitrace domain decomposition method (LCMT-DDM) decomposes the space where the composite target is located into some closed sub-regions with uniform materials, and uses Robin transmission conditions (RTCs) to couple adjacent sub-regions, which not only improves the iterative convergence characteristics of the equation, but also reduces the computational and storage complexity. For example, the literature "R. Zhao, Y. Chen, X.-M. Gu, Z. Huang, H. Bagci, and J. Hu, "A local coupling multitrace domain decomposition method for electromagnetic scattering from multilayered dielectric objects," IEEE Trans. Antennas Propag., vol. 68, no. 10, pp. 7099-7108, 2020" and the literature "R. Zhao, P. Li, J. Hu, and H.Bagci, "Amultitrace surface integral equation method for PEC / dielectric composite objects," IEEE Antennas Wireless Propag.Lett., vol.20, no.8, pp.1404-1408, 2021"; However, if the composite target contains fine structures or high-contrast dielectric sub-regions, it is required to refine the mesh to improve the calculation accuracy. At this time, iteratively solving the LCMT-DDM equation requires too many iterations. Summary of the invention

[0003] The purpose of the present invention is to provide a coated aircraft electromagnetic scattering simulation method based on multi-resolution preprocessing, which is used to complete the electromagnetic scattering simulation calculation of the coated target, accelerate the iterative convergence while ensuring the simulation calculation accuracy, and effectively reduce the memory requirement.

[0004] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] An electromagnetic scattering simulation method for a coated aircraft based on multi-resolution preprocessing, characterized by comprising the following steps:

[0006] Step 1. Decompose the coated target into multiple closed sub-regions with uniform materials, discretize the surface of each sub-region using conformal triangular meshes, and define RWG basis functions within the obtained triangular element pairs;

[0007] Step 2. For each sub-region, use the mesh aggregation method to generate macro-elements with irregular shapes and construct hierarchical meshes;

[0008] Step 3. For each sub-region, define gRWG (generalized RWG) basis functions within the macro-element pairs, and use the charge conservation of the inter-layer gRWG basis to represent the gRWG basis of the l-th layer as a linear combination of the gRWG basis of the (l - 1)-th layer, where l = 2, 3,..., L, L is the number of layers of the hierarchical mesh (L = Y + 1, Y is the number of mesh aggregation times), and the gRWG basis of the first layer degenerates into the RWG basis;

[0009] Step 4. For each sub-region, use singular value decomposition to decompose the gRWG basis of the l-th layer into curl basis and irrotational basis, and the obtained result is the MR (multi-resolution) basis function of the l-th layer;

[0010] Step 5. Use the recurrence relation to generate the global RWG-MR transformation matrix that converts the RWG basis of the first layer to all MR bases of the first L layers;

[0011] Step 6. Set Robin transmission conditions (RTCs), construct the LCMT-DDM linear equation, and symmetrize the LCMT-DDM linear equation;

[0012] Step 7. Based on the symmetrized LCMT-DDM equation, use the global RWG-MR transformation matrix to construct the MR-LCMT-DDM equation and calculate the electromagnetic scattering of the coated target.

[0013] Further, the specific process of Step 5 is as follows:

[0014] In the n-th sub-region, let be the current gRWG-MR transformation matrix of the l-th layer, be the current gRWG basis reconstruction matrix between the (l - 1)-th layer and the l-th layer, be the transformation matrix between the current RWG basis of the first layer and all current MR bases of the first l layers, then is expressed as:

[0015]

[0016] In the nth sub-region, let be the transformation matrix between the first-layer magnetic current RWG basis and all the magnetic current MR bases of the previous l layers. If the nth sub-region is a dielectric or free space, then If the nth sub-region is a metal sub-region, then is an empty matrix;

[0017] Let be the transformation matrix between the first-layer electromagnetic current RWG basis and all the electromagnetic current MR bases of the previous l layers in the nth sub-region. The matrix blocks on its main diagonal are successively and The remaining part is an all-zero matrix;

[0018] Suppose the coated target has X sub-regions, then the global RWG-MR transformation matrix is The matrix blocks on its main diagonal are successively The remaining part is an all-zero matrix.

[0019] Furthermore, in step 6, the Robin transmission condition is specifically:

[0020] Suppose the coated target (composite target) consists of a closed dielectric body and a closed metal body. Therefore, the space is decomposed into three sub-regions: free space Ω0, dielectric sub-region Ω1, and metal sub-region Ω2. The boundary of sub-region Ω m is The unit normal vector of the inner normal is n m , and the contact surface between sub-regions m≠n. On , the equivalent current J m and the equivalent magnetic current M m are defined. On , the equivalent current J2 is defined;

[0021] In order to ensure the continuity of the tangential electromagnetic field between sub-regions and construct an LCMT-DDM equation that can be symmetrized, the Robin transmission conditions (RTCs) independent of Ω2 are set as:

[0022]

[0023] where m = {0, 1} ∩ n = {0, 1} ∩ {m≠n}, and r represents the field point;

[0024] The Robin transmission conditions (RTCs) related to Ω2 are:

[0025]

[0026] Among them, m = {0, 1}, and r represents the field point.

[0027] Furthermore, in step 6, the symmetrization process is as follows:

[0028] In the impedance matrix, multiply the matrix block containing the integral operator by the imaginary number ±j, and multiply the sparse matrix block containing the inner product of the normal electromagnetic current by the imaginary number ±j;

[0029] In the unknown coefficient vector, multiply the magnetic current vector by the imaginary number j;

[0030] In the excitation vector, multiply the magnetic field vector by the imaginary number j;

[0031] Symmetrizing the LCMT-DDM linear equation can reduce the memory consumption of the matrix by nearly half and reduce the memory requirement.

[0032] Furthermore, the specific process of step 7 is as follows:

[0033] Let the impedance matrix obtained by discretely symmetrizing the LCMT-DDM equation with the RWG basis be Z RWG , C be the unknown coefficient vector, and V be the excitation vector. Then the linear equation system is Z RWG ·C = V;

[0034] Multiply Z by the global RWG-MR transformation matrix RWG and its transpose matrix to obtain the MR basis impedance matrix

[0035]

[0036] Select the elements on the diagonal of Z MR , take the reciprocal of the square root of the element value, and construct a diagonal matrix D -1 / 2 with the same dimension size; then use D -1 / 2 to perform diagonal preprocessing on the MR basis matrix equation to obtain the MR-LCMT-DDM equation as:

[0037]

[0038] Among them, is the unknown coefficient vector of the multi-resolution preprocessing;

[0039] Use the restarted generalized minimum residual method (GMRES) to iteratively solve the equation to obtain Then the original unknown coefficient vector C is: For calculating the electromagnetic scattering of a coated target.

[0040] It should be noted that the core creation of the present invention lies in: introducing multi-resolution (MR) preconditioning on the basis of the local coupling multitrace domain decomposition method (LCMT-DDM). First, new Robin transmission conditions (RTCs) are set, and based on this, the LCMT-DDM equation is constructed; then the LCMT-DDM equation is symmetrized, and further the MR-LCMT-DDM equation is constructed; finally, the equation is solved to obtain the unknown coefficient vector, and then the electromagnetic scattering of the coated target is calculated. Among them, the basic theory of the local coupling multitrace domain decomposition method (LCMT-DDM) is well-known prior art in the field, and the present invention will not elaborate further. For reference, see the literature "R. Zhao, Y. Chen, X.-M. Gu, Z. Huang, H. Bagci, and J. Hu, “A local coupling multitrace domain decomposition method for electromagnetic scattering from multilayered dielectric objects,” IEEE Trans. Antennas Propag., vol. 68, no. 10, pp. 7099-7108, 2020", "R. Zhao, P. Li, J. Hu, and H. Bagci, “A multitrace surface integral equation method for PEC / dielectric composite objects,” IEEE Antennas Wireless Propag. Lett., vol. 20, no. 8, pp. 1404-1408, 2021", "F. P. Andriulli, F. Vipiana, and G. Vecchi, “Hierarchical bases for nonhierarchic 3-D triangular meshes,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2288-2297, 2008", "F. Vipiana and G.Vecchi, “Anovel, symmetrical solenoidal basis for the MoM analysis of closed surfaces,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 1294 - 1299, 2009” and “F. Vipiana, P. Pirinoli, and G. Vecchi, “A multiresolution method of moments for triangular meshes,” IEEE Trans. Antennas Propag., vol. 53, no. 7, pp. 2247 - 2258, 2005”.

[0041] Based on the above technical solutions, the beneficial effects of the present invention are as follows:

[0042] The present invention provides a method for simulating electromagnetic scattering of coated aircraft based on multiresolution preprocessing, which is used to calculate the electromagnetic scattering of composite targets. Compared with the traditional local coupling domain decomposition method, the proposed symmetrization method can reduce the memory requirement by about half, and the matrix property can be further improved through multiresolution preprocessing, significantly accelerating the iterative convergence without affecting the numerical accuracy. Description of the Drawings

[0043] Figure 1 It is a geometric model diagram of a coated cube in an embodiment of the present invention.

[0044] Figure 2 It is an aggregated mesh diagram generated by MR preprocessing for four sub - regions in an embodiment of the present invention.

[0045] Figure 3 It is an iterative error diagram of GMRES(300) for a coated cube in an embodiment of the present invention.

[0046] Figure 4 It is a bistatic RCS diagram of a coated cube in an embodiment of the present invention. Detailed Embodiment

[0047] To make the objectives, technical solutions, and beneficial effects of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and embodiments.

[0048] This embodiment provides a method for simulating electromagnetic scattering of coated aircraft based on multiresolution preprocessing. Taking the electromagnetic scattering of a coated cube as an example, the bistatic radar cross section (RCS) is calculated. The specific steps are as follows:

[0049] Step 1. The geometric model of the coated cube is as Figure 1 shown. The thickness of the outermost dielectric coating is 50 mm, and the relative permittivity is ε r = 9.0, and the relative permeability is μ r = 1.0; the thickness of the middle dielectric coating is 50 mm, and the relative permittivity is ε r = 4.0, and the relative permeability is μ r = 1.0; the side length of the internal metal cube is 200 mm;

[0050] LCMT-DDM decomposes the space into four closed sub-regions according to the material properties: (1) free space, (2) the outermost dielectric coating, (3) the middle dielectric coating, (4) the metal cube; assume that the plane wave (E i , H i ) is incident along the -z axis, the frequency is 100 MHz, and the wavelength in the outermost coating is λ d ; use conformal triangular meshes to discretize the surfaces of each sub-region, select λ d / 45 as the average meshing size, and the total number of elements in the four sub-regions are 2484, 3972, 2508, and 1020 respectively; define the electromagnetic current RWG basis functions in the triangular element pairs, and the total number of unknowns is 28422;

[0051] Step 2. For each sub-region, use the mesh aggregation scheme and aggregate once to aggregate the first-layer triangular elements into the second-layer irregularly shaped macro-elements, obtaining a set of two-layer meshes; the aggregated mesh diagrams of the four sub-regions generated by the MR preprocessing are as Figure 2 shown, and each gray level represents a macro-element;

[0052] Step 3. For each sub-region, define the gRWG basis in the macro-element pairs, and use the charge conservation of the inter-layer gRWG basis to represent the second-layer gRWG basis as a linear combination of the first-layer RWG basis;

[0053] Step 4. For each sub-region, use the singular value decomposition to decompose the first-layer RWG basis and the second-layer gRWG basis into curl bases and divergence-free bases respectively, and the obtained results are the first-layer and second-layer MR basis functions;

[0054] Step 5. Use the recurrence relation to generate the global transformation matrix that converts the first-layer RWG basis to all the MR bases of the first two layers The matrix blocks on the main diagonal are successively and the rest are all-zero matrices;

[0055] Step 6. Set the Robin transmission conditions, construct the LCMT-DDM linear equation, and symmetrize the LCMT-DDM linear equation;

[0056] Step 7. Multiply both sides of the symmetrized LCMT-DDM equation by and combine diagonal preconditioning to obtain the MR-LCMT-DDM equation; use the restarted GMRES iteration to solve the equation, and then calculate the bistatic RCS of the target as follows:

[0057] Suppose the impedance matrix obtained by discretizing the symmetrized LCMT-DDM equation with RWG basis is Z RWG , C is the vector of unknown coefficients, V is the excitation vector, and the linear equation system is Z RWG ·C = V; use the global RWG-MR transformation matrix and its transpose matrix to multiply with Z RWG to obtain the MR basis impedance matrix Use the reciprocal of the square root of the elements on the diagonal of Z MR to construct the diagonal matrix D -1 / 2 , and then perform diagonal preconditioning on the MR basis matrix equation to obtain the MR-LCMT-DDM equation as follows

[0058]

[0059] Use the restarted generalized minimal residual algorithm (GMRES(300)) with m = 300, set 0.001 as the iteration convergence threshold, and iteratively solve the equation to obtain the vector Then the vector of unknown coefficients Calculate the bistatic RCS of HH polarization using C.

[0060] In this embodiment, taking LCMT-DDM and the diagonally preconditioned LCMT-DDM (DP-LCMT-DDM) as comparative examples, the residual errors of each iteration of LCMT-DDM, DP-LCMT-DDM, and MR-LCMT-DDM are as Figure 3 shown; the condition number of the LCMT-DDM impedance matrix is 16495.3, and it is required to iterate 876 times to reach the convergence threshold of 0.001; the condition number of the DP-LCMT-DDM impedance matrix is 4344.4, reduced to 536 iterations, having a certain ability to promote iteration convergence; while the condition number of the MR-LCMT-DDM impedance matrix is 3190.6, only 238 iterations are required, which can effectively improve the iteration convergence characteristics of the system; thus, it can be seen that the impedance matrix of LCMT-DDM is no longer a well-conditioned matrix under relatively dense meshing conditions, however, MR preconditioning can significantly accelerate iteration convergence, and the effect is better than that of DP. Then, using the software FEKO, for this coated cube, take λ dFor the dissection size of / 100, the total number of triangular elements is 26146, and the RCS is calculated; referring to the data of FEKO, the relative root-mean-square error (RMSE) of the RCS of LCMT-DDM is 0.0041, the RMSE of the RCS of DP-LCMT-DDM is 0.0033, and the RMSE of the RCS of MR-LCMT-DDM is 0.0038. The errors are all in the same order of magnitude, indicating similar precision; the bistatic RCS curve of the coated cube is as Figure 4 shown. The RCS of all three methods is in good agreement with the FEKO reference results; thus, it can be seen that the use of the preprocessing method will not significantly change the numerical calculation precision.

[0061] As described above, it is only the specific implementation manner of the present invention. Any feature disclosed in this specification, unless specifically described, can be replaced by other equivalent or similar-purpose alternative features; all the disclosed features, or all the steps in all the methods or processes, except for the mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for simulating electromagnetic scattering of coated aircraft based on multi-resolution preprocessing, characterized in that: The following steps are involved: Step 1. Decompose the coating target into multiple closed sub-regions with uniform materials, discretize the surface of each sub-region using a conformal triangle mesh, and define the RWG basis function within the discretized triangle unit pairs; Step 2. For each sub-area, use the grid aggregation method to generate irregularly shaped macro units and construct a stacked grid; Step 3. For each sub-area, define the gRWG basis function within the macro unit pair, and use the charge conservation of the inter-layer gRWG basis to express the gRWG basis of the lth layer as a linear combination of the gRWG basis of the l-1th layer, l = 2, 3, ..., L, L is the number of layers of the stacked grid; Step 4. For each sub-region, use singular value decomposition to decompose the gRWG basis of the lth layer into a curl basis and a curl-free basis, and the result is the MR basis function of the lth layer; Step 5. Generate a global RWG-MR transformation matrix that transforms the first-layer RWG basis into all MR bases of the first L layers using the recursive relationship; Step 6. Set the Robin transmission condition, construct the LCMT-DDM linear equation, and symmetrize the LCMT-DDM linear equation; Step 7. Based on the symmetric LCMT-DDM equation, the MR-LCMT-DDM equation is constructed using the global RWG-MR transformation matrix, and the electromagnetic scattering of the coated target is calculated.

2. The method for simulating electromagnetic scattering of a coated aircraft based on multi-resolution preprocessing according to claim 1, characterized in that: The specific process of step 5 is: In the nth subarea, let is the current gRWG-MR conversion matrix of the lth layer, is the gRWG-based reconstruction matrix of the current between the l-1th layer and the lth layer, is the conversion matrix between the first layer current RWG basis and the first l layers of all current MR basis, then It is expressed as: In the nth subarea, let is the conversion matrix between the first layer of magnetic flux RWG basis and all the magnetic flux MR basis of the first l layers. If the nth sub-area is a medium or free space, then If the nth sub-region is a metal sub-region, then is an empty matrix; set up is the conversion matrix between the first layer of electromagnetic current RWG basis of the nth sub-area and the first l layers of all electromagnetic current MR basis, and the matrix blocks on the main diagonal are and The rest is an all-zero matrix; Assuming that the coating target has X sub-areas, the global RWG-MR conversion matrix is The matrix blocks on the main diagonal are The rest is an all-zero matrix.

3. The method for simulating electromagnetic scattering of a coated aircraft based on multi-resolution preprocessing according to claim 1, characterized in that: In step 6, the Robin transmission conditions are as follows: The space is decomposed into three sub-regions: free space Ω0, dielectric sub-region Ω1, metal sub-region Ω2, and sub-region Ω m The boundary is The inner normal unit vector is n m , the contact surface between the sub-regions exist The equivalent current J is defined above m and the equivalent magnetic current M m ,exist The equivalent current J2 is defined above; The Robin transmission condition that is independent of Ω2 is set as: Wherein, m={0,1}∩n={0,1}∩{m≠n}, r represents the field point; The Robin transmission condition related to Ω2 is: J m -n m ×M m +J2=0,r∈Γ m2 n m ×J m +M m -n2×J2=0,r∈Γ m2 , J2+J m +n m ×M m =0,r∈Γ 2m Wherein, m={0,1}, and r represents a field point.

4. The method for simulating electromagnetic scattering of coated aircraft based on multi-resolution preprocessing according to claim 1, characterized in that: In step 6, the symmetrization process is: In the impedance matrix, the integral operator The matrix block of is multiplied by the imaginary number ±j, and the sparse matrix block containing the inner product of the normal electromagnetic current is multiplied by the imaginary number ±j; In the unknown coefficient vector, multiply the magnetic current vector by the imaginary number j; In the excitation vector, the magnetic field vector is multiplied by the imaginary number j.

5. The method for simulating electromagnetic scattering of coated aircraft based on multi-resolution preprocessing according to claim 1, characterized in that: The specific process of step 7 is: Assume that the impedance matrix obtained by discretizing the LCMT-DDM equation of the RWG basis is Z RWG , C is the unknown coefficient vector, V is the excitation vector; Using the global RWG-MR transformation matrix Construct the MR-based impedance matrix: Select Z MR For the elements on the diagonal, take the reciprocal of the square root of the element value and construct a diagonal matrix D with the same dimension size -12 ; Use D again -12 After diagonal preprocessing of the MR basis matrix equation, the MR-LCMT-DDM equation is obtained as follows: in, is the unknown coefficient vector of multi-resolution preprocessing; The restarted generalized minimum residual algorithm is used to iteratively solve the equation to obtain Then the original unknown coefficient vector C is: Used to calculate electromagnetic scattering from coated targets.

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