An internal and external solution method for obtaining electromagnetic scattering characteristics of cavity targets

Abstract

The present invention discloses an internal and external solution method for obtaining the electromagnetic scattering characteristics of a cavity-containing target, which relates to the field of electromagnetic fields and microwave technology. The method comprises the following steps: decomposing the cavity-containing structure into two parts, the cavity interior and the cavity exterior, establishing a Huygens equivalent surface on the aperture surface of the cavity interior and the cavity exterior; utilizing the continuity conditions of the current and electromagnetic field to ensure the consistency of the electromagnetic modeling solution before and after the internal and external partitions; selecting different solution methods for the internal and external structures respectively, using a cascade method combined with a fast direct solution technology for calculation inside the cavity, and using a parallel multi-layer fast multipole algorithm for calculation outside the cavity; finally, using an iterative algorithm to iteratively solve the internal and external regions to obtain the RCS scattering characteristics of the entire cavity-containing structure that meet the calculation requirements. The present invention improves the flexibility of electromagnetic scattering modeling of cavity-containing targets, solves the internal resonance problem caused by the cavity structure, and significantly improves the ability to solve electromagnetic scattering of cavity-containing targets.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic fields and microwave technologies, and in particular to an internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity-containing target. Background Art

[0002] Cavity structures are a common type of structure found in modern weapon systems. Examples include aircraft air intakes, radar pods, surface slots, and small holes. Therefore, most military targets can be considered cavity-containing targets. Cavity structures are a special type of scatterer, typically acting as a strong scattering source when illuminated by radar waves. This is generally believed to be caused by multiple reflections within the cavity. However, the scattering characteristics of a cavity structure are actually dependent on the cavity's aperture, shape, size, inner wall shape, depth, and material, and external support, resulting in a highly complex scattering mechanism. For various weapon systems containing cavity structures, their strong scattering properties pose a challenge to their stealth design. Therefore, research on precise modeling and efficient computational techniques for electromagnetic scattering from cavity-containing targets will help improve target stealth design capabilities, shorten stealth design research cycles, and save research funds, significantly contributing to the development of stealth technology.

[0003] For structures containing cavities, if the cavity aperture or depth is larger than the electromagnetic wavelength, the electromagnetic scattering process is much more complex than for targets without cavities. First, from the perspective of geometric optics, due to the complex internal shape of the cavity, the incident electromagnetic wave typically undergoes multiple reflections before finally exiting the cavity, and sometimes may never exit the cavity. This poses significant difficulties for high-frequency ray methods based on geometric optics to solve cavity scattering. Second, from the perspective of electromagnetic boundary integral equation theory, the cavity in the cavity-containing target exhibits near-resonant characteristics. This characteristic, similar to the internal resonance of a closed cavity, increases the condition number of the integral equation operator. Although choosing the appropriate type of integral equation, such as the mixed-field integral equation, can avoid spurious solutions, the high matrix condition number significantly reduces the convergence rate of the matrix iteration algorithm, seriously affecting the solution speed and computational accuracy of the electromagnetic scattering calculation for the cavity-containing target. How to improve the accuracy and computational efficiency of electromagnetic modeling of cavity targets has always been a difficult problem in the field of computational electromagnetics research. It also has a great impact on the stealth design of cavity weapon equipment targets. Therefore, it is very necessary to study electromagnetic modeling and numerical calculation techniques that can improve the computational efficiency of the electromagnetic scattering characteristics of cavity targets. Summary of the Invention

[0004] The present invention aims to provide an internal and external solution method for obtaining the electromagnetic scattering characteristics of a cavity target, so as to solve the problems of low efficiency and poor accuracy in the existing calculation of electromagnetic scattering of cavity targets.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] An internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity-containing target comprises the following steps:

[0007] S1, internal and external geometric partitioning of the cavity target;

[0008] S2. Solving the closed area inside the cavity: Using the cascade method and combining it with direct solution technology, the electromagnetic scattering inside the cavity is solved;

[0009] S3. Solution of cavity external system: For the cavity aperture external system, a rigorous surface integral equation method combined with a parallel multi-layer fast multipole algorithm is used to model and analyze the calculation;

[0010] S4. Establish transmission conditions on the aperture surface to ensure that the field distribution after partitioning is the same as the field distribution in the integrated modeling;

[0011] S5. Solve the scattering characteristics of the entire cavity structure: Use an iterative algorithm to iteratively solve the internal and external regions to obtain the RCS scattering characteristics of the entire cavity structure that meet the calculation requirements.

[0012] Furthermore, the step S1 specifically includes:

[0013] S101, dividing the cavity-containing target into two regions, an inner region and an outer region, according to the geometric structural characteristics of the target and the cavity, and setting an aperture plane between the inner and outer regions of the cavity;

[0014] S102, marking the geometric surfaces corresponding to the inner and outer regions of the cavity-containing structure, as well as the aperture surface. Preferably, the geometric surfaces of the inner and outer regions of the cavity, as well as the aperture surface, are marked by assigning numbers;

[0015] S103. Grid division is performed on the surfaces of the inner and outer regions. After the grid division is completed, the identification number of the surface region will be assigned to all grids contained in the region.

[0016] Furthermore, in step S2, for the inner domain with complex coupling relationship and poor matrix properties, the cascade method is selected and combined with the fast direct solution method to solve it, including the following steps:

[0017] S201, segmenting the internal geometric structure of the cavity;

[0018] S202. Based on the surface integral equation method, the aperture admittance matrix of each section of the cavity structure is discretely obtained;

[0019] S203, cascading the admittance matrices of each segment, using a direct solver to solve the inverse matrix of the admittance matrix, and obtaining the overall aperture admittance matrix of the cavity inner domain;

[0020] S204. Calculate the equivalent magnetic flux at the outlet diameter according to the generalized network formula and the equivalent principle, and finally calculate the scattering of the cavity inner domain.

[0021] Furthermore, in step S202, the aperture admittance matrix of the adjacent segmented cavity structure is expressed as

[0022] [a a ]=([A aa ]-[A ac ][A cc ] -1 [A ca ]) -1 ([B aa ]-[A ac ][A cc ] -1 [B ca ])[b a ]=[Y ap ][b a ]

[0023] Where [a] and [b] are the unknown surface magnetic field coefficient vector and the unknown surface equivalent magnetic current, A and B represent the impedance matrices of adjacent cavities, respectively. The subscript "a" represents the aperture surface part, and the subscript "c" represents the conductor wall part.

[0024] Furthermore, the step S3 specifically includes:

[0025] S301, establishing a surface integral equation for the area outside the cavity aperture. Based on the characteristics of the external area, an electric field integral equation (EFIE) or a hybrid field integral equation (CFIE) may be established and solved using a multi-layer fast multipole algorithm (MLFMA);

[0026] S302, discretizing the geometric structure surface of the external area using a triangular mesh, establishing a current basis function and performing three-dimensional spatial grouping using an octree grouping format;

[0027] S303, obtaining the coupling relationship between the sub-scatterers in the nearby groups by direct calculation;

[0028] S304, for the mutual coupling relationship between sub-scatterers in non-nearby groups, based on the tree structure, using multi-layer grouping, layer-by-layer aggregation, layer-by-layer transfer and layer-by-layer configuration;

[0029] S305. Use MPI combined with OpenMP hybrid parallel computing technology to accelerate the solution of the MLFMA algorithm.

[0030] Furthermore, the step S4 specifically includes:

[0031] S401. Establishing a Huygens equivalent surface at the cavity aperture surface;

[0032] S402. Establishing the transmission conditions of the electromagnetic field based on the field transfer coupling model.

[0033] Furthermore, in step S5, the Gauss-Seidel iteration technique is used to iteratively solve the internal and external systems.

[0034] The principle and beneficial effects of this technical solution:

[0035] The present invention decomposes the original cavity structure problem into two sub-areas, the inner domain and the outer domain, by introducing an equivalent aperture surface. The coupling between different sub-areas is achieved through the transmission condition matrix on the equivalent aperture surface, ensuring the decoupling of the inner domain and the outer domain. The inner domain scattering problem with complex coupling relationship and poor matrix properties is divided into multiple independent small problems, which are solved by the cascade method combined with the fast direct solution method, thereby greatly reducing the amount of calculation; and for the outer domain with better matrix properties, an efficient iterative algorithm based on parallel MLFMA is used to solve it, thereby maximizing the efficiency of solving the sub-area problem. The hybrid solution technology based on the internal-external system can better play the advantages of the fast direct algorithm and the iterative algorithm, and provides an efficient and stable way to solve complex cavity targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a technical scheme for solving the internal and external electromagnetic scattering of cavity targets;

[0037] Figure 2 Schematic diagram of the decomposition of the internal and external systems of the cavity target;

[0038] Figure 3 It is a segmented schematic diagram of the cavity cascade method;

[0039] Figure 4 Schematic diagram of the admittance matrix of adjacent segmented cavity structures;

[0040] Figure 5 Schematic diagram of multi-layer sparse decomposition of direct solution technology matrix;

[0041] Figure 6 Schematic diagram of the mutual coupling between neutron scatterers in the multi-layer fast multipole method;

[0042] Figure 7 This is the flow chart of the Gauss-Seidel iterative algorithm;

[0043] Figure 8 Schematic diagram of the carrier target with an air inlet cavity structure. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] The module block diagram of the cavity target scattering modeling and calculation method based on the internal and external solution technology is as follows Figure 1 The core functions and working mechanisms are as follows:

[0046] S1, inner and outer partitions of the cavity-containing structure;

[0047] The cavity target is decomposed into two regions, inner and outer, at the cavity aperture surface. The purpose of partitioning is to enclose the internal structure of the cavity into an independent closed solution region. The specific steps include:

[0048] S101, according to the geometric structure characteristics of the target and the cavity, the cavity-containing target is divided into two areas, the inner cavity area and the outer cavity area, and the aperture surface is set between the inner and outer cavity areas, such as Figure 2 As shown;

[0049] S102, marking the geometric surfaces corresponding to the inner and outer regions of the cavity-containing structure, as well as the aperture surface. Preferably, the geometric surfaces of the inner and outer regions of the cavity, as well as the aperture surface, are marked by assigning numbers;

[0050] S103. Grid division is performed on the surfaces of the inner and outer regions. After the grid division is completed, the identification number of the surface region will be assigned to all grids contained in the region.

[0051] For any cavity structure, it is necessary to rationally select the partitioning aperture surface to ensure the relative independence of the inner and outer domain structures and avoid the existence of structural singularities on the partitioning aperture surface. The inner and outer domains are connected by the continuity of the field on the aperture surface, that is, a generalized network formula is established to connect the inner and outer domain problems. It is expressed as follows:

[0052] {[Y in ]+[Y out ]}[b]=[I]

[0053] Among them [Y in ] is the solution of the admittance matrix of the inner domain, [Y out ] is the admittance matrix of the external domain, [I] is the incident source vector on the aperture surface, and [b] is the equivalent magnetic flux vector of the unknown aperture surface.

[0054] S2. Solution inside the closed cavity: Use the cascade method combined with direct solution technology to solve the electromagnetic scattering inside the cavity.

[0055] For the inner domain with complex coupling relationship and poor matrix properties, the cascade method is selected and combined with the fast direct solution method to solve it. The specific steps include the following:

[0056] S201, decompose the internal geometric structure of the cavity into several segments along the length direction of the cavity, such as Figure 3Each segment is surrounded by the cavity wall and the apertures at both ends to form a closed boundary, and the integral equation is established on the closed boundary.

[0057] S202, based on the surface integral equation method, the aperture admittance matrix [Y ap ].like Figure 4 As shown, the aperture admittance matrix of two adjacent segmented cavity structures in area A and area B is expressed as

[0058] [a a ]=([A aa ]-[A ac ][A cc ] -1 [A ca ]) -1 ([B aa ]-[A ac ][A cc ] -1 [B ca ])[b a ]=[Y ap ][b a ]

[0059] Where [a] and [b] are the unknown surface magnetic field coefficient vector and the unknown surface equivalent magnetic current, A and B represent the impedance matrices of cavity A and B respectively, the subscript "a" represents the aperture part, and the subscript "c" represents the conductor wall part. [Y ap ] is the aperture admittance matrix, which links the aperture equivalent magnetic current with the aperture magnetic field.

[0060] S203. Cascading each segment to obtain the overall aperture admittance matrix within the cavity: During the calculation process, a fast and direct technique, the interpolation decomposition method, is used to invert the admittance matrix. The interpolation decomposition method is based on the linear relationship between the basis function groups. Interpolation decomposition is used to extract the largest linearly independent group of the basis function group. Its far-field matrix can be coupled by corresponding selected basis functions. Since the number of selected basis functions is much smaller than the entire basis function group, the sparse representation of the impedance matrix is:

[0061]

[0062] Where L, S, R and D all have sparse matrix forms, such as Figure 5 After obtaining the aperture admittance matrix of each segment, the cascade algorithm is used to connect them to obtain the generalized admittance matrix of the entire cavity aperture surface.

[0063] S204. Calculate the equivalent magnetic flux at the outlet diameter according to the generalized network formula and the equivalent principle, and finally calculate the scattering of the cavity inner domain.

[0064] S3. Numerical solution of the cavity external system: The cavity external system is still treated as an independent closed structure, and a rigorous surface integral equation method combined with a parallel multi-layer fast multipole algorithm is used for modeling and calculation. The specific steps include:

[0065] S301, establishing a surface integral equation for the area outside the cavity aperture. Based on the characteristics of the external area, an electric field integral equation (EFIE) or a hybrid field integral equation (CFIE) may be established and solved using a multi-layer fast multipole algorithm (MLFMA);

[0066] S302, discretizing the geometric structure surface of the external area using a triangular mesh, establishing a current basis function and performing three-dimensional spatial grouping using an octree grouping format;

[0067] S303, obtaining the coupling relationship between the sub-scatterers in the nearby groups by direct calculation;

[0068] S304, for the mutual coupling relationship between sub-scatterers in non-nearby groups, based on the tree structure, multi-layer grouping, layer-by-layer aggregation, layer-by-layer transfer and layer-by-layer configuration are used to achieve it, such as Figure 6 As shown;

[0069] S305. Use MPI combined with OpenMP hybrid parallel computing technology to accelerate the solution of the MLFMA algorithm.

[0070] S4. Establish transmission conditions on the aperture surface to ensure that the field distribution after partitioning is the same as the field distribution in the integrated modeling;

[0071] S401. Establish a Huygens equivalent surface at the cavity aperture surface. Surface currents and surface magnetic fluxes exist inside and outside the Huygens surface.

[0072] S402, establishing a transmission condition of the electromagnetic field based on a field transfer coupling model;

[0073] According to the continuity conditions of the electric field and magnetic field, the equivalent current and equivalent magnetic current on the equivalent surface meet the transmission conditions:

[0074]

[0075] From the field-source relationship, we can further obtain:

[0076]

[0077] Among them E sca (r) and H sca (r) represents the scattered field, η0 represents the free space wave impedance, and the L operator and K operator are defined as:

[0078]

[0079] in represents the free space Green's function, and k0 represents the free space wave number.

[0080] S5, internal and external iterative solution

[0081] The Gauss-Seidel iteration technique is used to iteratively solve the internal and external systems. The specific flow chart is as follows: Figure 7 When the solutions of the internal and external systems meet the convergence conditions, they can be used to solve the scattered field distribution of the entire cavity target.

[0082] The specific implementation process is as follows:

[0083] like Figure 8 The target is shown as a carrier with an air inlet cavity. The target is 3.80 m long, the cavity is approximately 2.46 m long, and the aperture dimensions are 0.42 m x 0.35 m. The scattering characteristics of the carrier with the cavity were investigated when a 10 GHz plane wave was irradiated from the cavity aperture.

[0084] Step 1: Use the internal and external solution technology proposed in the present invention to simulate the electromagnetic scattering characteristics. First, geometrically partition the target, and divide the geometric surface of the cavity-containing carrier target into the area inside the cavity and the area outside the cavity.

[0085] Step 2: Use the cascade method and its direct solver to solve the interior of the closed cavity.

[0086] Step 3: Use parallel MLFMA technology to iteratively solve the cavity external system.

[0087] Step 4: Establish transmission conditions on the aperture surface between the inner and outer areas.

[0088] Step 5: Use the Gauss-Seidel iterative algorithm to iteratively solve the inner and outer regions to obtain the RCS scattering characteristics of the entire cavity-containing low-scattering carrier structure.

[0089] Step 6: Comparative analysis of the iterative convergence of the internal / external solver and the integrated modeling solver: Setting the convergence to a relative error of 0.001, the traditional integrated modeling solver requires 251 iterations, while the internal / external solver of the present invention requires only 36. This shows that the iterative convergence of the internal / external solver of the present invention is superior to that of the integrated modeling solver.

[0090] The above is only an embodiment of the present invention, and the common knowledge such as the specific technical solutions and / or characteristics in the solution are not described in detail here. It should be pointed out that for those skilled in the art, without departing from the technical solution of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the description can be used to interpret the content of the claims.

Claims

1. An internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target, characterized in that: The steps include: S1, internal and external geometric partitioning of the cavity target; S2. Solving the closed region inside the cavity: For the inner region with complex coupling relationships and poor matrix properties, the cascade method is used in combination with direct solution technology to solve the electromagnetic scattering inside the cavity, including the following steps: S201, segmenting the internal geometric structure of the cavity; S202. Based on the surface integral equation method, the aperture admittance matrix of each section of the cavity structure is discretely obtained; S203, cascading the admittance matrices of each segment, using a direct solver to solve the inverse matrix of the admittance matrix, and obtaining the overall aperture admittance matrix of the cavity inner domain; S204, calculating the equivalent magnetic flux at the outlet according to the generalized network formula and the equivalent principle, thereby finally calculating the scattering of the cavity inner region; S3. Solution of cavity external system: For the cavity aperture external system, a rigorous surface integral equation method combined with a parallel multi-layer fast multipole algorithm is used to model and analyze the calculation; S4. Establish transmission conditions on the aperture surface to ensure that the field distribution after partitioning is the same as the field distribution in the integrated modeling; S5. Solve the scattering characteristics of the entire cavity structure: Use an iterative algorithm to iteratively solve the internal and external regions to obtain the RCS scattering characteristics of the entire cavity structure that meet the calculation requirements.

2. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 1, characterized in that: The step S1 specifically includes: S101, dividing the cavity-containing target into two regions, an inner region and an outer region, according to the geometric structural characteristics of the target and the cavity, and setting an aperture plane between the inner and outer regions of the cavity; S102, marking the geometric surfaces corresponding to the inner and outer regions of the cavity-containing structure, as well as the aperture surface, by assigning numbers to the geometric surfaces of the inner and outer regions of the cavity, as well as the aperture surface; S103. Grid division is performed on the surfaces of the inner and outer regions. After the grid division is completed, the identification number of the surface region will be assigned to all grids contained in the region.

3. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 1, characterized in that: In step S202, the aperture admittance matrix of the adjacent segmented cavity structure is expressed as [a a ]=([A aa ]-[A ac ][A cc ] -1 [A ca ]) -1 ([B aa ]-[A ac ][A cc ] -1 [B ca ])[b a ]=[Y ap ][b a ] Where [a] and [b] are the unknown surface magnetic field coefficient vector and the unknown surface equivalent magnetic current, A and B represent the impedance matrices of adjacent cavities, respectively. The subscript "a" represents the aperture surface, and the subscript "c" represents the conductor wall.

4. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 1, characterized in that: The step S3 specifically includes: S301, establishing a surface integral equation for the area outside the cavity aperture. Based on the characteristics of the external area, an electric field integral equation (EFIE) or a hybrid field integral equation (CFIE) may be established and solved using a multi-layer fast multipole algorithm (MLFMA); S302, discretizing the geometric structure surface of the external area using a triangular mesh, establishing a current basis function and performing three-dimensional spatial grouping using an octree grouping format; S303, obtaining the coupling relationship between the sub-scatterers in the nearby groups by direct calculation; S304, for the mutual coupling relationship between sub-scatterers in non-nearby groups, based on the tree structure, using multi-layer grouping, layer-by-layer aggregation, layer-by-layer transfer and layer-by-layer configuration; S305. Use MPI combined with OpenMP hybrid parallel computing technology to accelerate the solution of the Multi-Level Fast Multipole Algorithm (MLFMA).

5. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 1, characterized in that: The step S4 specifically includes: S401. Establishing a Huygens equivalent surface at the cavity aperture surface; S402. Establishing the transmission conditions of the electromagnetic field based on the field transfer coupling model.

6. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 1, characterized in that: In step S5, the Gauss-Seidel iteration technique is used to iteratively solve the internal and external systems.

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