Internal and external solving method for obtaining electromagnetic scattering characteristics of target with cavity

Abstract

The invention discloses an internal and external solving method for obtaining electromagnetic scattering characteristics of a cavity-containing target, and relates to the technical field of electromagnetic fields and microwaves, and the method comprises the following steps: decomposing a cavity-containing structure into a cavity internal part and a cavity external part, and building a Huygens equivalent surface on the aperture surface of the boundary between the cavity internal part and the cavity external part; the consistency of electromagnetic modeling solutions before and after internal and external partitioning is ensured by utilizing continuity conditions of current and an electromagnetic field; different solving methods are selected in the inner structure and the outer structure respectively, the interior of the cavity is calculated by combining a cascade method with a rapid direct solving technology, the exterior of the cavity is calculated by adopting a parallel multilayer rapid multi-pole algorithm, and finally, iterative solving of the inner region and the outer region is carried out by utilizing an iterative algorithm, so that the RCS scattering characteristic of the whole cavity-containing structure meeting the calculation requirement is obtained. According to the method, the flexibility of electromagnetic scattering modeling of the target with the cavity is improved, the problem of internal resonance caused by a cavity structure is solved, and the electromagnetic scattering solving capability of the target with the cavity is remarkably improved.

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 the electromagnetic scattering characteristics of cavity-containing targets. Background Art

[0002] Cavity structures are a type of structure widely present in modern weapon systems. For example, aircraft intakes, radar compartments, surface slots, and small holes are all common cavity structures. Therefore, most military targets can be regarded as cavity-containing targets. Cavity structures are a special type of scatterer. Under the irradiation of radar waves, they usually appear as a very strong scattering source, generally considered to be generated by multiple internal reflections within the cavity. In fact, however, the scattering characteristics of cavity structures are related to the aperture shape, size, inner wall shape, depth, material of the cavity, as well as the external carrier of the cavity, and the scattering mechanism is very complex. For various weapon systems with cavity structures, the strong scattering characteristics of the cavity structures pose challenges to their stealth design. Therefore, carrying out research on accurate electromagnetic scattering modeling and efficient calculation technologies for cavity-containing targets will help improve the stealth design ability of targets, shorten the research cycle of stealth design, and save research funds, which is of great significance for the development of stealth technologies.

[0003] For cavity-containing structures, when the cavity aperture size or depth is greater than the electromagnetic wavelength, their electromagnetic scattering process is much more complex than that of cavity-free targets. First, from the perspective of geometric optics, due to the complex internal shape of the cavity, incident electromagnetic waves generally have to undergo multiple reflections back and forth within the cavity before finally exiting the cavity, and sometimes they may even never exit the cavity. This will bring great difficulties to solving cavity scattering using the high-frequency ray method based on geometric optics. Second, from the perspective of the electromagnetic field boundary integral equation theory, the cavity in a cavity-containing target has near-resonant characteristics. This characteristic is similar to the internal resonance characteristic of a closed cavity, which will increase the condition number of the integral equation operator. Although choosing an appropriate type of integral equation such as the mixed-field integral equation can avoid the generation of spurious solutions, due to the always high condition number of the matrix, the convergence speed of the matrix iteration algorithm drops significantly, seriously affecting the solution speed and calculation accuracy of the electromagnetic scattering calculation of the entire cavity-containing target. How to improve the electromagnetic modeling accuracy and calculation efficiency of cavity-containing targets has always been a difficult problem in the field of computational electromagnetics, and it also has a greater impact on the stealth design of cavity-containing weapon equipment targets. Therefore, it is very necessary to study electromagnetic modeling and numerical calculation technologies that can improve the calculation efficiency of the electromagnetic scattering characteristics of cavity-containing 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 cavity-containing targets to solve the problems of low calculation efficiency and poor accuracy in the existing electromagnetic scattering calculation of cavity-containing targets.

[0005] To achieve the above object, the present invention provides the following technical solutions:

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

[0007] S1. Internal and external geometric partitioning of the cavity-containing target;

[0008] S2. Solving the closed region inside the cavity: Using the cascading method and combining with the direct solution technique to solve the electromagnetic scattering inside the cavity;

[0009] S3. Solving the external system of the cavity: For the external system of the cavity aperture, adopting the strict surface integral equation method combined with the parallel multi-level fast multipole algorithm for modeling and analysis calculation;

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

[0011] S5. Solving the scattering characteristics of the overall cavity-containing structure: Using the iterative algorithm to perform iterative solution of the internal and external regions, and obtaining the RCS scattering characteristics of the overall cavity-containing structure that meet the calculation requirements.

[0012] Further, the step S1 specifically includes:

[0013] S101. According to the geometric structure characteristics of the target and the cavity, dividing the cavity-containing target into two regions, namely inside the cavity and outside the cavity, and setting an aperture surface between the inside and outside regions of the cavity;

[0014] S102. Identifying the geometric surfaces corresponding to the internal and external regions of the cavity-containing structure, as well as the aperture surface. Preferably, the geometric surfaces of the internal and external regions of the cavity and the aperture surface are identified by setting numbers;

[0015] S103. Performing mesh division on the surfaces of the internal and external regions. After the mesh dissection is completed, the identification numbers of the surface regions will be assigned to all the meshes included in that region.

[0016] Further, in step S2, for the internal domain with complex coupling relationships and poor matrix properties, the cascading method is selected and combined with the fast direct solution method for solution, including the following steps:

[0017] S201. Segmenting the internal geometric structure of the cavity;

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

[0019] S203. Cascading the admittance matrices of each segment, and using a direct solver to solve the inverse matrix of the admittance matrix to obtain the overall aperture admittance matrix of the internal domain of the cavity;

[0020] S204. Calculate the equivalent magnetic current on the aperture according to the generalized network formula and the equivalence principle, and finally calculate the scattering in the cavity domain.

[0021] Further, in step S202, the aperture admittance matrix of adjacent segmented cavity structures 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 vectors and the unknown surface equivalent magnetic currents respectively, 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] Further, the specific steps of step S3 include:

[0025] S301. Establish the surface integral equation for the external region of the cavity aperture. According to the characteristics of the external region, an electric field integral equation (EFIE) or a combined field integral equation (CFIE) can be established, and the multi-level fast multipole algorithm (MLFMA) is used for solving;

[0026] S302. Discretize the surface of the external region geometry with triangular meshes, establish current basis functions and perform three-dimensional spatial grouping in the form of an octree;

[0027] S303. The coupling relationship between sub-scatterers within the nearby group is obtained through direct calculation;

[0028] S304. For the coupling relationship between non-nearby group sub-scatterers, based on the tree structure, it is realized by using multi-level grouping, layer-by-layer aggregation, layer-by-layer transfer and layer-by-layer configuration;

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

[0030] Further, the specific steps of step S4 include:

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

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

[0033] Further, in step S5, the Gauss-Seidel iteration technique is adopted to perform iterative solutions for the internal and external systems.

[0034] Principle and beneficial effects of this technical solution:

[0035] In the present invention, by introducing an equivalent aperture surface, the original cavity-containing structure problem is decomposed into two sub-regions, namely the internal region and the external region. The coupling between different sub-regions is realized through the transmission condition matrix on the equivalent aperture surface, ensuring the decoupling of the internal region and the external region. The internal region scattering problem with complex coupling relationships and poor matrix properties is divided into multiple independent small problems, which are solved by the cascade method combined with a fast direct solution method, thus greatly reducing the amount of calculation; while for the external region with good matrix properties, an efficient iterative algorithm based on parallel MLFMA is adopted for solution, thereby maximizing the solution efficiency of the sub-region problems. The hybrid solution technique based on the internal-external system can better exert the advantages of the fast direct algorithm and the iterative algorithm, providing an efficient and stable approach for solving complex cavity targets. Description of the drawings

[0036] Figure 1 It is a technical solution diagram for internal and external solutions of electromagnetic scattering of cavity-containing targets;

[0037] Figure 2 Schematic diagram of the principle of decomposition of the internal and external systems of cavity-containing targets;

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

[0039] Figure 4 It is a schematic diagram of the admittance matrix of the adjacent segmented cavity structure;

[0040] Figure 5 It is a schematic diagram of the multi-layer sparse decomposition of the direct solution technology matrix;

[0041] Figure 6 It is a schematic diagram of the mutual coupling between sub-scatterers in the multi-layer fast multipole method;

[0042] Figure 7 It is a flow chart of the Gauss-Seidel iteration algorithm;

[0043] Figure 8 It is a schematic diagram of a carrier target with a cavity structure with an air inlet; Detailed implementation manners

[0044] The present invention will be described in detail below according to the 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 used to limit the present invention.

[0045] The block diagram of the scattering modeling and calculation method for cavity-containing targets based on the internal and external solution technology is as Figure 1 shown. The functions and working mechanisms of its core part are as follows:

[0046] S1. Internal and external partitioning of the cavity-containing structure;

[0047] At the aperture plane of the cavity, the cavity-containing target is decomposed into an internal and an external region. The purpose of the partitioning is to enclose the internal structure of the cavity as 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 an internal region inside the cavity and an external region outside the cavity, and an aperture plane is set between the internal and external regions of the cavity, as Figure 2 shown;

[0049] S102. Identify the geometric surfaces corresponding to the internal and external regions of the cavity-containing structure, as well as the aperture plane. Preferably, the geometric surfaces of the internal and external regions of the cavity and the aperture plane are identified by setting numbers;

[0050] S103. Mesh the surfaces of the internal and external regions. After the mesh dissection is completed, the identification numbers of the surface regions will be assigned to all the meshes contained in that region.

[0051] For any cavity structure, it is necessary to reasonably select the partitioning aperture plane to ensure the relative independence of the internal and external domain structures and avoid the singularity of the structure on the partitioning aperture plane. The internal and external domains are connected by the continuity of the fields on the aperture plane, that is, a generalized network formula is established to connect the internal and external domain problems. Its expression is as follows:

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

[0053] where [Y in is the solution of the admittance matrix of the internal domain, [Y out is the admittance matrix of the external domain, [I] is the incident source vector on the aperture plane, and [b] is the equivalent magnetic current vector of the unknown aperture plane.

[0054] S2. Solving inside the closed cavity: Use the cascading method and combine it with the direct solution technology to solve the electromagnetic scattering inside the cavity.

[0055] For the internal domain with complex coupling relationships and poor matrix properties, select the cascading method and combine it with the fast direct solution method to solve, which specifically includes the following steps:

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

[0057] S202. Based on the surface integral equation method, discretely obtain the aperture admittance matrix [Y ap of each cavity structure section. As Figure 4 shown, the aperture admittance matrices of two adjacent segmented cavity structures in area A and area B are 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 vector of unknown surface magnetic field coefficients and the unknown surface equivalent magnetic current respectively, A and B represent the impedance matrices of area A and area B of the cavity respectively, the subscript "a" represents the aperture surface part, and the subscript "c" represents the conductor wall part. [Y ap is the aperture admittance matrix, which relates the aperture equivalent magnetic current to the aperture magnetic field.

[0060] S203. Cascade each section to obtain the overall aperture admittance matrix of the inner domain of the cavity: In the calculation process, the fast direct technology - interpolation decomposition method needs to be used to invert the matrix of the admittance matrix. The interpolation decomposition method is based on the linear relationship between the basis function groups, and uses interpolation decomposition to extract the maximum linearly independent group of the basis function groups, and its far - field region matrix can be coupled through the 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 are all in the form of sparse matrices, as Figure 5 shown. After obtaining the aperture admittance matrix of each section, use the cascade algorithm to connect them to obtain the generalized admittance matrix of the entire cavity aperture surface.

[0063] S204. Calculate the equivalent magnetic current on the aperture according to the generalized network formula and the equivalence principle, and thus finally calculate the scattering in the inner domain of the cavity.

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

[0065] S301. Establish the surface integral equation for the external region of the cavity aperture. According to the characteristics of the external region, an electric field integral equation (EFIE) or a combined field integral equation (CFIE) can be established, and the multi-level fast multipole algorithm (MLFMA) is used for solution;

[0066] S302. Discretize the surface of the external region geometry using triangular meshes, establish current basis functions and perform three-dimensional spatial grouping, using the octree grouping form;

[0067] S303. The coupling relationship between sub-scatterers within the nearby group is obtained through direct calculation;

[0068] S304. For the coupling relationship between non-nearby group sub-scatterers, based on the tree structure, it is realized by using multi-level grouping, layer-by-layer aggregation, layer-by-layer transfer, and layer-by-layer configuration, as Figure 6 shown;

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

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

[0071] S401. Establish a Huygens equivalent surface at the cavity aperture surface, where there are surface currents and surface magnetic currents on the inner and outer sides of the Huygens surface;

[0072] S402. Establish the transmission condition of the electromagnetic field based on the field transfer coupling model;

[0073] From the continuity conditions of the electric and magnetic fields, it can be seen that the equivalent currents and equivalent magnetic currents on the equivalent surface satisfy the transmission conditions:

[0074]

[0075] From the field source relationship, it can be further obtained:

[0076]

[0077] where E sca (r) and H sca (r) represent the scattered fields, η 0 respectively represent the free space wave impedance, and the L operator and K operator are defined as:

[0078]

[0079] wherein represents the free-space Green's function, and k 0 respectively represent the free-space wavenumbers.

[0080] S5. Inner and outer iterative solution

[0081] The Gaussian-Seidel iterative technique is used for iterative solution of the inner and outer systems. The specific flow chart is as Figure 7 shown. After the solutions of the inner and outer systems satisfy the convergence conditions, they can be used to solve the scattering field distribution of the cavity-containing target as a whole.

[0082] The specific implementation process is as follows:

[0083] As Figure 8 shown, a certain carrier target with an air inlet cavity structure. The target is 3.80 m long, the cavity is about 2.46 m long, and the aperture size is 0.42 m × 0.35 m. The scattering characteristics of the cavity-containing carrier are investigated when a plane wave with a frequency of 10 GHz irradiates from the aperture direction of the cavity.

[0084] Step 1: Use the inner and outer solution technique proposed by the present invention for electromagnetic scattering characteristic simulation. First, the target is geometrically partitioned, and the geometric surface of the cavity-containing carrier target is divided into the inner cavity region and the outer cavity region.

[0085] Step 2: Solve the inside of the closed cavity using the cascading method and its direct solver.

[0086] Step 3: Use the parallel MLFMA technique to perform iterative solution of the outer cavity system.

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

[0088] Step 5: Use the Gaussian-Seidel iterative algorithm to perform iterative solution of the inner and outer regions, and obtain the RCS scattering characteristics of the cavity-containing low-scattering carrier structure as a whole.

[0089] Step 6: Compare and analyze the iterative convergence of the inner and outer solution techniques and the integrated modeling solution: Set the convergence to a relative error of 0.001. The traditional integrated modeling technique requires 251 iterations, while the inner and outer solution technique of the present invention only requires 36 iterations. It can be seen that the iterative convergence of the inner and outer solution technique proposed by the present invention is better than that of the integrated modeling solution technique.

[0090] The above are only embodiments of the present invention, and common general technical solutions and / or characteristics in the solutions are not described in detail herein. It should be noted that for those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicality of the patent. The protection scope required by this application shall be subject to the content of its claims, and the specific implementation manners and the like recorded in the specification 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 area inside the cavity: Using the cascade method and combining it with the direct solution technology, the electromagnetic scattering inside the cavity is solved; S3. Solution of the cavity external system: For the cavity aperture external system, a strict 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 inner and outer regions to obtain the RCS scattering characteristics of the entire cavity structure that meets 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 surface between the inner and outer regions of the cavity; S102, marking the geometric surfaces corresponding to the inner region and the outer region of the cavity-containing structure, and the caliber surface, preferably, marking the geometric surfaces of the inner and outer regions of the cavity, and the caliber surface by setting numbers; S103, meshing the surfaces of the inner and outer regions. After meshing is completed, the identification number of the surface region will be assigned to all the meshes 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 S2, the cascade method is selected for the inner domain with complex coupling relationship and poor matrix properties and solved in combination with the direct solver, including the following steps: S201, segmenting the internal geometric structure of the cavity; S202, based on the surface integral equation method, discretely obtain the aperture admittance matrix of each section of the cavity structure; S203, cascading each section of the admittance matrix, 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. Calculate the equivalent magnetic flux on the outlet diameter according to the generalized network formula and the equivalent principle, and finally calculate the scattering of the cavity inner domain.

4. The internal and external solution method for obtaining electromagnetic scattering characteristics of a cavity target according to claim 3, 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 part, and the subscript "c" represents the conductor wall part.

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 S3 specifically includes: S301, establishing a surface integral equation of the area outside the cavity aperture, and according to the characteristics of the external area, an electric field integral equation (EFIE) or a hybrid field integral equation (CFIE) can be established, and a multi-layer fast multipole algorithm (MLFMA) is used to solve it; S302, discretizing the geometric structure surface of the external area by using a triangular grid, establishing a current basis function and performing three-dimensional spatial grouping in an octree grouping form; S303, obtaining the coupling relationship between sub-scatterers in the nearby groups by direct calculation; S304, for the mutual coupling relationship between sub-scatterers in non-adjacent groups, based on the tree structure, using multi-layer grouping, layer-by-layer aggregation, layer-by-layer transfer and layer-by-layer configuration to achieve; S305. Use MPI combined with OpenMP hybrid parallel computing technology to accelerate the solution of the Multi-Level Fast Multipole Algorithm (MLFMA).

6. 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. Establish a Huygens equivalent surface at the cavity aperture surface; S402. Establishing the transmission condition of the electromagnetic field based on the field transfer coupling model.

7. 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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