A domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problem of large platform

Abstract

The application belongs to the field of electromagnetic numerical methods, and specifically provides a regional decomposition equivalent source-high frequency coupling solving method for electromagnetic radiation problems of an electric large platform. First, in the modeling stage, a multi-scale complex model is modeled separately, a virtual equivalent spherical surface is constructed for an antenna array, a regional decomposition algorithm is used to calculate the electromagnetic field on the spherical surface, a near-field equivalent source file containing three-dimensional field components of the spherical coordinate system is derived, and a spherical near-field equivalent source reflecting the array mutual coupling characteristics is constructed according to the equivalent principle. Then, the equivalent source file is imported into the physical optical simulation area of the electric large platform, the near-field incident electromagnetic field generated by the platform surface is calculated, and the induced current on the platform surface is quickly solved through the physical optical method. Finally, the direct radiation field of the equivalent source and the secondary radiation field of the platform induced current are superposed in the far field vector, and finally the rapid and high-precision electromagnetic simulation of the radiation characteristics of the antenna array on the electric large platform is realized.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic numerical methods, specifically providing a domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems of antenna arrays mounted on electrically large platforms. Background Technology

[0002] Array antennas possess advantages such as high gain, high directivity, and flexible beam control, and are widely used in radar detection, satellite communication, and other fields. In practical engineering applications, array antennas are usually not independent, but are tightly mounted on large-sized carriers (i.e., electrically large platforms) such as ships, aircraft, and spacecraft. The large electrically large platform structure will produce platform effects such as scattering, reflection, and blocking on the antenna's radiation characteristics (such as radiation pattern and gain). Therefore, in order to accurately evaluate the actual working performance of the antenna system, electromagnetic simulation analysis of the integrated antenna array-electrical large platform must be performed.

[0003] However, solving such multi-scale electromagnetic radiation problems faces enormous computational challenges. On the one hand, if traditional full-wave numerical algorithms (such as the method of moments and the finite element method) are used, the extremely large size of the electrically large platform leads to a huge number of unknowns, requiring a large amount of computation time and memory, and often exceeding the limits of computer hardware and thus becoming unsolvable. On the other hand, high-frequency asymptotic algorithms such as the physical optics method (PO) have extremely high computational efficiency in dealing with electrically large platform scattering problems, but these methods are based on approximations such as electromagnetic waves satisfying far-field approximation and tangential plane approximation, which cannot accurately handle the complex fine structure inside the array antenna and the real strong mutual coupling effect between antenna elements, resulting in distortion of array antenna calculations.

[0004] Therefore, how to organically combine high-precision numerical solutions for antenna arrays with high-efficiency high-frequency computation on the power-scale platform to achieve rapid and high-precision evaluation of the radiation characteristics of large-scale arrays on the power-scale platform is one of the current challenges in electromagnetic simulation technology research on the power-scale platform. Summary of the Invention

[0005] The purpose of this invention is to provide a domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems of electric power system platforms. This method addresses the problems of excessive computational resource consumption of full-wave algorithms and the inability of high-frequency algorithms to accurately handle the real mutual coupling effects inside the antenna array in existing integrated simulations of antenna arrays and electric power system platforms. In the simulation solution process, this invention uses domain decomposition technology to solve and export a spherical near-field equivalent source file containing three components of the electromagnetic field in spherical coordinates. Combined with physical optics methods to process the radiation of the platform's induced field, this effectively reduces simulation memory consumption and significantly improves solution efficiency.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems on open university platforms includes the following steps:

[0008] Step 1: Based on the engineering application scenario, independently construct a three-dimensional geometric model of the array antenna, denoted as the antenna model, as the full-wave solution region; independently construct a three-dimensional geometric model of the power grid platform, denoted as the platform model, as the physical optics (PO) region for high-frequency solution.

[0009] Step 2: In the full-wave solution domain, solve for the electric and magnetic fields on the radiation boundary of the antenna array based on the finite element domain decomposition method (FE-DDM);

[0010] Step 3: Construct an external virtual closed sphere that completely surrounds the antenna model as the near-field equivalent source sphere. Based on the electric and magnetic fields on the radiation boundary of the antenna array, perform near-field-near-field transformation using the Stratton-Chu integral equation to calculate the electric and magnetic fields on the near-field equivalent source sphere. Extract the electromagnetic field distribution of the sphere and export it as a near-field equivalent source file.

[0011] Step 4: Import the near-field equivalent source file to the predetermined position in the physical optics region, use the spatial octree to accelerate the model occlusion judgment, and identify and mark the bright area elements and dark area elements on the surface of the power platform.

[0012] Step 5: For the bright area surface element, calculate the near-field incident magnetic field generated by the near-field equivalent source sphere at each bright area surface element using the Stratton-Chu integral equation based on the free space Green's function; then, based on the physical optics approximation theory, solve for the PO induced current on the platform model surface according to the near-field incident magnetic field of the bright area surface element.

[0013] Step 6: Based on the specified output observation angle range, use near-field and far-field transformation to calculate the direct radiation far-field of the near-field equivalent source sphere in free space and the secondary scattering far-field generated by the physical optical induced current on the surface of the Open University model; then perform vector superposition of the two to obtain the total radiation far-field parameters of the antenna array mounted on the Open University platform.

[0014] Furthermore, the specific process of step 3 is as follows:

[0015] Step 3.1: Construct an external virtual closed sphere that completely surrounds the array antenna, serving as the near-field equivalent source sphere. ; Calculate the near-field electromagnetic field at discrete grid nodes on the near-field equivalent source sphere using the free-space Green's function:

[0016] ,

[0017] ,

[0018] Where G represents the Green's function in free space, specifically:

[0019] ,

[0020] Represents the vector coordinates of discrete grid nodes on the near-field equivalent source sphere. This represents the vector coordinates of the grid nodes on the radiation boundary of the array antenna. Vacuum wavenumber;

[0021] and These represent the electric and magnetic fields at discrete grid nodes on the near-field equivalent source sphere, respectively. and These represent the electric and magnetic fields on the radiation boundary of the antenna array, respectively. and These are the permittivity and permeability of free space, respectively. Let be the unit outward normal vector of the radiating boundary surface of the antenna array. For the radiation boundary surface of the antenna array, Represents the angular frequency of electromagnetic waves. Represents the Hamiltonian operator;

[0022] Step 3.2: Integrate the electromagnetic fields of the discrete grid nodes on the near-field equivalent source sphere in spherical coordinates to obtain the directional components of the electric and magnetic fields in the spherical coordinate system. , These represent the radial component, polar component, and azimuth component of the electric field, respectively. The radial, polar, and azimuth components of the magnetic field are represented respectively; and the output is encapsulated into an NFD data file according to the Structured Markup Language specification, serving as the near-field equivalent source file.

[0023] Furthermore, in step 4, the near-field equivalent source file import process is as follows:

[0024] Import the near-field equivalent source file into the physical optics region. Based on the actual installation position and physical attitude of the array antenna on the power grid platform, translate and rotate the platform model to make the relative spatial attitude of the near-field equivalent source sphere and the platform model consistent with the engineering application scenario.

[0025] Furthermore, in step 4, the spatial octree construction process is as follows:

[0026] Calculate the global minimum axis-aligned bounding box (AABB) that completely encloses all mesh elements of the platform model, and use it as the root node of the octree;

[0027] Using the center point of the box as a reference, the bounding box space is recursively divided into eight equal parts through three mutually perpendicular planes to generate child nodes;

[0028] Based on the spatial coordinates of the grid cells, the grid cells are assigned to the corresponding child nodes. When the number of grid cells contained in a child node drops below a preset threshold or the recursion depth of the octree reaches the maximum set number of levels, the splitting of this branch is stopped, and this child node is treated as a leaf node.

[0029] Furthermore, in step 4, the process of determining model occlusion is as follows:

[0030] The geometric center of the near-field equivalent source sphere is marked as the equivalent source point. Using the equivalent source point as the emission origin, test rays are projected onto the geometric center point of each target surface element on the platform model surface. In the intersection test between the ray and the target surface element, the ray first intersects with the octree node bounding box, eliminating non-intersecting spatial branches. When the ray enters a leaf node containing the target surface element, the Möller-Trumbore triangle intersection algorithm is executed to calculate the spatial distance between the target surface element and the equivalent source point. All surface elements traversed by the ray are judged, and the surface element closest to the equivalent source point will occlude other surface elements on the ray. If the target surface element is not occluded by other surface elements, it is determined to be a bright area surface element; otherwise, it is a dark area surface element.

[0031] Furthermore, the Möller–Trumbore triangle intersection algorithm is as follows:

[0032] Let the three vertices of the triangular mesh be... ,set up , Let the coordinates of the centroid of the triangular mesh be the parameters. Then, any point inside the triangular mesh is represented as:

[0033] ,

[0034] The ray originates from the equivalent source point, and its direction is marked as follows: The ray equation is then expressed as:

[0035] ,

[0036] in, Indicates the equivalent source point, This is the distance between the equivalent source point and the intersection point;

[0037] By aligning the ray equation with any point inside the triangular mesh, we obtain the linear matrix equation:

[0038] ,

[0039] Solve the above linear matrix equation when there is a solution and it satisfies If the ray intersects with the target triangular mesh, it is determined that the ray intersects with the target triangular mesh; otherwise, they do not intersect.

[0040] Furthermore, the specific process of step 5 is as follows:

[0041] Step 5.1: Calculate the current on the near-field equivalent source sphere based on the near-field equivalent source file. and magnetic current :

[0042] , ,

[0043] in, and These represent the electric and magnetic fields on the near-field equivalent source sphere, respectively. is the normal vector of the near-field equivalent source sphere;

[0044] The near-field incident magnetic field of the grid elements in the PO region was calculated based on the Stratton-Chu integral equation. :

[0045] ,

[0046] in, Let G represent the center of the m-th grid cell in the PO region, and let G be the Green's function in free space. Let k be the near-field equivalent source sphere, and k be the spatial wavenumber. is the dielectric constant of free space;

[0047] Step 5.2: For the bright area element, calculate the PO induced current generated by the near-field equivalent source sphere at the center coordinates of the bright area element. :

[0048] ,

[0049] in, The outward normal vector of the bright area element; Represents the geometric occlusion function: .

[0050] Furthermore, when the bright area element has a coated surface, PO induced current correction is performed. The correction process is as follows:

[0051] The near-field incident magnetic field generated by the near-field equivalent source sphere at the center of the bright region element is decomposed into local TE polarization components. and TM polarization components Calculate the corresponding reflection coefficients respectively. and ;

[0052] The PO induced current on the coated surface is expressed as:

[0053] .

[0054] Furthermore, the specific process of step 6 is as follows:

[0055] For a specified discrete observation angle Calculate the far field of direct radiation from the near-field equivalent source sphere in free space. :

[0056] ,

[0057] in, Indicates the polar angle. Indicates azimuth. Let be the permeability in free space. The angular frequency of the electromagnetic wave. Let k be the distance from the far-field observation point to the origin, and k be the space wavenumber. For the near-field equivalent source sphere, and For the near-field equivalent source sphere, the current and magnetic current are... The unit vector of the observation point. The equivalent source vector;

[0058] Calculate the far-field secondary scattering generated by the induced current on the surface of the electrical engineering model. :

[0059] ,

[0060] in, For the bright area element of PO region, Indicates the induced current in PO;

[0061] Finally, the total far-field radiation is obtained by superposition. : .

[0062] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0063] This invention provides a domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems on an open university platform. First, during the modeling stage, the complex multi-scale model is modeled separately, avoiding the tedious operation and huge computational overhead of overall joint modeling. Then, a virtual equivalent sphere is constructed separately for the antenna array, and the electromagnetic field on the sphere is efficiently calculated using the domain decomposition algorithm (FE-DDM), extracting the complete three-component values ​​in spherical coordinates. Next, this is exported as a near-field equivalent source file containing the three-dimensional field components in spherical coordinates, and based on the equivalence principle, a spherical near-field equivalent source that accurately reflects the mutual coupling characteristics of the array is constructed in subsequent calculations. Then, this equivalent source file is imported into the physical optics simulation area of ​​the open university platform, and the near-field incident electromagnetic field generated on the platform surface is rigorously calculated. The induced current on the platform surface is then quickly solved using the physical optics method (PO). Finally, the direct radiation field of the equivalent source and the secondary radiation field of the induced current on the platform are superimposed in the far-field vector, ultimately achieving a fast and high-precision electromagnetic simulation of the radiation characteristics of the antenna array on the open university platform.

[0064] Compared with traditional simulation methods, the advantages of this invention include: 1) significantly reducing computational resource consumption; 2) ensuring high physical accuracy of array characteristics and near-field coupling, strictly preserving the strong mutual coupling effect and edge effect inside the array using the domain decomposition algorithm, and accurately calculating the near-field coupling incident field from the equivalent source to the large platform based on complete three-dimensional field components; 3) using a regular closed sphere as the data transfer surface for the full-wave and high-frequency regions, containing files with three components in the spherical coordinate system, with standardized and stable interaction methods, ensuring the efficiency of the solution and the accuracy of the calculation results. Attached Figure Description

[0065] Figure 1 This is a schematic flowchart of the domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems on the power grid platform in this invention.

[0066] Figure 2 This is a schematic diagram of a ship model in an embodiment of the present invention.

[0067] Figure 3 This is a far-field three-dimensional radiation pattern according to an embodiment of the present invention.

[0068] Figure 4 This is a current distribution diagram according to an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0070] This embodiment provides a domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems of power computer platforms. Taking a large ship platform (i.e., a power computer platform) operating in the microwave frequency band as an example, and the ship platform is equipped with a large-scale phased array antenna, the specific process is as follows: Figure 1 As shown, it includes the following steps:

[0071] Step 1: Independent modeling of the 3D multi-scale model;

[0072] When dealing with multi-scale electromagnetic coupling problems in the integrated simulation of antenna arrays and electrically powered platforms, there is a huge electrical size gap between the hundreds or even thousands of operating wavelengths of the electrically powered dimensions of the ship platform and the extremely small and delicate feeding structure inside the antenna. If traditional joint full-wave modeling is used, it will result in extremely high aspect ratios in the finite element mesh, extremely poor matrix condition numbers, and an excessive number of unknowns. Therefore, in the three-dimensional geometric modeling stage, this embodiment establishes three-dimensional geometric models of the antenna array and the electrically powered platform separately, dividing them into an antenna array region for full-wave solution and a physical optics (PO) region for high-frequency solution. That is, an array antenna model is established for full-wave solution and a ship platform model is established for high-frequency approximate solution. The ship model is as follows: Figure 2 As shown;

[0073] Step 2: Solve for the electric and magnetic fields on the radiation boundary of the antenna array based on the finite element domain decomposition method (FE-DDM);

[0074] Within the entire solution domain, for large-scale array antenna models with numerous electrically small details, finite element domain division (FE-DDM) is used for high-precision, low-memory independent solutions. The specific process is as follows:

[0075] Step 2.1: Subdomain partitioning and boundary value problem construction of the solution domain;

[0076] Based on the overall large-scale array antenna structure, a small-scale antenna array with m×n elements in the central part is extracted as the sub-antenna array required for simulation, where m≥5 and n≥5. Considering the arrangement characteristics of the array antenna, each antenna element and its adjacent local envelope space are divided into an independent sub-region; let i be the sub-region containing... This indicates that the interface between two adjacent sub-regions is represented by... This means that within each sub-region, the high-frequency electromagnetic field strictly satisfies the following vector wave equation:

[0077] (1)

[0078] (2)

[0079] in, Let be the electric field vector within the sub-region. For external current source, Let be the relative permittivity of region i. Let be the relative permeability of region i. and , , Vacuum wavenumber, symbol , , The interface normal vector;

[0080] Step 2.2: Galerkin constructs a weak finite element model;

[0081] Vector basis functions are used internally in the finite element method. Tests were conducted using basis functions at the region interfaces, specifically the Robin boundary. and By conducting the test, we can obtain the following results:

[0082] (3)

[0083] (4)

[0084] (5)

[0085] in, , ;

[0086] Furthermore, by replacing half of the surface integral of (3) with the surface integral of (4), constructing a symmetric matrix, and combining it with (5), we can obtain the solution equation for the finite element domain decomposition method:

[0087] (6)

[0088] Step 2.3: By reusing the array structure matrix, construct the matrix equations for solving the finite element domain decomposition and obtain the electric and magnetic fields on the radiation boundary of the antenna array.

[0089] The domain decomposition solution to equation (6) can be written in matrix form, let This represents the finite element domain decomposition submatrix block of subregion i. The submatrix block represents the interface portion between subregions i and j. This represents the unknown quantity of the electric field to be determined. This represents the port excitation of the antenna array. Furthermore, assuming there are P antenna excitation elements in total, to adjust the feed amplitude and phase in real time to obtain the corresponding radiation pattern, each port excitation needs to be solved sequentially. Therefore, a total of P right-hand side terms need to be solved. The final matrix form of the finite element domain decomposition solution equation is:

[0090] (7)

[0091] Because antenna elements (single antenna elements) have a repeating structure, the antenna subdomain matrix... and No need to calculate all the matrices, only some matrices need to be calculated. Assuming an antenna array calculation model with 49 regions, after multiplexing, when solving matrix (7), only the matrices corresponding to 9 sub-regions and the connection matrices corresponding to 18 interfaces need to be stored, without storing all the matrices. Then, by solving matrix (7), the electric field solution under the excitation of the antenna excitation unit can be obtained. Finally, the electric and magnetic fields on the radiation boundary of the entire array antenna are obtained by using matrix multiplexing technology.

[0092] Step 3: Near-field integral extraction and export of structured equivalent source files;

[0093] Step 3.1: Construct an external virtual closed sphere that completely surrounds the array antenna. , as the near-field equivalent source sphere; the near-field electromagnetic field at discrete grid node r on the near-field sphere is calculated using the free-space Green's function;

[0094] Green's function in free space:

[0095] (8)

[0096] in, This represents the vector coordinates of a discrete mesh node r on the sphere. This represents the vector coordinates of the grid nodes on the radiation boundary of the array antenna. Vacuum wavenumber;

[0097] Near-field electromagnetic field at discrete sampling point r on the sphere:

[0098] (9)

[0099] (10)

[0100] in, and These represent the electric and magnetic fields on the radiation boundary, respectively. and Let be the permittivity and permeability of free space, respectively, and let G represent the Green's function of free space. Let be the unit outward normal vector of the radiating boundary surface. For the radiating boundary surface, Represents the angular frequency of electromagnetic waves. Represents the Hamiltonian operator;

[0101] Step 3.2: Integrate the electromagnetic fields of the near-field equivalent source spherical discrete grid nodes according to the three-dimensional complex component data in spherical coordinates to obtain the three directional components of the electric and magnetic fields in the spherical coordinate system. , These represent the radial component, polar component, and azimuth component of the electric field, respectively. The radial, polar, and azimuth components of the magnetic field are represented respectively; and the output is encapsulated into a specific NFD data file according to the Structured Markup Language specification, serving as the equivalent source file.

[0102] Step 4: Import the equivalent source file to the corresponding position of the ship model, and then use the spatial octree to accelerate the model visibility occlusion judgment.

[0103] Step 4.1 Importing the equivalent source file: Import the above NFD format near-field equivalent source file into the high-frequency solution area containing the ship model PO mesh. Based on the actual installation position and physical attitude of the array antenna on the ship, perform geometric operations such as translation and rotation on the ship model to ensure that the relative spatial attitude between the near-field equivalent source sphere and the ship model is consistent with the real engineering scene.

[0104] Step 4.2, Spatial Octree Construction and Ray Tracing: The surface of the power plant ship platform contains hundreds of thousands or even millions of triangular facets. If global ray tracing is used for occlusion detection, its time complexity is O(n log n). , The number of triangle facets is given. To avoid the time-consuming intersection calculations during ray tracing, this invention introduces a spatial octree algorithm. Taking this embodiment as an example, firstly, the global minimum axis-aligned bounding box (AABB) that can completely enclose all mesh facets of the ship model is calculated, and it is used as the root node of the octree. Then, based on the center point of the box, the bounding box space is recursively divided into eight equal parts through three mutually perpendicular planes to generate child nodes. According to the spatial coordinates of the mesh facets, the model facets are assigned to the corresponding child nodes. When the number of triangle facets contained in a child node drops below a preset threshold or the recursion depth of the octree reaches the maximum set number of layers, the division of that branch is stopped, and that node becomes a leaf node. This process transforms the complex 3D discrete facets into a hierarchical spatial index structure, transforms the complex 3D space into a hierarchical bounding box structure, and reduces the time complexity of subsequent occlusion judgment to a minimum. ;

[0105] After the octree is constructed, occlusion is determined on the model. Using the geometric center of the near-field equivalent source sphere (referred to as the equivalent source point) as the origin, test rays are projected onto the geometric center of each target triangle element on the surface of the ship model. In the intersection test between the ray and the element, the ray first intersects with the bounding box of the octree node and quickly eliminates non-intersecting spatial branches. When the ray enters the leaf node containing the element, the accurate Möller-Trumbore triangle intersection algorithm is executed to calculate the spatial distance between the target triangle element and the equivalent source point.

[0106] The Möller–Trumbore triangle intersection algorithm is as follows:

[0107] Let the three vertices of a triangular mesh be... ,set up , Here are the centroid coordinates of the triangular mesh. Any point inside a triangle can be represented by its three vertices and the centroid coordinates as follows:

[0108] (11)

[0109] The ray originates from the equivalent source point and travels in the following direction. Then the equation of the ray can be expressed as:

[0110] (12)

[0111] in, Indicates the equivalent source point, Let be the distance between the equivalent source point and the intersection point (the intersection point of the ray and the triangular mesh); to determine whether the triangular mesh element intersects with the ray, let equation (11) and equation (12) be equal, and we get the linear matrix equation:

[0112] (13)

[0113] If the linear equation has a solution and satisfies:

[0114] (14)

[0115] This indicates that the ray intersects the triangular mesh; otherwise, it does not. This method determines all triangular meshes traversed by the ray. The triangular mesh closest to the equivalent source point will occlude other triangular meshes on the ray. If the target triangular element is not occluded by other elements on the model, it is determined to be a bright area element; if it is occluded by other elements on the model, it is determined to be a dark area element. Based on this, a geometric occlusion function for the element is defined. :

[0116] (15)

[0117] Step 5: Solve for the exact integral of the Stratton-Chu near-field incidence and the induced current on the PO surface;

[0118] Step 5.1: High-precision numerical integration of the incident field of the bright area element: Traditional hybrid algorithms typically treat the antenna as an equivalent far-field point source for high-frequency calculations, which can lead to significant near-field phase errors when dealing with large antenna arrays closely attached to electrically large platforms. This invention employs the Stratton-Chu integral equation to rigorously calculate the near-field incident coupling effect of the near-field equivalent source sphere on the ship model surface; the current on the equivalent source sphere is calculated using the equivalent source file imported in Step 4. and magnetic current :

[0119] (16)

[0120] (17)

[0121] in, and These represent the electric and magnetic fields on the equivalent source sphere, respectively. This is the normal vector of the equivalent source sphere;

[0122] The magnetic field of the grid elements in the PO region was calculated using the Stratton-Chu integral equation:

[0123] (18)

[0124] in, The magnetic field of the grid elements in the PO region. Let G represent the center of the m-th grid cell in the PO region, and let G be the Green's function in free space. Let k be the equivalent source sphere, and k be the space wavenumber. is the dielectric constant of free space;

[0125] Step 5.2, Surface induced current solution under physical optics approximation: Based on the physical optics (PO) high-frequency asymptotic theory, the high-frequency scattering effect of the electrically large platform is determined by the surface induced current it excites;

[0126] For an ideal conducting plane, based on the principle of local tangent plane approximation, the induced current on the model surface is calculated: for bright area elements, the induced current is equal to twice the cross product of its outward normal vector and the incident magnetic field; for obscured dark area elements, their induced current is directly forced to zero; for the bright area elements selected in step 4, the surface induced current generated by the equivalent spherical source at the center coordinates of the bright area element is calculated. :

[0127] (19)

[0128] in, Let m be the center of the face element of the m-th grid in the PO region. The outward normal vector of the mesh element; this expression utilizes Automatically set the dark area current to zero;

[0129] Furthermore, when the surface of the open university platform has a radar-absorbing coating, a dielectric coating layer, or an equivalent impedance material, the response of the platform surface to incident electromagnetic waves is no longer equivalent to that of an ideal conductor surface. The surface induced current needs to be corrected by considering the electromagnetic parameters of the coating material. Let the equivalent relative permittivity, relative permeability, and conductivity of the coating material on the m-th PO surface element be respectively... , and The material thickness is Under high-frequency approximation conditions, each triangular element can be locally equivalent to a planar layered dielectric structure, where the incident wave undergoes reflection, transmission, and internal material loss. For thin coatings, the electromagnetic response can be described using equivalent surface impedance boundary conditions, i.e.:

[0130] (20)

[0131] in, Let m be the external normal vector of the m-th face element. and These represent the tangential electric field and tangential magnetic field on the surface of the element, respectively. The equivalent surface impedance is determined by the electromagnetic parameters, thickness, and operating frequency of the coating material. For a uniform single-layer coating material, its equivalent surface impedance can be approximated using transmission line theory as follows:

[0132] (twenty one)

[0133] in, and These are the characteristic impedance and propagation constant of the coating material, respectively. This is the equivalent load impedance of the coated backing structure; when the coated backing is a metal platform, the backing can be approximated as an ideal conductor boundary.

[0134] In physical optics calculations, the effect of coating materials on surface induced current can be corrected using local reflection coefficients. The incident field generated by the equivalent source at the center of the bright region surface element is decomposed into local TE polarization components and TM polarization components, and the corresponding reflection coefficients are calculated for each. and Then the equivalent PO induced current on the coated surface can be expressed as:

[0135] (twenty two)

[0136] in, and Let be the components of the incident magnetic field in the local TE and TM polarization directions, respectively; for an ideal conductor surface, we have , The above formula can be degenerated into the surface induced current form under the traditional physical optics approximation; for the platform surface with absorbing or dielectric coating materials, the reflection coefficient amplitude is usually smaller than that of an ideal conductor and has a phase change related to material loss and thickness, which can reflect the suppression effect of the coating material on the platform's secondary scattering field.

[0137] Step 6: Discrete domain superposition extraction of characteristic parameters of the far-field system radiation field;

[0138] Discrete observation angles specified for actual engineering projects (e.g., a specific elevation or azimuth plane), the system's total electromagnetic radiation far field It is formed by the independent calculation and superposition of two vector parts: the first part is the primary far field formed by the direct radiation of the imported equivalent source in free space. The calculation formula is as follows:

[0139] (twenty three)

[0140] in, The distance from the far-field observation point to the origin. The unit vector of the observation point. For the equivalent source point vector, For wave impedance, It is a closed equivalent source sphere.

[0141] In the second part, because the materials of the ship platform are designed as ideal conductors, when illuminated by an equivalent source, an induced current will be generated on the bright area surface of the ship platform, radiating a secondary far-field radiation in a specific observation direction. The calculation formula is as follows:

[0142] (twenty four)

[0143] in, This is the bright element surface area of ​​the PO region;

[0144] Finally, by superimposing the far-field electric field vectors of the two, the total radiated electric field of the system in the far region is obtained as follows:

[0145] (25)

[0146] Based on the above steps, such as Figure 3 The image shows the far-field three-dimensional radiation pattern of a complete system consisting of a ship model and an array antenna model, as shown below. Figure 4 The diagram shows the induced current distribution of a ship model affected by the electromagnetic field of an array antenna; Figure 3 As can be seen, this invention calculates the main beam pointing and sidelobe distribution of the antenna's far-field three-dimensional radiation pattern under complex carrier environments; from Figure 4 The induced current distribution diagram on the surface of the ship model shown illustrates the current details accurately solved on the surface of the ship model after dividing the bright and dark areas by spatial ray tracing (the induced current in the dark area is strictly zero). The attached figure shows that, in cases where traditional methods are difficult to solve due to the limitation of electrically large mesh size, the method of this invention can accurately calculate the complete system consisting of the ship model and the array antenna model.

[0147] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems on open university platforms, characterized in that, Includes the following steps: Step 1: Independently construct a three-dimensional geometric model of the array antenna, denoted as the antenna model, as the full-wave solution region; An independent three-dimensional geometric model of the Open University platform is constructed, denoted as the platform model, which serves as the physical optical region for high-frequency solution. Step 2: In the full-wave solution domain, solve for the electric and magnetic fields on the radiation boundary of the antenna array based on the finite element domain decomposition method; Step 3: Construct an external virtual closed sphere that completely surrounds the antenna model as the near-field equivalent source sphere. Based on the electric and magnetic fields on the radiation boundary of the antenna array, perform a near-field-to-near-field transformation using the Stratton-Chu integral equation to calculate the electric and magnetic fields on the near-field equivalent source sphere. Extract the corresponding electromagnetic field distribution from the sphere and export it as a near-field equivalent source file. The specific process is as follows: Step 3.1: Construct an external virtual closed sphere that completely surrounds the array antenna, serving as the near-field equivalent source sphere. ; Calculate the near-field electromagnetic field at discrete grid nodes on the near-field equivalent source sphere using the free-space Green's function: ， ， Where G represents the Green's function in free space, specifically: ， Represents the vector coordinates of discrete grid nodes on the near-field equivalent source sphere. This represents the vector coordinates of the grid nodes on the radiation boundary of the array antenna. Vacuum wavenumber; and These represent the electric and magnetic fields at discrete grid nodes on the near-field equivalent source sphere, respectively. and These represent the electric and magnetic fields on the radiation boundary of the antenna array, respectively. and These are the permittivity and permeability of free space, respectively. Let be the unit outward normal vector of the radiating boundary surface of the antenna array. For the radiation boundary surface of the antenna array, Represents the angular frequency of electromagnetic waves. Represents the Hamiltonian operator. Represents the imaginary unit; Step 3.2: Integrate the electromagnetic fields of the discrete grid nodes on the near-field equivalent source sphere in spherical coordinates to obtain the directional components of the electric and magnetic fields in the spherical coordinate system. , These represent the radial component, polar component, and azimuth component of the electric field, respectively. The radial, polar, and azimuth components of the magnetic field are represented respectively; and the output is encapsulated into an NFD data file according to the Structured Markup Language specification, serving as the near-field equivalent source file. Step 4: Import the near-field equivalent source file to the predetermined position in the physical optics region, use spatial octree acceleration to determine model occlusion, and identify and mark the bright and dark surface elements on the surface of the power platform. Step 5: For the bright area surface element, calculate the near-field incident magnetic field generated by the near-field equivalent source sphere at each bright area surface element using the Stratton-Chu integral equation based on the free space Green's function; then, based on the physical optics approximation theory, solve for the PO induced current on the platform model surface according to the near-field incident magnetic field of the bright area surface element. Step 6: Based on the specified output observation angle range, use near-field and far-field transformation to calculate the direct radiation far-field of the near-field equivalent source sphere in free space and the secondary scattering far-field generated by the physical optical induced current on the surface of the Open University model; then perform vector superposition of the two to obtain the total radiation far-field parameters of the antenna array mounted on the Open University platform.

2. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the open university platform according to claim 1, characterized in that, In step 4, the near-field equivalent source file import process is as follows: Import the near-field equivalent source file into the physical optics region. Based on the actual installation position and physical attitude of the array antenna on the power grid platform, translate and rotate the platform model to make the relative spatial attitude of the near-field equivalent source sphere and the platform model consistent with the real scene.

3. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the Open University platform according to claim 1, characterized in that, In step 4, the spatial octree construction process is as follows: Calculate the global minimum axis-aligned bounding box that completely surrounds all mesh elements of the platform model, and use it as the root node of the octree; Using the center point of the box as a reference, the bounding box space is recursively divided into eight equal parts through three mutually perpendicular planes to generate child nodes; Based on the spatial coordinates of the grid cells, the grid cells are assigned to the corresponding child nodes. When the number of grid cells contained in a child node drops below a preset threshold or the recursion depth of the octree reaches the maximum set number of levels, the splitting of this branch is stopped, and this child node is treated as a leaf node.

4. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the Open University platform according to claim 1, characterized in that, In step 4, the process of determining model occlusion is as follows: The geometric center of the near-field equivalent source sphere is marked as the equivalent source point. Using the equivalent source point as the emission origin, test rays are projected onto the geometric center point of each target surface element on the platform model surface. In the intersection test between the ray and the target surface element, the ray first intersects with the bounding box of the octree node, eliminating non-intersecting spatial branches. When the ray enters a leaf node containing the target surface element, the Möller-Trumbore triangle intersection algorithm is executed to calculate the spatial distance between the target surface element and the equivalent source point. All surface elements passed through by the ray are judged. The surface element closest to the equivalent source point will occlude other surface elements on the ray. If the target surface element is not occluded by other surface elements, it is determined to be a bright area surface element; otherwise, it is a dark area surface element.

5. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the power university platform according to claim 4, characterized in that, The Möller–Trumbore triangle intersection algorithm is as follows: Let the three vertices of the triangular mesh be... ,set up , Given the centroid coordinates of the triangular mesh, any point inside the triangular mesh... Represented as: ， The ray originates from the equivalent source point, and its direction is marked as follows: The ray equation is then expressed as: ， in, Represents rays, Indicates the equivalent source point, This is the distance between the equivalent source point and the intersection point; By aligning the ray equation with any point inside the triangular mesh, we obtain the linear matrix equation: ， Solve the above linear matrix equation when there is a solution and it satisfies If the ray intersects with the target triangular mesh, it is determined that the ray intersects with the target triangular mesh; otherwise, they do not intersect.

6. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the Open University platform according to claim 1, characterized in that, The specific process of step 5 is as follows: Step 5.1: Calculate the current on the near-field equivalent source sphere based on the near-field equivalent source file. and magnetic current : ， ， in, and These represent the electric and magnetic fields on the near-field equivalent source sphere, respectively. is the normal vector of the near-field equivalent source sphere; The near-field incident magnetic field of the grid elements in the PO region was calculated based on the Stratton-Chu integral equation. : ， in, This represents the center of the m-th grid cell in the PO region. Represents the imaginary unit. Represents the angular frequency of electromagnetic waves. Let G be the permittivity of free space, G be the Green's function of free space, and k be the space wavenumber. Represents the Hamiltonian operator. For near-field equivalent source sphere; Step 5.2: For the bright area element, calculate the PO induced current generated by the near-field equivalent source sphere at the center coordinates of the bright area element. : ， in, The outward normal vector of the bright area element; Represents the geometric occlusion function: .

7. The domain decomposition equivalent source-high frequency coupling solution method for the electromagnetic radiation problem of the Open University platform according to claim 6, characterized in that, When the bright area element has a coated surface, PO induced current correction is performed. The correction process is as follows: The near-field incident magnetic field generated by the near-field equivalent source sphere at the center of the bright region element is decomposed into local TE polarization components. and TM polarization components Calculate the corresponding reflection coefficients respectively. and ; The PO induced current on the coated surface is expressed as: 。 8. The domain decomposition equivalent source-high frequency coupling solution method for electromagnetic radiation problems on open university platforms according to claim 1, characterized in that, The specific process of step 6 is as follows: For a specified discrete observation angle Calculate the far field of direct radiation from the near-field equivalent source sphere in free space. : ， in, Indicates the polar angle. Indicates azimuth. Represents the imaginary unit. Let be the permeability in free space. The angular frequency of the electromagnetic wave. Let k be the distance from the far-field observation point to the origin, and k be the space wavenumber. For the near-field equivalent source sphere, and For the near-field equivalent source sphere, the current and magnetic current are... The unit vector of the observation point. The equivalent source vector; Calculate the far-field secondary scattering generated by the induced current on the surface of the electrical engineering model. : ， in, For the bright area element of PO region, Indicates the induced current in PO; Finally, the total far-field radiation is obtained by superposition. : .

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