Method and system for analyzing electromagnetic scattering of large-scale cluster targets based on parallel equivalence principle

Abstract

The application discloses a kind of based on parallel equivalent principle Large-scale cluster target electromagnetic scattering analysis method and system, specifically for: the geometric modeling and equivalent surface construction of each target unit in cluster target are carried out, and discrete surface element information is generated;Start parallel computing process, adopt greedy algorithm distribution target-equivalent surface pair;The computing process group corresponding to each subdomain is divided into blocks according to two-dimensional Cartesian coordinate grid, and the transfer operator matrix between subdomains is divided into blocks according to the same two-dimensional computing process grid, and global parallel iteration solving cycle is carried out, to update the equivalent surface flow of this subdomain;Using the equivalent surface flow of each subdomain after convergence as equivalent source, through far-field radiation integration synthesis entire cluster target in specified observation direction Radar scattering cross section (RCS).The application has good parallel scalability and computing efficiency, is suitable for complex and varied cluster target scene, reduces memory requirement and computing time overhead, improves computing efficiency, and has strong engineering practicability.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic computing technology, and in particular to a method and system for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence. Background Technology

[0002] Electromagnetic scattering characteristics refer to the phenomenon where electromagnetic waves, during propagation, encounter objects or inhomogeneous media, and their direction, phase, or energy redistribute due to interaction with matter. Its core lies in describing how incident electromagnetic waves are "scattered" in various directions, and this can be quantified using parameters such as radar cross section (RCS), polarization characteristics, and frequency response. The analysis of electromagnetic scattering characteristics of large-scale swarm targets, such as UAV swarms and satellite formations, is a cutting-edge topic and a major challenge in the fields of computational electromagnetics and target characteristics. These targets typically consist of numerous, spatially complex electrically large scatterers, resulting in an extremely high degree of freedom in their overall electromagnetic model and an exponentially increasing demand for computational resources. Traditional serial or small-scale parallel schemes based on the Method of Moments (MoM) and its fast algorithms, such as the Multilevel Fast Multipole Algorithm (MLFMA), are insufficient to handle such problems.

[0003] In recent years, parallel computing techniques for high-performance computing (HPC) architectures have provided a way to solve this problem. For example, reference 1 (Kang, L., et al. "A Massively Parallel Multilevel Fast Multipole Algorithm for Large-Scale Scattering Problems with over 100 Million Unknowns." IEEE Transactions on Antennas and Propagation, vol. 66, no. 9, 2018, pp. 4669-82.) addresses the challenge of solving matrix equations in the method of moments (MoM) for solving electromagnetic scattering problems of electrically large targets, proposing a multilevel fast multipole algorithm for large-scale parallel computing. This work, by optimizing parallel communication modes and load balancing strategies, successfully solved an electromagnetic model with over 100 million unknowns on thousands of processor cores, verifying the feasibility of parallel computing techniques in ultra-large-scale electromagnetic problems. Reference 2 (Liu, Xin-Duo, et al. "Massive Parallelization of Multilevel Fast Multipole Algorithm for 3-DElectromagnetic Scattering Problems on SW26010 Many-Core Cluster." The Journal of Supercomputing, vol. 80, no. 7, 2024, pp. 8702-18.) further extends the parallel multilevel fast multipole algorithm to the domestic SW26010 many-core processor platform. By designing a parallel scheme based on a hybrid programming model of MPI and Athread, it achieves high-efficiency acceleration in computationally intensive steps such as matrix filling and aggregation configuration, demonstrating the application potential of heterogeneous parallel architecture in electromagnetic computing. Patent CN103870654A proposes an electromagnetic scattering simulation method based on a hybrid parallel method of moments (MoM) and physical optics. It divides the rough surface into a physical optics region and the radar target into a parallel MoM region. Through a region decomposition and iterative coupling mechanism, it handles the electromagnetic scattering problem of the composite model, effectively reducing memory consumption and improving simulation efficiency.

[0004] However, the aforementioned methods still face challenges when dealing with cluster targets composed of a large number of discrete scatterers. The parallel multilayer fast multipole algorithm suffers from high communication overhead and decreased parallel expansion efficiency in cross-node data communication and modeling of mutual coupling between heterogeneous targets. Meanwhile, hybrid methods based on domain decomposition have not yet fully utilized the characteristics of current advanced heterogeneous computing hardware, and there is still room for optimization in areas such as computational task allocation and heterogeneous node load balancing. The equivalence principle algorithm, as a domain decomposition method based on equivalent surface encapsulation, is naturally suitable for handling multi-body separated targets, but its parallelization research on large-scale heterogeneous clusters is still insufficient, and its performance potential needs further exploration. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence, which has low memory consumption, short computation time, high computational efficiency, and strong engineering applicability.

[0006] The technical solution to achieve the purpose of this invention is: a method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence, comprising the following steps:

[0007] Step 1, Geometric Modeling and Equivalent Surface Construction: For the cluster targets to be analyzed, perform independent geometric modeling for each target unit; construct a closed spherical equivalent surface that completely encloses the outer contour for each target unit; perform 3D meshing on the surface of the target unit and the corresponding equivalent surface to generate discrete surface element information;

[0008] Step 2, Load Balancing and Distributed Data Initialization: Start the parallel computing process, use a greedy algorithm to allocate target-equivalent faces, and iteratively allocate tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status to achieve balanced partitioning;

[0009] Step 3: Parallel computation of scattering and transfer operators: The computation process groups corresponding to each subdomain are divided into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently computes the scattering submatrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to compute the transfer submatrix block corresponding to the coordinate, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces.

[0010] Step 4: Parallel Iterative Solution of Hybrid Basis Functions: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters a global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator. The equivalent surface flow of the subdomain is updated using the conversion relationship between the RWG basis function and the BOR mode current until the global residual satisfies the preset convergence criterion.

[0011] Step 5, Electromagnetic property extraction: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

[0012] A large-scale cluster target electromagnetic scattering analysis system based on the parallel equivalence principle, the system being used to implement the aforementioned large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle, the system comprising:

[0013] Geometric Modeling and Equivalent Surface Construction Module: For the cluster targets to be analyzed, each target unit is independently geometrically modeled; a closed spherical equivalent surface that completely surrounds the outer contour is constructed for each target unit; the surface of the target unit and the corresponding equivalent surface are respectively meshed in three dimensions to generate discrete surface element information;

[0014] Load balancing and data distributed initialization module: Starts parallel computing processes, uses a greedy algorithm to allocate target-equivalent faces, and iteratively allocates tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status, so as to achieve balanced partitioning;

[0015] The parallel computation module for scattering and transfer operators divides the computation process groups corresponding to each subdomain into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently calculates the scattering matrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to calculate the transfer matrix block corresponding to the coordinate, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces.

[0016] Hybrid basis function parallel iterative solution module: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters the global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator; it updates the equivalent surface flow of its own subdomain by using the conversion relationship between the RWG basis function and the BOR mode current until the global residual satisfies the preset convergence criterion.

[0017] Electromagnetic property extraction module: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

[0018] A computer device includes a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the computer instructions to perform the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle.

[0019] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle.

[0020] Compared with the prior art, the present invention has the following significant advantages: (1) It has good parallel scalability and computational efficiency, and is suitable for heterogeneous accelerated computing platforms; (2) It provides a high-precision and high-flexibility unified simulation framework that supports high-intensity heterogeneous parallel computing, and is suitable for complex and diverse cluster target scenarios; (3) It combines the rotational symmetric moment method in the parallel computing framework to model the coupling effect between equivalent surfaces, which significantly reduces memory requirements and computation time overhead, improves computational efficiency, and has strong engineering practicality. Attached Figure Description

[0021] Figure 1 This is a flowchart of the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle of the present invention.

[0022] Figure 2 This is a schematic diagram of the three-dimensional spatial distribution of 120 drones in an embodiment of the present invention.

[0023] Figure 3 This is a schematic diagram showing the dimensions and spacing of a single UAV in an embodiment of the present invention.

[0024] Figure 4 This is a schematic diagram illustrating the computation time and parallel efficiency test results for 120 drone models based on the computation result of 8640 cores, and extended to 11520 cores, 17280 cores, and 34560 cores respectively in this embodiment of the invention.

[0025] Figure 5 This is a schematic diagram comparing the bistatic radar cross sections of 120 UAVs under a 1 GHz incident wave using 8640 cores and expanded to 34560 cores in an embodiment of the present invention. Detailed Implementation

[0026] This invention provides a method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence, comprising the following steps:

[0027] Step 1, Geometric Modeling and Equivalent Surface Construction: For the cluster targets to be analyzed, perform independent geometric modeling for each target unit; construct a closed spherical equivalent surface that completely encloses the outer contour for each target unit; perform 3D meshing on the surface of the target unit and the corresponding equivalent surface to generate discrete surface element information;

[0028] Step 2, Load Balancing and Distributed Data Initialization: Start the parallel computing process, use a greedy algorithm to allocate target-equivalent faces, and iteratively allocate tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status to achieve balanced partitioning;

[0029] Step 3: Parallel computation of scattering and transfer operators: The computation process groups corresponding to each subdomain are divided into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently computes the scattering submatrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to compute the transfer submatrix block corresponding to the coordinate, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces.

[0030] Step 4: Parallel Iterative Solution of Hybrid Basis Functions: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters a global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator. The equivalent surface flow of the subdomain is updated using the conversion relationship between the RWG basis function and the BOR mode current until the global residual satisfies the preset convergence criterion.

[0031] Step 5, Electromagnetic property extraction: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

[0032] As a specific example, step 1 is as follows:

[0033] Step 1.1: Perform independent 3D geometric modeling for each metal target unit, and construct a closed spherical equivalent surface that completely surrounds the outer contour for each target unit, maintaining a set distance between the equivalent surface and the target surface;

[0034] Step 1.2: Discretize the surface of the target unit and the equivalent surface using triangular facets. The maximum side length of the facet is no greater than one-tenth of the wavelength corresponding to the incident wave frequency.

[0035] Step 1.3: Number all triangular facets and points, and record the three vertex numbers and three-dimensional coordinates of each triangular facet;

[0036] Step 1.4: Determine the common edge and number it, and establish the logical relationship between the common edge and the adjacent positive and negative triangle elements.

[0037] As a specific example, step 2 is as follows:

[0038] Step 2.1: Start the parallel computing process and use a greedy algorithm to allocate target-equivalent faces. Based on the computational complexity of the subdomain and the real-time resource status, combined with the evaluation model, the computing tasks are iteratively allocated to the computing process group with the lowest load.

[0039] Step 2.2: Each computation process group independently reads the mesh data of the metal target and equivalent surface in the assigned subdomain, including the vertex coordinates, vertex indices, normal vectors, and positive and negative triangle numbers corresponding to the common edges of all triangular facets.

[0040] Step 2.3: Each computing process group initializes the local data structure of the subdomain in memory based on the read grid data, completes the pre-allocation of scattering operators and transfer operators, and realizes the distributed loading of computing tasks and data.

[0041] As a specific example, step 2.1 is as follows:

[0042] Step 2.1.1: Within the framework of the method of moments combined with domain decomposition, subdomains The computational complexity is not linearly related to the grid size, but is determined by multiple factors including matrix filling, local solving, and boundary interactions, resulting in a total computational cost that increases with the number of unknowns in the subdomain. It exhibits high-order nonlinear growth, as detailed below:

[0043] Matrix filling: subfield Impedance matrix filling requires calculating the interactions between all basis function pairs, and the computational cost is proportional to the number of basis function pairs. Even with acceleration techniques (such as adaptive cross approximation), the near-field part still retains the dominance of the squared terms;

[0044] Local solution: In the domain decomposition framework, each subdomain needs to independently solve the local matrix equation; if a direct solution method (such as LU decomposition) is used, the computational complexity is O(log n). If an iterative solution method is used, the complexity of each iteration is O(n log n). The number of iterations is determined by the subfield condition number. Therefore, the cubic term is a core component of the subfield solution cost.

[0045] Boundary interaction: Coupling between subdomains is achieved through transmission conditions, requiring repeated exchange of boundary information and updates to boundary conditions—a global iterative process. The computational cost in each iteration is proportional to the number of unknowns on the boundary; within the domain decomposition framework, the number of boundary unknowns equals the total number of unknowns in the subdomain. Therefore, the total computational cost of boundary interactions can be expressed as: Multiply by the number of iterations, which is usually a constant independent of the size of the subdomain.

[0046] Matrix filling exhibits quadratic growth, local solution exhibits cubic growth, and boundary interaction exhibits linear growth. These three factors together constitute the high-order nonlinear characteristics of subdomain computational complexity.

[0047] Step 2.1.2: Use a cubic polynomial model to characterize the mesh size. That is, the first Number of unknowns and computational complexity in each subdomain Mapping between:

[0048] (1)

[0049] in, For the first The estimated computational cost for each subdomain; For the first The grid size of a subdomain is typically measured by the number of unknowns or the number of grid cells; coefficients , , , The weighted least squares method was used to fit the data, where For the fitting coefficients of the cubic term, For the fitting coefficients of the quadratic term, For the fitting coefficients of the first-order term, These are the fitting coefficients for the constant term;

[0050] No. Estimated completion time of each node Composed of computation time and communication time, it is expressed as:

[0051] (2)

[0052] Where Q is the total number of subdomains obtained through domain decomposition; To make the first The computational cost of each subdomain is allocated to the first subdomain. The proportion of nodes; For the first The total amount of resources required for the computation of each subdomain; For the first The computing power coefficient of each node; For the first Communication overhead coefficient per unit computational cost between each subdomain and other subdomains;

[0053] Step 2.1.3: The optimization objective is to minimize the longest node completion time T.

[0054] (3)

[0055] This is a function to find the maximum value in a set of numbers; The minimum value function represents finding the minimum value in a set of numbers; This indicates the longest node completion time. This represents the total number of parallel computing nodes. Indicates the first Estimated completion time for each node;

[0056] Subdomain computational integrity constraints:

[0057] (4)

[0058] Node resource capacity constraints:

[0059] (5)

[0060] For each node Total resource capacity;

[0061] Based on the model optimization results, each computation process group only needs to read and store the grid topology data of its assigned subdomain, complete the distributed initialization of the data, and output the allocation matrix. and maximum completion time T;

[0062] Step 2.1.4: To evaluate performance, define the following metrics;

[0063] Load balancing coefficient based on completion time :

[0064] (6)

[0065] coefficient The closer a value is to 1, the smaller the difference in completion time between nodes, and the more balanced the load; when all nodes complete in equal times... =1; when the difference is extremely large. Approaching 0;

[0066] Load balancing coefficient based on computational cost Without considering communication overhead, the load balancing is measured solely by computational load:

[0067] (7)

[0068] When the performance of nodes is heterogeneous, it is necessary to assess whether the allocation matches the node capabilities, and define a fairness index based on load balancing weighted by computing power. :

[0069] (8)

[0070] Considering the differences in node computing power, A larger value indicates a fairer allocation; when all nodes have the same computational load, When the maximum deviation equals the average, ;

[0071] Average node utilization :

[0072] (9)

[0073] This reflects the average percentage of busy time for each node during the entire parallel process. A higher value indicates less idle time;

[0074] Represents the longest completion time among all nodes, and the minimum node utilization. for:

[0075] (10)

[0076] Reflecting the relative idleness of the lightest-loaded node helps identify load bottlenecks.

[0077] As a specific example, step 3 is as follows;

[0078] Step 3.1: To achieve the mapping between computing tasks and computing process resources, the computing process group responsible for computing each subdomain is divided into a two-dimensional Cartesian coordinate grid. The topology of this grid corresponds to the block partitioning strategy of the scattering operator and the transfer operator matrix, ensuring that each computing process node logically corresponds to a specific sub-block of the operator matrix and is responsible for all computing tasks related to that specific sub-block.

[0079] Set the dimension of the computation process grid to 1. The process coordinates are represented as ,in For row index, Column indices are used, all counting from 0; the operator matrix is ​​correspondingly divided into... If there are multiple sub-blocks, then the computation process... The corresponding submatrix index Determined by row priority: ;

[0080] This mapping relationship ensures precise alignment between computing tasks and computing process resources, effectively improves data locality, reduces communication overhead, and lays an efficient topological foundation for subsequent parallel computing.

[0081] Step 3.2: Using the RWG basis functions of the metal target surface and the equivalent surface, establish the scattering matrix between the internal target and the surrounding equivalent surface in parallel calculation; for each rotationally symmetric equivalent surface, construct and calculate the mode coupling matrix between the equivalent surfaces of different subdomains in the Fourier mode space, forming a dimension reduction transfer operator for calculating the electromagnetic coupling between equivalent surfaces.

[0082] The scattered electromagnetic current on the equivalent surface satisfies the following relationship:

[0083] (11)

[0084] calculate When there are separate targets, , The number of the equivalent surface and , , ; , They are the first Incident electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface It is the first Equivalent operators for each objective, It is the first The and the first Transit operators between equivalent surfaces;

[0085] The computation process group is divided according to a two-dimensional Cartesian coordinate grid. Each computation process node in the grid is responsible for computing a sub-matrix block of a scattering operator and its associated Q-1 transfer operator sub-matrix blocks. It independently executes the computation tasks of all corresponding sub-matrix blocks by allocating a DCU acceleration card to achieve matrix filling.

[0086] Due to the orthogonal equivalent operator formed by the direct interaction of RWG basis functions and BoR basis functions Both computational and storage complexity reach ,in This indicates the number of RWG basis functions on the internal metal. The modulus represents the number of trigonometric basis functions along the generatrix on the equivalent sphere, and Mod represents the total number of positive modes. Therefore, orthogonal mode transfer matrices are used only for interactions between different sub-regions. The calculation requires that the equivalent sphere be expanded using both RWG and BoR basis functions to obtain the equivalent electromagnetic current.

[0087] As a specific example, step 4 is as follows:

[0088] Step 4.1: Set initial equivalent surface current or equivalent magnetic current for the equivalent surface of each subdomain as the initial value for iterative solution;

[0089] Step 4.2: In each iteration, each calculation process independently calculates the local scattering field generated by the equivalent surface current of the current subdomain using the scattering operator calculated in step 3.

[0090] Step 4.3: Each calculation process receives and accumulates the radiation contribution from the equivalent surface current of all other subdomains to its own subdomain by calling the transfer operator calculated in step 3, thus forming the total excitation field acting on its own subdomain.

[0091] Step 4.4: Combining the local scattered field and total excitation field calculated in Steps 4.2 and 4.3, solve the update equation of the equivalent surface current according to the electromagnetic boundary conditions of the equivalent surface; this process achieves efficient calculation through the rapid current conversion between RWG basis functions and BOR basis functions.

[0092] Step 4.5: After each iteration, calculate the relative residual norm of the global equivalent current solution in parallel; determine whether the residual is lower than the preset convergence tolerance: if it is lower than the tolerance, the iteration is considered to have converged and step 4.6 is executed; if it is not lower than the tolerance, the updated equivalent surface current is used as the new current solution and the process returns to step 4.2 for the next iteration.

[0093] Step 4.6: After the iteration converges, each calculation process synchronizes the final equivalent surface current solution, providing a data foundation for subsequent near-field and far-field calculations.

[0094] As a specific example, step 5 is as follows:

[0095] Step 5.1: Treat the equivalent surface electromagnetic current obtained after the iterative convergence of each subdomain as an independent equivalent radiation source;

[0096] Step 5.2: For each equivalent radiation source, apply the far-field radiation integral formula to calculate the far-field scattered electric field vector generated in the specified observation direction; superimpose the far-field scattered electric field vectors of all equivalent radiation sources in the same observation direction to obtain the total scattered electric field of the entire cluster target in that observation direction.

[0097] Step 5.3: According to the definition of Radar Cross Section (RCS), the radar cross section of the entire cluster of targets in a specified observation direction is: the ratio of the power density scattered by the target towards the receiver to the power density of the incident wave at the target within a unit solid angle. times.

[0098] This invention also provides a large-scale cluster target electromagnetic scattering analysis system based on the parallel equivalence principle. This system is used to implement the aforementioned large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle. The system includes:

[0099] Geometric Modeling and Equivalent Surface Construction Module: For the cluster targets to be analyzed, each target unit is independently geometrically modeled; a closed spherical equivalent surface that completely surrounds the outer contour is constructed for each target unit; the surface of the target unit and the corresponding equivalent surface are respectively meshed in three dimensions to generate discrete surface element information;

[0100] Load balancing and data distributed initialization module: Starts parallel computing processes, uses a greedy algorithm to allocate target-equivalent faces, and iteratively allocates tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status, so as to achieve balanced partitioning;

[0101] The parallel computation module for scattering and transfer operators divides the computation process groups corresponding to each subdomain into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently calculates the scattering matrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to calculate the transfer matrix block corresponding to the coordinate, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces.

[0102] Hybrid basis function parallel iterative solution module: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters the global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator; it updates the equivalent surface flow of its own subdomain by using the conversion relationship between the RWG basis function and the BOR mode current until the global residual satisfies the preset convergence criterion.

[0103] Electromagnetic property extraction module: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

[0104] The present invention also provides a computer device, including: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle.

[0105] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps in the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle.

[0106] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0107] Example

[0108] The analysis of electromagnetic scattering characteristics of large-scale cluster targets faces a dramatic increase in computational complexity due to their complex geometry, significant electromagnetic coupling effects, and enormous electrical size. Traditional serial computing methods suffer from severe computational bottlenecks and storage limitations, making it difficult to meet the requirements of computational efficiency and accuracy in practical engineering applications.

[0109] like Figure 1 As shown in the figure, this embodiment presents a method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence, comprising the following steps:

[0110] Step 1: Geometric Modeling and Equivalent Surface Construction: For the cluster targets to be analyzed, perform independent geometric modeling for each target element; construct a closed, fictitious equivalent surface that completely encloses its outer contour for each target element; perform 3D meshing on the surface of the target element and the corresponding equivalent surface to generate discrete surface element information, as follows:

[0111] Step 1.1: Perform accurate 3D geometric modeling for each metal target, and construct a closed spherical equivalent surface that completely surrounds the outer contour of each target. The equivalent surface must maintain an appropriate distance from the target surface.

[0112] Step 1.2: Discretize the target surface and equivalent surface using triangular facets. The maximum side length of the facet is no greater than one-tenth of the wavelength corresponding to the incident wave frequency.

[0113] Step 1.3: Number all triangular facets and points, and record the three vertex numbers and three-dimensional coordinates of each triangular facet;

[0114] Step 1.4: Determine the common edges and assign them numbers, and establish the logical relationship between the common edges and adjacent positive and negative triangle elements.

[0115] Step 2, Load Balancing and Distributed Data Initialization: Start the parallel computing process and use a greedy algorithm to allocate target-equivalent faces. Based on the computational complexity of the subdomain and the real-time resource status, iteratively allocate tasks to the computing process group with the lowest load to achieve balanced partitioning, as follows:

[0116] Step 2.1: Based on the grid size and computational complexity of each subdomain, and using the following evaluation model, iteratively allocate computational tasks to the computational process group with the lowest load, thereby achieving a highly balanced task partitioning;

[0117] Step 2.1.1: Within the framework of the method of moments combined with domain decomposition, subdomains The computational complexity is not simply linearly related to its mesh size, but is determined by multiple factors including matrix filling, local solving, and boundary interactions, resulting in a total computational cost that increases with the number of unknowns in the subdomain. It exhibits high-order nonlinear growth, as detailed below;

[0118] Matrix filling: subfield Filling the impedance matrix requires calculating the interactions between all basis function pairs, and the computational cost is strictly proportional to the number of basis function pairs. Even with acceleration techniques (such as adaptive cross approximation), the near-field part still retains the dominance of the squared terms.

[0119] Local solution: In the domain decomposition framework, each subdomain needs to independently solve its local matrix equations. If a direct solution method (such as LU decomposition) is used, the computational complexity is O(log n). If an iterative solution method is used, the complexity of each iteration is O(n log n). The number of iterations is determined by the subfield condition number. Therefore, the cubic term is a core component of the subfield solution cost.

[0120] Boundary interaction: Coupling between subdomains is achieved through transmission conditions, requiring repeated exchange of boundary information and updates to boundary conditions—a global iterative process. The computational cost in each iteration is proportional to the number of unknowns on the boundary; within the domain decomposition framework, the number of boundary unknowns equals the total number of unknowns in the subdomain. Therefore, the total computational cost of boundary interactions can be expressed as: Multiply by the number of iterations, which is usually a constant independent of the size of the subdomain.

[0121] In summary, matrix filling exhibits quadratic growth, local solution exhibits cubic growth, and boundary interaction exhibits linear growth. These three factors together constitute the high-order nonlinear characteristics of subdomain computation.

[0122] Step 2.1.2: Use a cubic polynomial model to characterize the mesh size. That is, the first Number of unknowns and computational complexity in each subdomain Mapping between:

[0123]

[0124] in, For the first The estimated computational cost for each subdomain; For the first The grid size of a subdomain is typically measured by the number of unknowns or the number of grid cells; coefficients , , , The weighted least squares method was used to fit the data, where For the fitting coefficients of the cubic term, For the fitting coefficients of the quadratic term, For the fitting coefficients of the first-order term, These are the fitting coefficients for the constant term;

[0125] No. Estimated completion time of each node Composed of computation time and communication time, it is expressed as:

[0126]

[0127] Where Q is the total number of subdomains obtained through domain decomposition; To make the first The computational cost of each subdomain is allocated to the first subdomain. The proportion of nodes; For the first The total amount of resources required for the computation of each subdomain; For the first The computing power coefficient of each node; For the first Communication overhead coefficient per unit computational cost between each subdomain and other subdomains;

[0128] Step 2.1.3: The optimization objective is to minimize the longest node completion time T.

[0129]

[0130] This is a function to find the maximum value in a set of numbers; The minimum value function represents finding the minimum value in a set of numbers; This indicates the longest node completion time. This represents the total number of parallel computing nodes. Indicates the first Estimated completion time for each node;

[0131] Subdomain computational integrity constraints:

[0132]

[0133] Node resource capacity constraints:

[0134]

[0135] For each node Total resource capacity;

[0136] Based on the model optimization results, each computation process group only needs to read and store the grid topology data of its assigned subdomain, complete the distributed initialization of the data, and output the allocation matrix. and maximum completion time T;

[0137] Step 2.1.4: To evaluate performance, define the following metrics;

[0138] Load balancing coefficient based on completion time :

[0139]

[0140] coefficient The closer a value is to 1, the smaller the difference in completion time between nodes, and the more balanced the load; when all nodes complete in equal times... =1; when the difference is extremely large. Approaching 0;

[0141] Load balancing coefficient based on computational cost Without considering communication overhead, the load balancing is measured solely by computational load:

[0142]

[0143] When the performance of nodes is heterogeneous, it is necessary to assess whether the allocation matches the node capabilities, and define a fairness index based on load balancing weighted by computing power. :

[0144]

[0145] Considering the differences in node computing power, A larger value indicates a fairer allocation; when all nodes have the same computational load, When the maximum deviation equals the average, ;

[0146] Average node utilization :

[0147]

[0148] This reflects the average percentage of busy time for each node during the entire parallel process. A higher value indicates less idle time;

[0149] Represents the longest completion time among all nodes, and the minimum node utilization. for:

[0150]

[0151] It reflects the relative idleness of the lightest loaded node.

[0152] This metric reveals the relative idleness of the lightest-loaded nodes, which helps identify load bottlenecks;

[0153] Step 2.2: Each computation process group independently reads the mesh data of the metal target and equivalent surface in its assigned subdomain, including the vertex coordinates, vertex indices, normal vectors, and positive and negative triangle numbers corresponding to the common edges of all triangular facets.

[0154] Step 2.3: Each computing process group initializes the local data structure of its subdomain in memory based on the read grid data, completes the pre-allocation of scattering operators and transfer operators, and realizes the distributed loading of computing tasks and data.

[0155] Step 3: Parallel computation of scattering and transfer operators: The computation process groups corresponding to each subdomain are divided into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently computes the scattering submatrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to compute the transfer submatrix block corresponding to its coordinates, thereby achieving efficient parallel modeling of the electromagnetic coupling effect between equivalent surfaces, as detailed below.

[0156] Step 3.1: To achieve efficient mapping between computing tasks and computing process resources, the computing process group responsible for computing each subdomain is divided into a two-dimensional Cartesian coordinate grid. The topology of this grid strictly corresponds to the block partitioning strategy of the scattering operator and the transfer operator matrix, ensuring that each computing process node logically corresponds to a specific sub-block of the operator matrix and is responsible for all computing tasks related to that sub-block.

[0157] Set the dimension of the computation process grid to 1. The process coordinates are represented as ,in For row index, Column indices are used, all counting from 0; the operator matrix is ​​correspondingly divided into... If there are multiple sub-blocks, then the computation process... The corresponding submatrix index Determined by row priority: ;

[0158] This mapping relationship ensures precise alignment between computing tasks and computing process resources, effectively improves data locality, reduces communication overhead, and lays an efficient topological foundation for subsequent parallel computing.

[0159] Step 3.2: Using the RWG basis functions of the metal target surface and the equivalent surface, establish the scattering matrix between the internal target and the surrounding equivalent surface in parallel calculation; for each rotationally symmetric equivalent surface, construct and calculate the mode coupling matrix between the equivalent surfaces of different subdomains in the Fourier mode space, forming a dimension reduction transfer operator for calculating the electromagnetic coupling between equivalent surfaces.

[0160] The scattered electromagnetic current on the equivalent surface satisfies the following relationship:

[0161]

[0162] calculate When there are separate targets, , The number of the equivalent surface and , , ; , They are the first Incident electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface It is the first Equivalent operators for each objective, It is the first The and the first Transit operators between equivalent surfaces;

[0163] The computation process group is divided according to a two-dimensional Cartesian coordinate grid. Each computation process node in the grid is responsible for computing a sub-matrix block of a scattering operator and its associated (Q-1) transfer operator sub-matrix blocks. It independently executes the computation tasks of all corresponding sub-matrix blocks by allocating a DCU acceleration card, thereby achieving efficient matrix filling.

[0164] Due to the orthogonal equivalent operator formed by the direct interaction of RWG basis functions and BoR basis functions Both computational and storage complexity reach ,in This indicates the number of RWG basis functions on the internal metal. The modulus represents the number of trigonometric basis functions along the generatrix on the equivalent sphere, and Mod represents the total number of positive modes. Therefore, orthogonal mode transfer matrices are used only for interactions between different sub-regions. The calculation requires that the equivalent sphere be expanded using both RWG and BoR basis functions to obtain the equivalent electromagnetic current.

[0165] Step 4: Parallel Iterative Solution of Hybrid Basis Functions: After each computational process independently calculates the initial equivalent flow of the subdomain, it enters a global parallel iterative solution loop. In each iteration, each computational process independently calculates the scattered field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator. The equivalent surface flow of the subdomain is updated using the conversion relationship between the RWG basis functions and the BOR mode current until the global residual satisfies the preset convergence criterion, as detailed below:

[0166] Step 4.1: Set initial equivalent surface current or equivalent magnetic current for the equivalent surface of each subdomain as the initial value for iterative solution;

[0167] Step 4.2: In each iteration, each calculation process independently calculates the local scattering field generated by the current of the equivalent surface in the current subdomain using the scattering operator constructed in step 3.

[0168] Step 4.3: Each calculation process efficiently receives and accumulates the radiation contribution from the equivalent surface current of all other subdomains to its own subdomain by calling the transfer operator calculated in step 3, forming the total excitation field acting on its own subdomain.

[0169] Step 4.4: Combining the local scattered field and total excitation field calculated in Steps 4.2 and 4.3, solve the update equation of the equivalent surface current according to the electromagnetic boundary conditions of the equivalent surface; this process achieves efficient calculation through the rapid current conversion between RWG basis functions and BOR basis functions.

[0170] Step 4.5: After each iteration, calculate the relative residual norm of the global equivalent current solution in parallel; determine whether the residual is lower than the preset convergence tolerance: if it is lower than the tolerance, the iteration is considered to have converged and step 4.6 is executed; if it is higher than the tolerance, the updated equivalent surface current is used as the new current solution and the process returns to step 4.2 for the next iteration.

[0171] Step 4.6: After the iteration converges, each calculation process synchronizes the final equivalent surface current solution, providing a data foundation for subsequent near-field and far-field calculations.

[0172] Step 5, Electromagnetic property extraction: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration, as follows:

[0173] Step 5.1: Treat the equivalent surface electromagnetic current obtained after the iterative convergence of each subdomain as an independent equivalent radiation source;

[0174] Step 5.2: For each equivalent radiation source, apply the far-field radiation integral formula to calculate the far-field scattered electric field vector generated in the specified observation direction; superimpose the far-field scattered electric field vectors of all equivalent radiation sources in the same observation direction to obtain the total scattered electric field of the entire cluster target in that observation direction.

[0175] Step 5.3: According to the definition of Radar Cross Section (RCS), the radar cross section of the entire cluster of targets in a specified observation direction is: the ratio of the power density scattered by the target towards the receiver to the power density of the incident wave at the target within a unit solid angle. times.

[0176] This embodiment uses a model of a 120-drone array as an example. Figure 2 As shown, the model consists of 120 drones, with overall dimensions of 141.6 meters × 21.2 meters × 21.0 meters. The dimensions of each drone model and the spacing between models are as follows. Figure 3 As shown, it is in The spacing in all directions is 10 meters. The radar simulation parameters are set as follows: operating frequency is set to 1 GHz, and plane wave incident direction is set to azimuth angle. Pitch angle The polarization mode is VV polarization. After discretization using the method of moments with RWG basis functions, the number of unknowns is 3,898,440. The initial computation task was deployed on a heterogeneous cluster with 30 computing nodes, initially configured with 960 CPU cores and 120 DCU accelerator cards, equivalent to 8,640 computing cores. To further evaluate the algorithm's strong scalability and parallel efficiency, the computation scale was gradually expanded to 11,520 cores, 17,280 cores, and 34,560 cores. The computation time and parallel efficiency test results are as follows: Figure 4 As shown, Figure 5 This demonstrates a comparison between the calculated Radar Cross Section (RCS) after scaling to 34560 cores and the original scale. Figure 5 As can be seen, the parallel architecture of the method of the present invention has accurate calculation results, parallel efficiency of over 95%, good parallel scalability and computational efficiency, significantly reduces memory requirements and computation time overhead, improves computational efficiency, and has strong engineering applicability.

[0177] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence, characterized in that, Includes the following steps: Step 1, Geometric Modeling and Equivalent Surface Construction: For the cluster targets to be analyzed, perform independent geometric modeling for each target unit; construct a closed spherical equivalent surface that completely encloses the outer contour for each target unit; perform 3D meshing on the surface of the target unit and the corresponding equivalent surface to generate discrete surface element information; Step 2, Load Balancing and Distributed Data Initialization: Start the parallel computing process, use a greedy algorithm to allocate target-equivalent faces, and iteratively allocate tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status to achieve balanced partitioning; Step 3: Parallel computation of scattering and transfer operators: The computation process groups corresponding to each subdomain are divided into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently computes the scattering submatrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to compute the transfer submatrix block corresponding to its coordinates, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces, as detailed below: Step 3.1: To achieve the mapping between computing tasks and computing process resources, the computing process group responsible for computing each subdomain is divided into a two-dimensional Cartesian coordinate grid. The topology of this grid corresponds to the block partitioning strategy of the scattering operator and the transfer operator matrix, ensuring that each computing process node logically corresponds to a specific sub-block of the operator matrix and is responsible for all computing tasks related to that specific sub-block. Set the dimension of the computation process grid to 1. The process coordinates are represented as ,in For row index, Column indices are used, all counting from 0; the operator matrix is ​​correspondingly divided into... If there are multiple sub-blocks, then the computation process... The corresponding submatrix index Determined by row priority: ; Step 3.2: Using the RWG basis functions of the metal target surface and the equivalent surface, establish the scattering matrix between the internal target and the surrounding equivalent surface in parallel calculation; for each rotationally symmetric equivalent surface, construct and calculate the mode coupling matrix between the equivalent surfaces of different subdomains in the Fourier mode space, forming a dimension reduction transfer operator for calculating the electromagnetic coupling between equivalent surfaces. The scattered electromagnetic current on the equivalent surface satisfies the following relationship: （11） calculate When there are separate targets, , The number of the equivalent surface and , , ; , They are the first Incident electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface , They are the first Scattered electric and magnetic flux densities on an equivalent surface It is the first Equivalent operators for each objective, It is the first The and the first Transit operators between equivalent surfaces; The computation process group is divided according to a two-dimensional Cartesian coordinate grid. Each computation process node in the grid is responsible for computing a sub-matrix block of a scattering operator and Q-1 related transfer operator sub-matrix blocks. It independently executes the computation tasks of all corresponding sub-matrix blocks by allocating a DCU acceleration card to achieve matrix filling. Here, DCU refers to depth computing unit. Step 4: Parallel iterative solution of hybrid basis functions: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters the global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator. The equivalent surface current of this subdomain is updated by utilizing the conversion relationship between the RWG basis functions and the BOR mode current until the global residual satisfies the preset convergence criterion. Step 5, Electromagnetic property extraction: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

2. The method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence as described in claim 1, characterized in that, Step 1 is described in detail as follows: Step 1.1: Perform independent 3D geometric modeling for each metal target unit, and construct a closed spherical equivalent surface that completely surrounds the outer contour for each target unit, maintaining a set distance between the equivalent surface and the target surface; Step 1.2: Discretize the surface of the target unit and the equivalent surface using triangular facets. The maximum side length of the facet is no greater than one-tenth of the wavelength corresponding to the incident wave frequency. Step 1.3: Number all triangular facets and points, and record the three vertex numbers and three-dimensional coordinates of each triangular facet; Step 1.4: Determine the common edge and number it, and establish the logical relationship between the common edge and the adjacent positive and negative triangle elements.

3. The method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence as described in claim 1, characterized in that, Step 2 is described in detail below: Step 2.1: Start the parallel computing process and use a greedy algorithm to allocate target-equivalent faces. Based on the computational complexity of the subdomain and the real-time resource status, combined with the evaluation model, the computing tasks are iteratively allocated to the computing process group with the lowest load. Step 2.2: Each computation process group independently reads the mesh data of the metal target and equivalent surface in the assigned subdomain, including the vertex coordinates, vertex indices, normal vectors, and positive and negative triangle numbers corresponding to the common edges of all triangular facets. Step 2.3: Each computing process group initializes the local data structure of the subdomain in memory based on the read grid data, completes the pre-allocation of scattering operators and transfer operators, and realizes the distributed loading of computing tasks and data.

4. The method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence as described in claim 3, characterized in that, Step 2.1 is as follows: Step 2.1.1: Within the framework of the method of moments combined with domain decomposition, subdomains The computational complexity is determined by multiple factors, including matrix filling, local solution, and boundary interaction. Among them, matrix filling grows quadratically, local solution grows cubically, and boundary interaction grows linearly. These three factors together constitute the high-order nonlinear characteristics of the computational complexity of the subdomain. Step 2.1.2: Use a cubic polynomial model to characterize the mesh size. That is, the first Number of unknowns and computational complexity in each subdomain Mapping between: （1） in, For the first The estimated computational cost for each subdomain; For the first The grid size of a subdomain is typically measured by the number of unknowns or the number of grid cells; coefficients , , , The weighted least squares method was used to fit the data, where For the fitting coefficients of the cubic term, For the fitting coefficients of the quadratic term, For the fitting coefficients of the linear term, The fitting coefficients are constant terms; No. Estimated completion time of each node Composed of computation time and communication time, it is expressed as: （2） Where Q is the total number of subdomains obtained through domain decomposition; To make the first The computational cost of each subdomain is allocated to the first subdomain. The proportion of nodes; For the first The total resources required for the computation of each subdomain; For the first The computing power coefficient of each node; For the first Communication overhead coefficient per unit computational cost between each subdomain and other subdomains; Step 2.1.3: The optimization objective is to minimize the longest node completion time T. （3） This is a function to find the maximum value in a set of numbers; The minimum value function represents finding the minimum value in a set of numbers; This indicates the longest node completion time. This represents the total number of parallel computing nodes. Indicates the first Estimated completion time for each node; Subdomain computational integrity constraints: （4） Node resource capacity constraints: （5） For each node Total resource capacity; Based on the model optimization results, each computation process group only needs to read and store the grid topology data of its assigned subdomain, complete the distributed initialization of the data, and output the allocation matrix. and maximum completion time T; Step 2.1.4: To evaluate performance, define the following metrics; Load balancing coefficient based on completion time : （6） coefficient The closer a value is to 1, the smaller the difference in completion time between nodes, and the more balanced the load; when all nodes complete in equal times... =1; when the difference is extremely large. Approaching 0; Load balancing coefficient based on computational cost Without considering communication overhead, the load balancing is measured solely by computational load: （7） When the performance of nodes is heterogeneous, it is necessary to assess whether the allocation matches the node capabilities, and define a fairness index based on load balancing weighted by computing power. : （8） Considering the differences in node computing power, A larger value indicates a fairer allocation; when all nodes have the same computational load, When the maximum deviation equals the average, ; Average node utilization : （9） This reflects the average percentage of busy time for each node during the entire parallel process. A higher value indicates less idle time; Represents the longest completion time among all nodes, and the minimum node utilization. for: （10） It reflects the relative idleness of the lightest loaded node.

5. The method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence as described in claim 1, characterized in that, Step 4 is as follows: Step 4.1: Set initial equivalent surface current or equivalent magnetic current for the equivalent surface of each subdomain as the initial value for iterative solution; Step 4.2: In each iteration, each calculation process independently calculates the local scattering field generated by the equivalent surface current of the current subdomain using the scattering operator calculated in step 3. Step 4.3: Each calculation process receives and accumulates the radiation contribution from the equivalent surface current of all other subdomains to its own subdomain by calling the transfer operator calculated in step 3, thus forming the total excitation field acting on its own subdomain. Step 4.4: Combining the local scattered field and total excitation field calculated in Steps 4.2 and 4.3, solve the update equation of the equivalent surface current according to the electromagnetic boundary conditions of the equivalent surface; this process is achieved through the current conversion between the RWG basis function and the BOR basis function. Step 4.5: After each iteration, calculate the relative residual norm of the global equivalent current solution in parallel; determine whether the residual is lower than the preset convergence tolerance: if it is lower than the tolerance, the iteration is considered to have converged and step 4.6 is executed; if it is not lower than the tolerance, the updated equivalent surface current is used as the new current solution and the process returns to step 4.2 for the next iteration. Step 4.6: After the iteration converges, each calculation process synchronizes the final equivalent surface current solution, providing a data foundation for subsequent near-field and far-field calculations.

6. The method for analyzing electromagnetic scattering of large-scale clustered targets based on the principle of parallel equivalence as described in claim 1, characterized in that, Step 5 is described in detail below: Step 5.1: Treat the equivalent surface electromagnetic current obtained after the iterative convergence of each subdomain as an independent equivalent radiation source; Step 5.2: For each equivalent radiation source, apply the far-field radiation integral formula to calculate the far-field scattered electric field vector generated in the specified observation direction; The total scattered electric field of the entire cluster of targets in that observation direction is obtained by superimposing the far-field scattered electric field vectors of all equivalent radiation sources in the same observation direction. Step 5.3: According to the definition of Radar Cross Section (RCS), the radar cross section of the entire cluster of targets in a specified observation direction is: the ratio of the power density scattered by the target towards the receiver to the power density of the incident wave at the target within a unit solid angle. times.

7. A large-scale cluster target electromagnetic scattering analysis system based on the parallel equivalence principle, characterized in that, This system is used to implement the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle as described in any one of claims 1 to 6, the system comprising: Geometric Modeling and Equivalent Surface Construction Module: For the cluster targets to be analyzed, each target unit is independently geometrically modeled; a closed spherical equivalent surface that completely surrounds the outer contour is constructed for each target unit; the surface of the target unit and the corresponding equivalent surface are respectively meshed in three dimensions to generate discrete surface element information; Load balancing and data distributed initialization module: Starts parallel computing processes, uses a greedy algorithm to allocate target-equivalent faces, and iteratively allocates tasks to the computing process group with the lowest load based on the computational complexity of the subdomain and the real-time resource status, so as to achieve balanced partitioning; The parallel computation module for scattering and transfer operators divides the computation process groups corresponding to each subdomain into blocks according to a two-dimensional Cartesian coordinate grid. Each computation process independently calculates the scattering matrix block it is responsible for based on its coordinate position, establishing a local mapping relationship between the electromagnetic current and the scattered field of the equivalent surface. At the same time, the transfer operator matrices between subdomains are divided into blocks according to the same two-dimensional computation process grid. Each computation process only needs to calculate the transfer matrix block corresponding to the coordinate, realizing parallel modeling of the electromagnetic coupling effect between equivalent surfaces. Hybrid basis function parallel iterative solution module: After each computation process independently calculates the initial equivalent flow of the subdomain, it enters the global parallel iterative solution loop. In each iteration, each computation process independently calculates the scattering field of its own subdomain and aggregates the coupling contributions from other subdomains through the transfer operator; it updates the equivalent surface flow of its own subdomain by using the conversion relationship between the RWG basis function and the BOR mode current until the global residual satisfies the preset convergence criterion. Electromagnetic property extraction module: Using the equivalent surface flow of each converged subdomain as an equivalent source, the radar cross section (RCS) of the entire cluster target in the specified observation direction is synthesized by far-field radiation integration.

8. A computer device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the large-scale cluster target electromagnetic scattering analysis method based on the parallel equivalence principle as described in any one of claims 1 to 6.

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