A method for calculating the scattering field of an electrically large scatterer

Abstract

The present application relates to a kind of electric large size scatterer scattering field calculation method, belong to electromagnetic field, and calculation method includes: using high-order curved side triangle element to the surface of curved surface scatterer is discretized, and using quadratic form equation to each curved side triangle region is fitted to curved surface;Local coordinate system is constructed and the coordinate transformation relationship is calculated;Three-dimensional curved area integral is converted into the pixelization integration of two-dimensional projection screen;Local radiation field is calculated based on physical optics method, and global scattering field is obtained by vector field synthesis;Parallel computing optimization is carried out.The present application uses quadratic form patch to fit complex curved surface, compared with traditional plane triangle grid, reduce the number of grid 50%~70%, substantially reduce the consumption of computing resource;Three-dimensional curved area integral is converted into two-dimensional plane integration by local coordinate system projection, and calculation complexity is simplified.

Description

Technical Field

[0001] This invention relates to the field of electromagnetics, and more particularly to a method for calculating the scattering field of an electrically large scatterer. Background Technology

[0002] Currently, the calculation of electromagnetic scattering from electrically large scatterers mainly faces the following challenges:

[0003] 1. High mesh generation complexity: Traditional planar triangular meshes require extremely small electrical size meshes (≤λ / 3) when discretizing complex surfaces, leading to a dramatic increase in the number of meshes and high computational resource consumption. 2. Surface element noise problem: Planar meshes approximate surfaces, introducing high-frequency noise, requiring further mesh refinement and exacerbating the computational burden. 3. Limitations of NURBS surface modeling: Although NURBS modeling has high accuracy, its nonlinear phase integration and boundary treatment are complex, making it difficult to apply efficiently to physical optics methods. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the scattering field of electrically large scatterers, thus solving the deficiencies of the prior art.

[0005] The objective of this invention is achieved through the following technical solution: a method for calculating the scattering field of an electrically large scatterer, the calculation method comprising:

[0006] S1. The surface of the curved scatterer is discretized using high-order curved triangular units, and a quadratic equation is used to fit the surface of each curved triangular region.

[0007] S2. Construct a local coordinate system and calculate the coordinate transformation relationships;

[0008] S3. Convert the three-dimensional surface integral into a pixelated integral for a two-dimensional projection screen;

[0009] S4. Calculate the local radiation field based on the physical optics method, and obtain the global scattering field through vector field synthesis;

[0010] S5, Parallel computing optimization.

[0011] S1 includes:

[0012] S101, High-order curved triangle mesh generation: The target surface is discretized using high-order curved triangle elements. Each element contains 7 control points, and the mesh is generated using commercial software. The mesh size is controlled between λ / 5 and λ / 8, where λ represents the working wavelength.

[0013] S102, Quadratic Surface Fitting: For each curvilinear triangular element, a quadratic equation is used. Perform local surface fitting, where, x andy These represent the coordinates in the parameter space. z This represents the height or normal displacement of a surface in actual physical space.

[0014] S103. Perform least squares optimization: using the coordinates of 7 control points ( Construct an overdetermined system of equations Solve for the coefficients , , , , and ,in, j represents the number, coordinate ( () represents the coordinates of the j-th point.

[0015] S2 includes:

[0016] S201. Local coordinate system setting: The origin O is the center of the curvilinear triangle. The U-axis is calculated using partial derivatives along the principal curvature direction of the surface, but the vector is... Along the normal direction of the surface, the unit vector of the W-axis is calculated from the gradient. The V-axis unit vector is determined by the cross product. Ensure that UVW forms a right-handed coordinate system, where, Represents the local U-axis unit vector. Represents the global X-axis unit vector. Represents the global Z-axis unit vector. Represents a local unit vector along the W-axis; Refers to the direction along the normal of the curved surface;

[0017] S202, Global coordinate to local coordinate transformation: Let any point... In the local coordinate system, it is represented as ,in, The coordinates of the target point in the global 3D space. This represents the coordinates of any point in the local coordinate system.

[0018] S3 includes:

[0019] S301. Transformation from surface integral to plane integral: Project the quadratic patch onto the local XOY plane, with the integration domain being the circumscribed rectangle. Where L is the length of the circumscribed rectangle of the projection plane, and H is the height of the circumscribed rectangle of the projection plane, the physical optics integral formula is transformed into ,in, Let k be the radiation density function, and k be the wave number. Let be the component of the wave vector difference in the local x-direction. This represents the component of the wave vector difference in the local y-direction;

[0020] S302, Pixelation Discretization: Dividing the projection area into... A rectangular pixel, each pixel having a size of [missing information]. ,in, Indicates the pixel size in the x-direction. Indicates the pixel size in the y-direction. This represents the number of pixels along the X direction. This represents the number of pixels along the Y direction.

[0021] S303. Valid integration determination: If the pixel center is located within the projection of the curved triangle, it is marked as valid; otherwise, it is skipped, and the direction spectrum calculation is accelerated by using fast Fourier transform.

[0022] S4 includes:

[0023] S401, Local Scattering Field Calculation: For each effective pixel, calculate the radiation contribution as follows: And calculate the vertical polarization and horizontal polarization components respectively, where, This represents the contribution of the scattered field from the j-th pixel. The x-coordinate of the pixel center This represents the y-coordinate of the pixel center;

[0024] S402, Global Field Synthesis: Transforming the local scattered field to the global coordinate system through coordinate transformation. ,in, This represents the total scattered field in the global coordinate system. This represents the total number of curvilinear triangular units. Indicates the first Local scattering field of each unit For the first The transformation matrix of each unit.

[0025] S5 includes:

[0026] S501, GPU acceleration: It adopts the CUDA parallel computing framework to distribute pixel integration tasks to multiple GPU cores;

[0027] S502, Load Balancing: Dynamically schedules computing units to ensure a balanced workload for each thread.

[0028] The present invention has the following advantages:

[0029] 1. Significantly Improved Computational Efficiency: By employing quadratic patch fitting for complex surfaces, the number of meshes is reduced by 50% to 70% compared to traditional planar triangular meshes, significantly lowering computational resource consumption. The 3D surface integral is transformed into a 2D plane integral through local coordinate system projection, simplifying computational complexity. Combined with GPU parallel computing technology, the computational speed is more than 3 times faster than traditional methods, making it suitable for rapid analysis of electrically large targets.

[0030] 2. High computational accuracy: The fitting error of the quadratic surface is less than 1%, which accurately approximates complex geometries, avoids the surface noise problem introduced by planar mesh discretization, and supports high-order phase integration, which can accurately handle nonlinear phase changes caused by the surface and improve the reliability of far-field scattering calculation.

[0031] 3. Clear physical meaning: The intermediate results based on the physical optics method (PO) (such as the radiation density function) intuitively reflect the electromagnetic scattering mechanism, which is convenient for engineering optimization design; and through the pixelation discretization method, the complex integral is transformed into a quantifiable image processing problem, which is convenient for result analysis and verification.

[0032] 4. Wide range of applications: Applicable to RCS (radar cross section) calculation and stealth design of electrically large and complex curved surface targets such as aircraft, missiles, and ships. It is compatible with multiple CAD model inputs and can directly process industrial design data without intermediate format conversion. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the process of the present invention;

[0034] Figure 2 A schematic diagram of a quadratic surface fitted at seven points;

[0035] Figure 3 A schematic diagram of the optical integral problem in field physics;

[0036] Figure 4 For projection area Schematic diagram;

[0037] Figure 5 A schematic diagram of the synthesis of integral fields of different unit PO. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application provided below with reference to the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The present invention will be further described below with reference to the accompanying drawings.

[0039] This invention specifically relates to a method for calculating the scattering field of electrically large scatterers based on quadratic patches and physical optics (PO), applicable to electromagnetic scattering analysis of complex curved surface targets such as aircraft and missiles. Figure 1 As shown, it specifically includes the following:

[0040] S1. Discretization of complex surfaces and quadratic patch fitting;

[0041] S101. Generation of high-order curved triangular mesh: The target surface is discretized using high-order curved triangular elements. Each element contains 7 control points (vertex + edge midpoint + face center point) to ensure geometric approximation accuracy. The mesh is generated using commercial software, and the mesh size is controlled between λ / 5 and λ / 8 (λ is the working wavelength).

[0042] S102, Quadratic surface fitting;

[0043] like Figure 2 As shown, for each curvilinear triangular element, a quadratic equation is used for local surface fitting:

[0044] ,

[0045] in, x and y These represent the coordinates in the parameter space; z It represents the height or normal displacement of a surface in actual physical space.

[0046] S103. Perform least squares optimization: using the coordinates of 7 control points ( Construct an overdetermined system of equations and solve for the coefficients. , , , , and :

[0047] ,

[0048] Among them, coordinates ( () represents the coordinates of the j-th point; j represents the number (i.e., the number currently being processed). (including the j-th control point used for fitting within the current cell), the fitting error is controlled to be <1%, ensuring geometric accuracy.

[0049] S2. Construction of local coordinate system and coordinate transformation;

[0050] S201, Definition of Local Coordinate System;

[0051] The origin O is the center point (the 7th point) of the curvilinear triangle.

[0052] U-axis: along the direction of the principal curvature of the surface, calculated from the partial derivatives:

[0053] ,

[0054] in, Represents the local U-axis unit vector; Represents the global X-axis unit vector; Represents the global Z-axis unit vector;

[0055] W-axis: Along the surface normal, calculated from the gradient.

[0056] ,

[0057] in, Represents a local unit vector along the W-axis; Refers to the direction along the normal of the curved surface.

[0058] V-axis: Determined by cross product Ensure that UVW forms a right-handed coordinate system, where, Represents the local V-axis unit vector.

[0059] S202, Transformation from global coordinates to local coordinates;

[0060] any point In the local coordinate system, it is represented as:

[0061] ,

[0062] in, Represents the coordinates of any point in the local coordinate system. The coordinates of the target point in the global three-dimensional space; The origin of the coordinate system is denoted as .

[0063] S3, Projection Integral and Pixelation Calculation;

[0064] S301, Conversion from surface integral to plane integral;

[0065] like Figure 3 and Figure 4 As shown, the quadratic patch is projected onto the local XOY plane, and the integration domain is the circumscribed rectangle. Where L is the length of the circumscribed rectangle of the projection plane, and H is the height of the circumscribed rectangle of the projection plane.

[0066] The physical optics integral formula is transformed into:

[0067] ,

[0068] in, Represents the scattered electric field; It is a radiation density function; Represents the projection area; Wave number; Let be the component of the wave vector difference in the local x-direction. This represents the component of the wave vector difference in the local y-direction.

[0069] S302, pixelated discrete;

[0070] like Figure 5 As shown, the projection area is divided into A rectangular pixel, each pixel having a size of [missing information]. ,in, and Indicates the pixel size in two directions. This represents the number of pixels along the X-direction (length direction). This represents the number of pixels along the Y-axis (height direction).

[0071] S303. Valid integration determination: If the pixel center is located within the projection of the curved triangle, it is marked as valid; otherwise, it is skipped. Fast Fourier Transform (FFT) is used to accelerate the direction spectrum calculation and improve integration efficiency.

[0072] S4. Physical Optical Field Calculation and Vector Synthesis;

[0073] S401, Local Scattering Field Calculation: For each effective pixel, calculate the radiation contribution:

[0074] ,

[0075] Where j represents the number, This represents the scattering field contribution of the j-th pixel.

[0076] Polarization processing: Calculate vertical polarization separately ( ) and horizontal polarization ( ) Quantity.

[0077] S402, Global Field Synthesis;

[0078] Transform the local scattered field to the global coordinate system using coordinate transformation:

[0079] ,

[0080] in, Represents the total scattered field in the global coordinate system. Represents the total number of curvilinear triangular units. Representing the Local scattering field of each unit For the first The transformation matrix of each unit.

[0081] S5, Parallel computing optimization;

[0082] S501, GPU acceleration: It adopts the CUDA parallel computing framework to distribute pixel integration tasks to multiple GPU cores.

[0083] S502, Load Balancing: Dynamically schedules computing units to ensure a balanced workload for each thread.

[0084] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and improvements, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for calculating the scattering field of an electrically large scatterer, characterized in that: The calculation method includes: S1. The surface of the curved scatterer is discretized using high-order curved triangular units, and a quadratic equation is used to fit the surface of each curved triangular region. S2. Construct a local coordinate system and calculate the coordinate transformation relationships; S3. Convert the three-dimensional surface integral into a pixelated integral for a two-dimensional projection screen; S4. Calculate the local radiation field based on the physical optics method, and obtain the global scattering field through vector field synthesis; S5, Parallel computing optimization; S3 includes: S301. Transformation from surface integral to plane integral: Project the quadratic patch onto the local XOY plane, with the integration domain being the circumscribed rectangle. Where L is the length of the circumscribed rectangle of the projection plane, and H is the height of the circumscribed rectangle of the projection plane, the physical optics integral formula is transformed into ,in, Let k be the radiation density function, and k be the wave number. Let be the component of the wave vector difference in the local x-direction. Let be the component of the wave vector difference in the local y-direction. Represents the scattered electric field. Represents the projection area. The coordinates of the target point in the global three-dimensional space; S302, Pixelation Discretization: Dividing the projection area into... A rectangular pixel, each pixel having a size of [missing information]. ,in, Indicates the pixel size in the x-direction. Indicates the pixel size in the y-direction. This represents the number of pixels along the X direction. Let x be the number of pixels along the Y direction, where x and y represent the coordinates in the parameter space. S303. Valid integration determination: If the pixel center is located within the projection of the curved triangle, it is marked as valid; otherwise, it is skipped, and the direction spectrum calculation is accelerated by using fast Fourier transform.

2. The method for calculating the scattering field of an electrically large scatterer according to claim 1, characterized in that: S1 includes: S101, High-order curved triangle mesh generation: The target surface is discretized using high-order curved triangle elements. Each element contains 7 control points, and the mesh is generated using commercial software. The mesh size is controlled between λ / 5 and λ / 8, where λ represents the working wavelength. S102, Quadratic Surface Fitting: For each curvilinear triangular element, a quadratic equation is used. Perform local surface fitting, where x and y represent the coordinates in the parameter space, and z represents the height or normal displacement of the surface in the actual physical space; S103. Perform least squares optimization: using the coordinates of 7 control points ( , , Construct an overdetermined system of equations Solve for the coefficients , , , , and ,in, j represents the number, coordinate ( , , () represents the coordinates of the j-th point.

3. The method for calculating the scattering field of an electrically large scatterer according to claim 2, characterized in that: S2 includes: S201. Local coordinate system setting: The origin O is the center of the curvilinear triangle. The U-axis is calculated using partial derivatives along the principal curvature direction of the surface, but the vector is... Along the normal direction of the surface, the unit vector of the W-axis is calculated from the gradient. The V-axis unit vector is determined by the cross product. Ensure that UVW forms a right-handed coordinate system, where, Represents the local U-axis unit vector. Represents the global X-axis unit vector. Represents the global Z-axis unit vector. Represents a local unit vector along the W-axis; Refers to the direction along the normal of the curved surface; S202, Global coordinate to local coordinate transformation: Let any point... In the local coordinate system, it is represented as ,in, Let the coordinates of the target point be in the global 3D space. This represents the coordinates of any point in the local coordinate system.

4. The method for calculating the scattering field of an electrically large scatterer according to claim 1, characterized in that: S4 includes: S401, Local Scattering Field Calculation: For each effective pixel, calculate the radiation contribution as follows: And calculate the vertical polarization and horizontal polarization components respectively, where, This represents the contribution of the scattered field from the j-th pixel. The x-coordinate of the pixel center This represents the y-coordinate of the pixel center; S402, Global Field Synthesis: Transforming the local scattered field to the global coordinate system through coordinate transformation. ,in, This represents the total scattered field in the global coordinate system. This represents the total number of curvilinear triangular units. Indicates the first Local scattering field of each unit For the first The transformation matrix of each unit.

5. The method for calculating the scattering field of an electrically large scatterer according to claim 1, characterized in that: S5 includes: S501, GPU acceleration: It adopts the CUDA parallel computing framework to distribute pixel integration tasks to multiple GPU cores; S502, Load Balancing: Dynamically schedules computing units to ensure a balanced workload for each thread.

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