Broadband scattering simulation method based on grid adaptive encryption

Abstract

The invention discloses a broadband scattering simulation method based on grid adaptive encryption, and belongs to the technical field of electromagnetic simulation. According to the method, independent self-adaptive grid encryption is carried out only at the lowest frequency point of the frequency band. For other frequency points in a frequency band, optimization grids are not independently generated any more, and optimization is guided by using error information at adjacent frequencies. And then, by adopting a Cauchy method, on the basis of frequency sampling points obtained by solving on the optimization grid, reconstructing response data between adjacent sampling points, thereby efficiently and accurately obtaining broadband electromagnetic response. According to the method disclosed by the invention, the grid at each frequency point can be efficiently optimized without carrying out independent adaptive optimization at each selected frequency point like a traditional adaptive encryption method, and meanwhile, the advantage that the adaptive encryption realizes higher precision with less unknown quantity is kept; the complex frequency band response can be efficiently and accurately reconstructed by using the Cauchy method.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic simulation technology, specifically relating to a broadband scattering simulation method based on adaptive mesh encryption. Background Technology

[0002] Broadband radar cross section (RCS) analysis plays a crucial role in engineering applications including target identification and radar design. One method for obtaining broadband scattering responses is the frequency domain approach, which first calculates the response of a finite number of frequency samples and then uses data reconstruction techniques to reconstruct the remaining frequency points. Common techniques often require solving a series of sampling frequencies under a fixed grid to prepare the information needed for reconstruction. However, the grid required for efficient and accurate solutions varies with frequency. If a single grid is used over a wide bandwidth, a grid suitable for high frequencies may introduce unnecessary computational burden at low frequencies, while a grid suitable for low frequencies may not be able to obtain sufficient computational accuracy at high frequencies. The Cauchy method does not impose grid restrictions; it models the amplitude-frequency response of the system as the ratio of two polynomials, allowing non-uniform frequency sampling and generating accurate frequency responses at relatively low computational cost. However, current techniques have not yet applied this method to the solution grid to improve flexibility. In addition, the efficiency of adaptive grid refinement techniques has been proven in single-frequency analysis, achieving good solution accuracy with fewer unknowns. However, adaptive refinement techniques have not yet been applied in broadband electromagnetic scattering analysis of integral equations. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a broadband scattering simulation method based on grid adaptive encryption.

[0004] The technical problem addressed by this invention is solved as follows:

[0005] A broadband scattering simulation method based on adaptive mesh encryption includes the following steps:

[0006] Step 1: Set the initial mesh size. Discretize the target model surface using a triangular mesh of the initial mesh size. The initial mesh size is greater than one-tenth of the maximum wavelength of the frequency band to be simulated. Set the refinement iteration number to 1. Based on the current mesh, solve for the target surface current and radar cross section (RCS) response at the lowest frequency point f0 of the frequency band to be simulated. Set the refinement iteration number to +1 to refine the current mesh.

[0007] Step 2: Solve for the target surface current and RCS response at the lowest frequency point f0 of the frequency band to be simulated;

[0008] Step 3: Determine whether the change in RCS response between two adjacent encryption iterations is less than a set threshold;

[0009] If not, evaluate the current discontinuity error of each grid based on the distribution of the target surface current; select the grid with the largest current discontinuity error for refinement, and return to step 2;

[0010] If so, output the current grid M0 and the corresponding target surface current I0, and proceed to step 4;

[0011] Step 4: Initialize the frequency index i = 0;

[0012] Step 5, at frequency point f i At point M, the computational grid is... i The current discontinuity error of each grid; setting the cell density ratio β and determining the next frequency point f. i+1 The β-section of the mesh with the largest current discontinuity error is selected for refinement, resulting in the optimized mesh M. i+1 ;

[0013] Step 6: Let i = i + 1, at frequency point f i At this location, based on grid M i Solving for the target surface current I i ;

[0014] Step 7: Determine the frequency point f i Whether the highest frequency point of the frequency band to be simulated has been reached;

[0015] If not, return to step 5;

[0016] If so, output grid { , , ..., } and its corresponding target surface current { , , ..., };

[0017] Step 8: Set the initial frequency sampling point sequence within the frequency band to be simulated, which consists of several frequency sampling points with equal step size;

[0018] Step 9: For each frequency sampling point, solve using the grid closest to it to obtain the target surface current and RCS response corresponding to the current frequency sampling point; based on the frequency sampling point and its corresponding RCS, use the Cauchy method to interpolate to obtain the full-band RCS response within the entire frequency band to be simulated.

[0019] Step 10: Verify the extreme points and frequency points where the curvature exceeds the set threshold in the interpolated full-band RCS response curve, and determine whether the error between the interpolation result and the simulation result based on the closest mesh meets the accuracy requirements.

[0020] If not, the verification is deemed to have failed, and the frequency points that failed the verification are added to the frequency sampling point sequence. Then, return to step 9.

[0021] If so, the interpolation result will be output as the final broadband RCS response.

[0022] Furthermore, in steps 1 and 2, the target surface current and RCS response are solved using the multilayer fast multipole method.

[0023] Furthermore, in step 3, the 30% to 50% portion of the mesh with the largest current discontinuity error is selected for refinement.

[0024] Furthermore, in step 5, the relationship between the adaptive encryption ratio β and the frequency point selection is expressed as:

[0025] .

[0026] Furthermore, in steps 1, 3, and 5, the specific process of refining the mesh is as follows: the midpoints of the three sides of the triangles in the mesh are interconnected to divide the mesh into four equal triangular meshes.

[0027] Furthermore, the specific implementation process of the Cauchy method in step 9 is as follows:

[0028] The RCS response is modeled as the ratio of two polynomials, expressed as:

[0029]

[0030] Where f represents frequency, This represents the RCS response at frequency f; P is the order of the numerator polynomial, 0 ≤ p ≤ P⁻¹. The coefficients are of order p. Let q be the order of the denominator polynomial, and 0 ≤ q ≤ Q-1. The coefficients are of order q.

[0031] The above formula is rewritten into a system of equations and solved to obtain the coefficient values, and then the RCS response is obtained.

[0032] The beneficial effects of this invention are:

[0033] The method described in this invention provides a broadband scattering simulation method based on mesh adaptive encryption, which is used to efficiently obtain broadband RCS response. This method does not require independent adaptive optimization at each selected frequency point as in traditional adaptive encryption methods, and can efficiently optimize the mesh at each frequency point, while maintaining the advantage of adaptive encryption in achieving high accuracy with fewer unknowns. The Cauchy method can efficiently and accurately reconstruct complex frequency band response. Attached Figure Description

[0034] Figure 1 The diagram shows a comparison between the adaptively optimized RCS result at the lowest frequency point of the frequency band and the reference RCS in the embodiment.

[0035] Figure 2 The example shows a comparison between the adaptively optimized RCS result at the highest frequency point of the frequency band and the reference RCS.

[0036] Figure 3 The image shows the broadband RCS response result obtained by the method described in the embodiment. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] This embodiment provides a broadband scattering simulation method based on adaptive mesh refinement. It obtains a high-quality optimized mesh at each frequency point within the frequency band without requiring independent adaptive refinement at each frequency. Subsequently, the optimized mesh is used to solve for the selected frequency sampling points using a data reconstruction method. Finally, the Cauchy method is employed to reconstruct the data between adjacent frequency sampling points, thereby efficiently and accurately obtaining the broadband electromagnetic response.

[0039] The method described in this embodiment specifically includes the following steps:

[0040] Step 1: Set the initial mesh size. Discretize the target model surface using a triangular mesh of the initial mesh size. The initial mesh size is greater than one-tenth of the maximum wavelength of the frequency band to be simulated. Set the refinement iteration number to 1. Based on the current mesh, solve for the target surface current and radar cross section (RCS) response at the lowest frequency point f0 of the frequency band to be simulated. Set the refinement iteration number to +1 to refine the current mesh.

[0041] Step 2: Solve for the target surface current and RCS response at the lowest frequency point f0 of the frequency band to be simulated.

[0042] In this embodiment, in steps 1 and 2, the multilayer fast multipole method is used to solve for the target surface current and RCS response.

[0043] Step 3: Determine whether the change in RCS response between two adjacent encryption iterations is less than a set threshold. ;

[0044] If not, evaluate the current discontinuity error of each grid based on the distribution of the target surface current; select the grid with the largest current discontinuity error for refinement, and return to step 2;

[0045] If so, output the current grid M0 and the corresponding target surface current I0, and proceed to step 4.

[0046] In this embodiment, in step 3, the 30% to 50% portion of the mesh with the largest current discontinuity error is selected for densification.

[0047] Step 4: Initialize the frequency index i = 0;

[0048] Step 5, at frequency point f i At the evaluation grid M i The current discontinuity error of each grid; setting the cell density ratio β and determining the next frequency point f. i+1 The β-section of the mesh with the largest current discontinuity error is selected for refinement, resulting in an optimized new mesh M. i+1 ;

[0049] In this embodiment, the relationship between the adaptive encryption ratio β and the frequency point selection in step 5 is expressed as follows:

[0050] .

[0051] In this embodiment, the specific process of refining the mesh in steps 1, 3 and 5 is as follows: the midpoints of the three sides of the triangle of the mesh are interconnected to divide the mesh into four equal triangular meshes.

[0052] Step 6: Let i = i + 1, at frequency point f i At this location, based on grid M i Solving for the target surface current I i ;

[0053] Step 7: Determine the frequency point f i Whether the highest frequency point of the frequency band to be simulated has been reached;

[0054] If not, return to step 5;

[0055] If so, the final optimization result is output, which includes a series of optimization grids covering the entire frequency band to be simulated. , , ..., } and its corresponding target surface current { , , ..., }

[0056] Step 8: Set the initial frequency sampling point sequence within the frequency band to be simulated, which consists of several frequency sampling points with equal step size;

[0057] Step 9: For each frequency sampling point, solve using the optimized grid closest to it to obtain the target surface current and RCS response at each grid point; then, based on the sampling results (frequency sampling points and their corresponding RCS), use the Cauchy method to interpolate to obtain the RCS response in the entire frequency band to be simulated.

[0058] In this embodiment, the specific implementation process of the Cauchy method in step 9 is as follows:

[0059] The RCS response is modeled as the ratio of two polynomials, expressed as:

[0060]

[0061] Where f represents frequency, This represents the RCS response at frequency f; P is the order of the numerator polynomial, 0 ≤ p ≤ P⁻¹. The coefficients are of order p. Let q be the order of the denominator polynomial, and 0 ≤ q ≤ Q-1. The coefficients are of order q.

[0062] The above formula is rewritten into a system of equations and solved to obtain the coefficient values, and then the RCS response is obtained.

[0063] Step 10: Verify the extreme points and high curvature points in the interpolated full-band RCS response curve to determine whether the interpolation result meets the accuracy requirements with the simulation result based on the closest mesh.

[0064] If not, the verification is deemed to have failed, and the frequency points that failed the verification are added to the frequency sampling point sequence. Then, return to step 9.

[0065] If so, the interpolation result will be output as the final broadband RCS response.

[0066] This embodiment analyzes a metal cube model with an edge length of 2.0m. A plane wave is incident on the top surface of the cube, the calculation frequency band is 0.3-1.2GHz, the initial mesh cell size is approximately 0.3 times the wavelength at 300MHz, and a threshold is set. The value is 0.05 dB; the total number of CRWG / MultiBranch-CRWG basis functions defined on the initial mesh is 3498; the adaptive mesh refinement at 300 MHz terminates after 3 iterations, resulting in the desired mesh. and current Next, while encrypting the grid, the frequency was increased, and settings were set. A series of optimized grids were obtained at frequencies of 424MHz, 600MHz, 849MHz, and 1200MHz, with corresponding unknowns of 6987, 14128, 28429, and 56600, respectively. Finally, based on these optimized grids, the Cauchy interpolation method was used to reconstruct the monostatic RCS response of the entire frequency band. To demonstrate the effectiveness of this invention, the bistatic RCS calculated using an adaptive optimized grid at 300MHz and a uniform grid with a cell size of 0.1 wavelength (7416 unknowns) was compared. Figure 1As shown; the bistatic RCS calculated using an adaptively optimized mesh at 1.2 GHz and a uniform mesh with a cell size of 0.1 wavelength (unknown quantity 116190) is compared. Figure 2 As shown in the figure, the method described in this embodiment does not require independent adaptive optimization at each selected frequency point, as is the case with traditional adaptive encryption methods. It can efficiently optimize the grid at each frequency point and achieve computational accuracy comparable to that of a uniform grid with fewer unknowns. Figure 3 The method described in this embodiment is presented as a comparison between the single-station RCS interpolation response calculated by the method described in this embodiment and the single-station RCS response calculated by point-by-point solution. Point-by-point calculation requires solving 901 frequency points, while the method described in this embodiment only requires calculating 60 sampling points. This proves that the Cauchy method of this invention can efficiently and accurately reconstruct the response of complex frequency bands.

[0067] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A broadband scattering simulation method based on adaptive mesh encryption, characterized in that, Includes the following steps: Step 1: Set the initial mesh size. Discretize the target model surface using a triangular mesh of the initial mesh size. The initial mesh size is greater than one-tenth of the maximum wavelength of the frequency band to be simulated. Set the number of refinement iterations to 1. Based on the current mesh, solve for the target surface current and radar cross section (RCS) response at the lowest frequency point f0 of the frequency band to be simulated. Increment the encryption iteration count by 1 and encrypt the current grid. Step 2: Solve for the target surface current and RCS response at the lowest frequency point f0 of the frequency band to be simulated; Step 3: Determine whether the change in RCS response between two adjacent encryption iterations is less than a set threshold; If not, assess the current discontinuity error of each grid based on the distribution of the target surface current; Select the part of the mesh with the largest current discontinuity error for refinement, and return to step 2; If so, output the current grid M0 and the corresponding target surface current I0, and proceed to step 4; Step 4: Initialize the frequency index i = 0; Step 5, at frequency point f i At point M, the computational grid is... i The current discontinuity error of each grid; setting the cell density ratio β and determining the next frequency point f. i+1 The β-section of the mesh with the largest current discontinuity error is selected for refinement, resulting in the optimized mesh M. i+1 ; Step 6: Let i = i + 1, at frequency point f i At this location, based on grid M i Solving for the target surface current I i ; Step 7: Determine the frequency point f i Whether the highest frequency point of the frequency band to be simulated has been reached; If not, return to step 5; If so, output grid { , , ..., } and its corresponding target surface current { , , ..., }; Step 8: Set the initial frequency sampling point sequence within the frequency band to be simulated, which consists of several frequency sampling points with equal step size; Step 9: For each frequency sampling point, use the grid closest to it to solve for the target surface current and RCS response corresponding to the current frequency sampling point. Based on the frequency sampling points and their corresponding RCS, the Cauchy method is used for interpolation to obtain the full-band RCS response within the entire frequency band to be simulated. Step 10: Verify the extreme points and frequency points where the curvature exceeds the set threshold in the interpolated full-band RCS response curve, and determine whether the error between the interpolation result and the simulation result based on the closest mesh meets the accuracy requirements. If not, the verification is deemed to have failed, and the frequency points that failed the verification are added to the frequency sampling point sequence. Then, return to step 9. If so, the interpolation result will be output as the final broadband RCS response.

2. The broadband scattering simulation method based on adaptive mesh encryption according to claim 1, characterized in that, In steps 1 and 2, the target surface current and RCS response are solved using the multilevel fast multipole method.

3. The broadband scattering simulation method based on adaptive grid encryption according to claim 1, characterized in that, In step 3, the 30% to 50% portion of the mesh with the largest current discontinuity error is selected for refinement.

4. The broadband scattering simulation method based on adaptive mesh encryption according to claim 1, characterized in that, In step 5, the relationship between the adaptive encryption ratio β and the frequency point selection is expressed as: 。 5. The broadband scattering simulation method based on adaptive mesh encryption according to claim 1, characterized in that, In steps 1, 3, and 5, the specific process of refining the mesh is as follows: the midpoints of the three sides of the triangles in the mesh are interconnected to divide the mesh into four equal triangular meshes.

6. The broadband scattering simulation method based on adaptive mesh encryption according to claim 1, characterized in that, The specific implementation process of the Cauchy method in step 9 is as follows: The RCS response is modeled as the ratio of two polynomials, expressed as: ； Where f represents frequency, This represents the RCS response at frequency f; P is the order of the numerator polynomial, 0 ≤ p ≤ P⁻¹. The coefficients are of order p. Let q be the order of the denominator polynomial, and 0 ≤ q ≤ Q-1. The coefficients are of order q. The above formula is rewritten into a system of equations and solved to obtain the coefficient values, and then the RCS response is obtained.

Images