A broadband adaptive mesh partitioning method and system

Abstract

A broadband adaptive mesh generation method and system are disclosed. The method includes: acquiring and initializing simulation scene parameters, simulation model information, and a mesh model; discretizing the broadband frequency range into multiple frequency points; for each frequency point, solving the Maxwell equations in the frequency domain based on the mesh model to obtain the scattering parameters of the simulation model at each frequency point; calculating the error index of each mesh cell at each frequency point, and calculating the encryption index based on each error index; determining whether the mesh cell needs encryption based on the encryption index, and adding a mark to each mesh cell that needs encryption at each frequency point; encryption of the marked mesh cells; resolving the Maxwell equations and scattering parameters using the encrypted mesh; determining whether the scattering parameters have converged based on the calculated convergence error; if the scattering parameters have not converged, iteratively executing the solution until the encryption process is completed until the scattering parameters converge, and outputting the current encrypted mesh as the final broadband adaptive mesh.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic simulation, and in particular to a broadband adaptive mesh generation method and system. Background Technology

[0002] With the technological development in electromagnetic engineering fields such as microwave radio frequency, wireless communication, and antenna radar, simulation objects are gradually developing towards broadband, large scale, and geometric complexity, such as multi-frequency antenna arrays, broadband resonant filters, and large-scale electromagnetic compatibility simulation models. The simulation analysis of these models needs to cover a wide frequency range or multiple discrete frequency points, and the geometric structure contains complex forms such as fine features, multi-layered media, and thin structures with high aspect ratios, which puts extremely high demands on the mesh generation technology of finite element electromagnetic simulation.

[0003] The finite element method (FEM) is the mainstream numerical method for solving Maxwell's equations, and mesh generation is a core prerequisite for finite element simulation. The accuracy and rationality of the mesh directly determine the accuracy of the simulation results and the computational efficiency. For broadband, large-scale, and complex electromagnetic models, traditional mesh generation methods mainly suffer from the following technical shortcomings:

[0004] First, to meet the wavelength requirements of high-frequency points in broadband simulations, global uniform meshing generates a massive number of mesh cells, leading to a surge in memory consumption and a significant increase in solution time, sometimes exceeding the processing capabilities of conventional computing devices and rendering large-scale models unsuitable for simulation. Second, existing conventional adaptive meshing techniques are mostly designed for single-frequency points, only capable of meshing for field distribution at a single frequency. If directly applied to broadband simulations, they result in insufficient mesh accuracy in regions with abrupt changes in field gradients at some frequencies, and over-mesh refinement in non-critical regions at other frequencies, making it difficult to balance simulation accuracy and computational efficiency across the entire broadband frequency range. Finally, the electric field distribution characteristics at different frequencies in broadband simulations vary significantly, and the distribution of high-error mesh cells also changes with frequency. Existing technologies lack effective integration of mesh cell error indices across multiple frequencies, failing to obtain a mesh error distribution suitable for the entire broadband, easily leading to substandard simulation accuracy at some frequencies. Summary of the Invention

[0005] This invention provides a broadband adaptive mesh generation method and system that can design precise mesh error indices by combining the physical nature of electromagnetic simulation, effectively integrate error data from multiple broadband frequencies, and achieve localized precise mesh densification. While ensuring simulation accuracy across the entire broadband frequency range, it minimizes the mesh size and improves the simulation computation efficiency of large-scale complex electromagnetic models, thus solving problems such as poor broadband adaptability and low computation efficiency in existing technologies.

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

[0007] Firstly, a broadband adaptive mesh generation method includes the following steps:

[0008] S1. Obtain and initialize simulation scene parameters, simulation model information, and mesh model; discretize the broadband frequency range into multiple frequency points;

[0009] S2. For each frequency point, solve the scattering parameters of the simulation model in the frequency domain form of Maxwell's equations based on the grid model to obtain the scattering parameters of the simulation model at each frequency point.

[0010] S3. Calculate the error index of each grid cell at each frequency point, and calculate the encryption index based on each error index; determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point.

[0011] S4. Encrypt the marked grid cells;

[0012] S5. Resolve Maxwell's equations and scattering parameters using the refined mesh; determine whether the scattering parameters have converged based on the calculated convergence error; if the scattering parameters have not converged, iterate from S2 to S5 until the scattering parameters converge, and output the current refined mesh as the final broadband adaptation mesh.

[0013] Preferably, S3 includes:

[0014] S31. For each frequency point, based on the finite element solutions of the electric and magnetic field values ​​obtained from Maxwell's equations, calculate the error index of each tetrahedral mesh element:

[0015]

[0016]

[0017]

[0018] in This is the error index for a single tetrahedron T. This is a contribution term to the error of the tetrahedral element. For all faces of tetrahedron T, For noodles Adjacent tetrahedrons The body's contribution item, A single face of a tetrahedron Error contribution term, It is the longest side of the tetrahedron. Let be the longest side of a single face of the tetrahedron. It is the vacuum wavenumber; , , , Based on the finite element solution of the electric field value The calculation shows that:

[0019]

[0020]

[0021]

[0022]

[0023] in For volume charge residual, residual current in volume, Surface charge jump difference, For surface current jump residuals, The permeability of free space, For surface jump operators: , For noodles Physical quantities of the units on both sides For noodles The normal vector from 1 to 2.

[0024] As a preferred option, S3 also includes:

[0025] S32. Calculate the weighted average of the grid cell error indices calculated at different frequency points to obtain the final error of the corresponding grid cell; calculate the encryption index based on the final error of each grid cell; at each frequency point, sort all grid cells from largest to smallest according to the error index, add a mark, and sum the error indices one by one until the sum of the error indices exceeds the encryption index; the marked grid cells are the grid cells that need to be encrypted at each frequency point.

[0026] As a preferred embodiment, in S32, the final error of all grid cells is summed, and half of the result is used as the encryption index.

[0027] As a preferred option, S3 also includes:

[0028] S33. Based on the number of grid cells that need to be encrypted at each frequency point, determine whether additional frequency points need to be added.

[0029] As a preferred approach, parallel computing frameworks are introduced in S2 and S3 to distribute the computation process to multiple computing nodes for parallel processing. Using the multi-threaded form of OpenMP or the MPI method, computational tasks at different frequencies are assigned to multiple threads or processes, thus parallelizing the Maxwell's equations and grid cell error calculation process at different frequencies.

[0030] As a preferred option, the encryption methods in S4 include:

[0031] Add a midpoint to the longest edge of the marked grid cell to divide the grid cell in two; or, regardless of the edge length of the grid cell, divide all edges of the marked grid cell in half.

[0032] As a preferred option, in S5:

[0033] Convergence error The formula is:

[0034]

[0035] in, Port indices for the scattering parameter matrix; Here are the scattering parameter values ​​from port i to port j. Modulo operation for complex numbers.

[0036] As a preferred embodiment, S5 includes:

[0037] If convergence error If the scattering parameters are less than a preset threshold, the simulation accuracy is met, iteration stops, and the currently refined mesh is output as the final broadband fit mesh; if the convergence error is... If the value is greater than the preset threshold and the number of iterations has not reached the maximum step size, then iterate from S2 to S5 until the scattering parameters converge.

[0038] Secondly, a broadband adaptive mesh generation system includes:

[0039] The initialization and broadband frequency discretization module is used to acquire and initialize simulation scene parameters, simulation model information, and mesh model; and to discretize the broadband frequency range into multiple frequency points.

[0040] The scattering parameter solution module is used to solve for each frequency point based on the mesh model in the frequency domain form of Maxwell's equations, and obtain the scattering parameters of the simulation model at each frequency point;

[0041] The error calculation and marking module is used to calculate the error index of each grid cell at each frequency point, calculate the encryption index based on each error index, determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point.

[0042] An encryption module is used to encrypt the marked grid cells;

[0043] The convergence determination module is used to resolve Maxwell's equations and scattering parameters using the refined mesh; it determines whether the scattering parameters have converged based on the calculated convergence error; if the scattering parameters have not converged, it iteratively executes the processes of the scattering parameter solution module, the error calculation and marking module, and the refinement module until the scattering parameters converge, and outputs the current refined mesh as the final broadband adaptive mesh; the broadband adaptive mesh generation system is used to execute the broadband adaptive mesh generation method and its steps as described in the first aspect.

[0044] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0045] 1. Unlike traditional techniques that optimize the grid only at a single specified frequency, this invention uses a technique that optimizes the grid across the entire operating frequency band. This allows the grid to cover the entire frequency band for error control, avoiding the biased approach of single-frequency optimization and resulting in higher simulation accuracy for broadband devices.

[0046] 2. Unlike the traditional single-threaded adaptive mesh generation technology, this invention adopts a multi-threaded adaptive mesh generation technology, which enables the mesh to generate cell indicators at different frequencies in parallel, resulting in higher mesh generation efficiency.

[0047] 3. This invention abandons the global uniform encryption method and achieves local precise encryption of the grid by calculating and integrating the grid cell error index of broadband multi-frequency points. This minimizes the grid size and avoids the problems of increased memory consumption and significantly increased solution time caused by massive grid cells. It significantly improves the simulation calculation efficiency of large-scale complex electromagnetic models and solves the problem that conventional computing devices cannot handle large-scale models due to excessively large grid size.

[0048] 4. This invention designs a grid error index based on the physical essence of electromagnetic simulation, which effectively integrates grid cell error data at multiple frequency points. It can obtain a grid error distribution that adapts to the entire bandwidth, avoiding the problem of substandard simulation accuracy at some frequency points caused by differences in field distribution characteristics at different frequency points, and making the grid division more in line with the physical characteristics of broadband electromagnetic simulation.

[0049] 5. The present invention can fully parallelize the calculation of grid cell errors at different frequency points, shortening the time required for calculating grid cell errors when solving multiple frequency points and improving efficiency. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0051] Figure 2 This is a model diagram of the conical sinusoidal spiral antenna of Embodiment 1 of the present invention;

[0052] Figure 3 This is a graph showing the S-parameter frequency sweep results of the conical sinusoidal spiral antenna of Embodiment 1 of the present invention. Detailed Implementation

[0053] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0054] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0055] Example 1:

[0056] This embodiment focuses on the electromagnetic simulation scenario of a conical sinusoidal spiral antenna. It applies the broadband adaptive mesh generation method of this invention to achieve accurate mesh generation of this complex electromagnetic model within a broadband frequency range of 2GHz-15GHz, balancing simulation accuracy and computational efficiency. This method is implemented based on a finite element electromagnetic simulation platform and is adapted for the generation and solving of tetrahedral unstructured meshes.

[0057] like Figure 1 The broadband adaptive mesh generation method shown includes the following steps:

[0058] S1. Obtain and initialize simulation scene parameters, simulation model information, and mesh model; discretize the broadband frequency range into n frequency points;

[0059] The system acquires user-input simulation scene parameters, initializes the mesh model, sets the maximum number of iterations, convergence error, and solver configuration. Simulation scene parameters include a wideband frequency range or multiple discrete frequency points, and the mesh model is a coarse tetrahedral mesh. Specifically, it includes:

[0060] First, the simulation scenario core parameters are received from the user. In this embodiment, the broadband frequency range is set to 2GHz-15GHz, which is discretized into n frequency points. At the same time, information such as the geometric structure, medium parameters, and port configuration of the simulation model is obtained.

[0061] The initial mesh model is a coarse tetrahedral mesh. The geometric model of the broadband resonant filter is initially meshed. The element size of the coarse mesh is determined based on the vacuum wavelength of the lowest frequency point (2GHz) of the broadband, and 1 / 10 of the wavelength is taken as the initial element reference size. The maximum number of iteration steps is set to 10 steps, and the convergence error is 0.02 (the relative error threshold of the S-parameter magnitude). The finite element solver parameters are configured, including the solver type (iterative solver), boundary conditions (ideal electric boundary for metal boundary, radiation boundary for external boundary), convergence criteria, etc.

[0062] S2. For each frequency point, the scattering parameters (s-parameters) of the simulation model at each frequency point are obtained by solving the mesh model in the frequency domain form of Maxwell's equations.

[0063] For the discretized n frequency points, the frequency domain form of Maxwell's equations is solved sequentially on the finite element simulation platform based on the mesh model, obtaining the full-port s-parameters of the simulation model at each frequency point. Specifically, the frequency domain form of Maxwell's equations is as follows:

[0064]

[0065]

[0066]

[0067]

[0068] in, For electric field strength, The magnetic field strength, For current density, For charge density, Angular frequency, Where is the dielectric constant. Permeability, It is the imaginary unit.

[0069] Solving this equation yields the finite element numerical solution of the electric field. Finite element numerical solution of magnetic field .

[0070] The s parameter is one The complex matrix essentially describes the relationship between the incident wave and the reflected / transmitted wave at the port. Therefore, it is necessary to convert the obtained electric and magnetic fields into the amplitude of the incident wave at the port. ) and the amplitude of the emitted wave ( For any port i, the electric field in its port plane and It can be decomposed into an incident field and a scattered field.

[0071]

[0072]

[0073] in, and For the incident field, and The scattered field is then calculated, followed by the Poynting vector at the port:

[0074]

[0075] in This indicates that only the real part is taken. Represents magnetic field The conjugate of complex numbers.

[0076] For port i, the incident power is defined respectively. and output power These correspond to the incident field power and the exit field power, respectively, through the port plane. Integrating the Poynting vector yields:

[0077]

[0078]

[0079] in This is the normal vector to the port plane. Incident power. With the amplitude of the incident wave and output power With the amplitude of the emitted wave The relationship is:

[0080]

[0081]

[0082] in, This is the characteristic impedance in free space.

[0083] The s-parameter matrix of an N-port is The first parameter of s The elements are ,in The amplitude of the emitted wave at the i-th port Only the incident wave at port j Incentives are generated.

[0084] S3. Calculate the error index of each grid cell at each frequency point, and calculate the encryption index based on each error index; determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point.

[0085] S31. For each frequency point, based on the numerical finite element solutions of the electric and magnetic fields obtained in S2, calculate the error index of each tetrahedral mesh element.

[0086]

[0087]

[0088]

[0089] in This is the error index for a single tetrahedron T. This is a contribution term to the error of the tetrahedral element. For all faces of tetrahedron T, For noodles Adjacent tetrahedrons The body's contribution item, A single face of a tetrahedron Error contribution term, It is the longest side of the tetrahedron. Let be the longest side of a single face of the tetrahedron. It is the vacuum wavenumber. , , , These four residuals are derived from the numerical finite element solution. The calculation shows that:

[0090]

[0091]

[0092]

[0093]

[0094] in For volume charge residual, residual current in volume, Surface charge jump difference, For surface current jump residuals, The permeability of free space, For surface jump operators: , For noodles Physical quantities of the units on both sides For noodles The normal vector from 1 to 2.

[0095] S32. Integrate the grid cell error indices calculated at different frequency points, and perform a weighted average of the grid cell errors calculated at different frequency points to obtain the final error of the grid cell; sum the error indices of all grid cells, and use half of this value as the encryption index.

[0096]

[0097] At each frequency point, all tetrahedral elements are sorted from largest to smallest according to their error indices. Then, starting from the first tetrahedron, the tetrahedron numbers are output until the sum of the errors of these tetrahedrons exceeds [the specified value]. This indicator;

[0098] Determine whether additional frequency points need to be added based on the required number of grid cells to be encrypted. For example, given a frequency sequence... Perform S2 operations on them respectively, and calculate their mesh cell errors and the number of mesh cells that need to be refined. The number of grid cells requiring encryption is even greater. and Insert a frequency point between them; if If the number of grids that need to be encrypted is greater, then... Frequency points are inserted on both sides respectively.

[0099] Furthermore, S2 and S3 introduce a parallel computing framework, which can distribute the computation process to multiple computing nodes for parallel processing. By using the multi-threaded form of OpenMP or the MPI method, the computation tasks at different frequencies can be assigned to multiple threads or processes, and the Maxwell's equations and grid cell error calculation process at different frequencies can be parallelized. In this way, the efficiency of the broadband adaptive grid encryption method and system can be greatly improved.

[0100] S4. Encrypt the marked grid cells;

[0101] Based on the encryption mark results, a local encryption operation is performed on the mesh model. The tetrahedral elements with encryption marks are divided into smaller mesh elements. For example, the longest edge is bisected by adding a midpoint on the longest edge of the tetrahedron and then dividing the tetrahedron in half; uniform bisecting is performed by bisecting all edges without distinguishing the edge length of the mesh elements, and so on.

[0102] During the densification process, the continuity and topological consistency of the mesh are ensured to avoid problems such as mesh overlap, point selection, and non-manifold edges, so as to ensure that the densified mesh meets the mesh quality requirements of finite element solution.

[0103] S5. Resolve Maxwell's equations and scattering parameters using the refined mesh; determine whether the scattering parameters have converged based on the calculated convergence error; if the scattering parameters have not converged, iterate from S2 to S5 until the scattering parameters converge, and output the current refined mesh as the final broadband adaptation mesh.

[0104] Using a new, encrypted mesh model, Maxwell's equations and s-parameter matrix are resolved, and the convergence error is calculated based on the new s-parameter results. The convergence error formula is:

[0105]

[0106] in For all port indices of the s-parameter matrix (e.g., for two-port devices) ); The s parameter values ​​are for ports i to j. Modulo operation for complex numbers.

[0107] like If the value is less than or equal to 0.02, it indicates that the S-parameters have converged, meeting the simulation accuracy requirements. Therefore, iteration stops, and the currently refined mesh is output as the final broadband-fitted mesh. If the error index is greater than 0.02 and the number of iterations has not reached 10, it indicates that the mesh accuracy still needs improvement. Return to step 2, re-integrate the error index based on the current mesh's S-parameter results, and mark and densify new high-error cells; if the maximum number of iterations (10) is reached but... If the requirements are still not met, the iteration will stop, the current mesh model will be output, and feedback on the iteration convergence status will be sent to the user.

[0108] This completes the entire adaptive mesh generation process for broadband. This method overcomes the shortcomings of traditional adaptive mesh generation techniques that are designed only for a single frequency point, effectively adapting to the needs of broadband simulation. It avoids the problems of insufficient mesh accuracy in some frequency gradient change regions and excessive mesh refinement in non-critical regions in broadband scenarios, ensuring simulation accuracy across the entire broadband frequency range.

[0109] like Figure 2 , Figure 3 As shown, Figure 2 This is a conical sinusoidal double-helix antenna model. Using the same initial mesh, three mesh refinement methods were applied: global meshing, single-frequency adaptive meshing, and broadband adaptive meshing. The refined meshes were then frequency-scanned, and the scattering parameters were calculated. Regarding the number of meshes, the final mesh counts using broadband adaptive meshing and single-frequency adaptive meshing were similar, both less than the global meshing method. However, in terms of accuracy, the results from broadband adaptive meshing were closer to those from global meshing, without exhibiting the resonant point shift seen in single-frequency adaptive meshing.

[0110] Example 2:

[0111] A broadband adaptive mesh generation system, comprising:

[0112] The initialization and broadband frequency discretization module is used to acquire and initialize simulation scene parameters, simulation model information, and mesh model; and to discretize the broadband frequency range into multiple frequency points.

[0113] The scattering parameter solution module is used to solve for each frequency point based on the mesh model in the frequency domain form of Maxwell's equations, and obtain the scattering parameters of the simulation model at each frequency point;

[0114] The error calculation and marking module is used to calculate the error index of each grid cell at each frequency point, calculate the encryption index based on each error index, determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point.

[0115] An encryption module is used to encrypt the marked grid cells;

[0116] The convergence determination module is used to resolve Maxwell's equations and scattering parameters using the encrypted mesh; it determines whether the scattering parameters have converged based on the calculated convergence error; if the scattering parameters have not converged, it iteratively executes the processes of the scattering parameter solution module, the error calculation and marking module, and the encryption module until the scattering parameters converge, and outputs the current encrypted mesh as the final broadband adaptation mesh.

Claims

1. A broadband adaptive mesh generation method, characterized in that, Includes the following steps: S1. Obtain and initialize simulation scene parameters, simulation model information, and mesh model; discretize the broadband frequency range into multiple frequency points; S2. For each frequency point, solve the scattering parameters of the simulation model in the frequency domain form of Maxwell's equations based on the grid model to obtain the scattering parameters of the simulation model at each frequency point. S3. Calculate the error index of each grid cell at each frequency point, and calculate the encryption index based on each error index; determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point. S4. Encrypt the marked grid cells; S5. Resolve Maxwell's equations and scattering parameters using the refined grid; The convergence error is used to determine whether the scattering parameters have converged. If the scattering parameters do not converge, iterate from S2 to S5 until the scattering parameters converge, and output the current refined mesh as the final broadband adapted mesh.

2. The broadband adaptive mesh generation method according to claim 1, characterized in that, S3 include: S31. For each frequency point, based on the finite element solutions of the electric and magnetic field values ​​obtained from Maxwell's equations, calculate the error index of each tetrahedral mesh element: ； ； ； in This is the error index for a single tetrahedron T. This is a contribution term to the error of the tetrahedral element. For all faces of tetrahedron T, For noodles Adjacent tetrahedrons The body's contribution item, A single face of a tetrahedron Error contribution term, It is the longest side of the tetrahedron. Let be the longest side of a single face of the tetrahedron. It is the vacuum wavenumber; , , , Based on the finite element solution of the electric field value The calculation shows that: ； ； ； ； in For volume charge residual, residual current in volume, Surface charge jump difference, For surface current jump residuals, The permeability of free space, For surface jump operators: , For noodles Physical quantities of the units on both sides For noodles The normal vector from 1 to 2.

3. The broadband adaptive mesh generation method according to claim 2, characterized in that, S3 also includes: S32. Calculate the weighted average of the grid cell error indices calculated at different frequency points to obtain the final error of the corresponding grid cell; calculate the encryption index based on the final error of each grid cell; at each frequency point, sort all grid cells from largest to smallest according to the error index, add a mark, and sum the error indices one by one until the sum of the error indices exceeds the encryption index; the marked grid cells are the grid cells that need to be encrypted at each frequency point.

4. The broadband adaptive mesh generation method according to claim 3, characterized in that, In S32, the final error of all grid cells is summed, and half of the result is used as the encryption index.

5. The broadband adaptive mesh generation method according to claim 3, characterized in that, S3 also includes: S33. Based on the number of grid cells that need to be encrypted at each frequency point, determine whether additional frequency points need to be added.

6. The broadband adaptive mesh generation method according to claim 1, characterized in that, S2 and S3 introduce a parallel computing framework, which distributes the computation process to multiple computing nodes for parallel processing. Using the multi-threaded form of OpenMP or the MPI method, computational tasks at different frequencies are assigned to multiple threads or processes, thus parallelizing the Maxwell's equations and grid cell error calculation process at different frequencies.

7. The broadband adaptive mesh generation method according to claim 1, characterized in that, The encryption methods in S4 include: Add a midpoint to the longest edge of the marked grid cell to divide the grid cell in two; or, regardless of the edge length of the grid cell, divide all edges of the marked grid cell in half.

8. The broadband adaptive mesh generation method according to claim 1, characterized in that, In S5: Convergence error The formula is: ； in, Port indices for the scattering parameter matrix; Here are the scattering parameter values ​​from port i to port j. Modulo operation for complex numbers.

9. A broadband adaptive mesh generation method according to claim 8, characterized in that, S5 include: If convergence error If the scattering parameters are less than a preset threshold, the simulation accuracy is met, iteration stops, and the currently refined mesh is output as the final broadband fit mesh; if the convergence error is... If the value is greater than the preset threshold and the number of iterations has not reached the maximum step size, then iterate from S2 to S5 until the scattering parameters converge.

10. A broadband adaptive mesh generation system, characterized in that, include: The initialization and broadband frequency discretization module is used to acquire and initialize simulation scene parameters, simulation model information, and mesh model; and to discretize the broadband frequency range into multiple frequency points. The scattering parameter solution module is used to solve for each frequency point based on the mesh model in the frequency domain form of Maxwell's equations, and obtain the scattering parameters of the simulation model at each frequency point; The error calculation and marking module is used to calculate the error index of each grid cell at each frequency point, calculate the encryption index based on each error index, determine whether the grid cell needs to be encrypted based on the encryption index, and add a mark to each grid cell that needs to be encrypted at each frequency point. An encryption module is used to encrypt the marked grid cells; The convergence determination module is used to resolve Maxwell's equations and scattering parameters using the refined mesh; The convergence error is used to determine whether the scattering parameters have converged. If the scattering parameters have not converged, the processes of the scattering parameter solution module, the error calculation and marking module, and the encryption module are iteratively executed until the scattering parameters converge. The current encrypted mesh is then output as the final broadband adaptive mesh. The broadband adaptive mesh generation system is used to execute the broadband adaptive mesh generation method and its steps as described in claim 1.

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