Grid adaptive encryption method based on error field energy

Abstract

The invention belongs to the field of electromagnetic field numerical solution, relates to antenna electromagnetic simulation, and particularly provides an error field energy-based grid adaptive encryption method, which comprises the following steps of: modeling a target antenna, introducing corresponding excitation and boundary conditions, determining an adaptive frequency point and a solution frequency band, and establishing an electromagnetic simulation model; secondly, carrying out primary division and finite element electromagnetic simulation calculation on a computational domain by adopting a tetrahedral mesh to obtain an electric field at each element node of the tetrahedral mesh, calculating energy corresponding to an error field on an interface of each element, and carrying out posterior error estimation; and finally, calculating a grid encryption strategy according to a posterior error, including an encryption unit and an encryption size, performing simulation calculation again after encryption, and repeating the process until a solution meets a precision requirement. In conclusion, according to the method, the part, not meeting the constraint condition, of the electromagnetic field solution serves as an error source, corresponding energy serves as posterior error estimation, and grid self-adaptive encryption is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic field numerical solution, relates to antenna electromagnetic simulation, and specifically provides a grid adaptive encryption method based on error field energy. Background Art

[0002] During the antenna design phase, numerical electromagnetic simulation is a key approach to evaluating far-field parameters (such as gain, directivity, and standing wave ratio) and near-field distribution. In the finite element method (FEM), the discretization accuracy of the model mesh directly impacts the accuracy of the calculation results. Generally, smaller mesh sizes provide a better fit to the geometric model and result in higher solution accuracy. However, finer meshes increase the memory requirements and time consumption of the solution. Therefore, when modeling antenna structures, denser meshes are deployed in areas with more dramatic electromagnetic field variations, based on the three-dimensional shape of the radiating element, the feed structure, the coupling region, or the location of the current-carrying edge. This ensures both simulation accuracy and computational efficiency.

[0003] However, manual mesh editing is not only labor-intensive but also highly dependent on the engineer's simulation experience, making it difficult to achieve both ideal simulation accuracy and efficiency. In contrast, adaptive mesh refinement methods offer a faster solution for antenna electromagnetic simulation. Their basic strategy is to first perform a fast simulation at a given frequency using a low mesh count. Based on analysis of the simulation results, the mesh distribution is automatically adjusted until the results meet the accuracy requirements. The final mesh structure is then determined for a complete numerical simulation. These methods, with their core feature of "physically defined meshing," achieve accurate results without requiring extensive manual adjustments by the user. Error estimation based on the fast simulation results is a crucial step in informing the current mesh adjustment strategy. A commonly used method is the a posteriori error estimation method based on residuals, which calculates the error estimate by calculating the residual value of the local field. While this method offers high positioning accuracy, its complex construction, high computational resource consumption, and difficulty in improving processing efficiency severely limit its practical value in simulation workflows. Therefore, there is an urgent need to develop an adaptive mesh refinement method with high computational efficiency, simple construction, and reliable accuracy to meet the high-performance simulation requirements of complex antenna systems. Summary of the Invention

[0004] The present invention aims to provide a mesh adaptive encryption method based on error field energy to address the problems of low solution efficiency and high manual intervention workload caused by global mesh encryption or manual editing in existing antenna electromagnetic simulations. It also addresses the slow computational speed of existing residual-based mesh adaptive encryption methods due to the complex calculation of a posteriori error estimates. The present invention proposes an electromagnetic field finite element mesh adaptive encryption method based on error field energy. This method uses the portion of the electromagnetic field solution that does not meet the constraints as an error source and the corresponding energy as a posteriori error estimate to achieve mesh adaptive encryption.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A grid adaptive encryption method based on error field energy, characterized by comprising the following steps:

[0007] A. Conduct finite element modeling of the target antenna structure, introduce excitation and boundary conditions, set adaptive frequency points, and establish an electromagnetic simulation model;

[0008] B. Perform tetrahedral meshing on the electromagnetic simulation model of the target antenna structure and globally number the points, edges, and faces on each discretized tetrahedral unit, while also performing local numbering within the tetrahedral unit.

[0009] C. Using the second-order vector stacked basis function and the finite element method, the numerical solution of the electric field on the tetrahedral grid is obtained;

[0010] D. Perform a posteriori error estimation based on the numerical solution of the electric field of the tetrahedral unit to obtain the error field energy of each tetrahedral unit;

[0011] E. Sort all tetrahedral elements in descending order of error field energy, set a percentage threshold, select tetrahedral elements in descending order of error field energy until the cumulative error reaches the percentage threshold of the total error, and mark the selected tetrahedral elements as elements to be encrypted;

[0012] F. Calculate the encryption size ratio of each unit to be encrypted and re-divide the tetrahedral mesh;

[0013] F. Repeat steps C to E until the finite element electromagnetic simulation results meet the preset goals.

[0014] Furthermore, in step C, the numerical solution of the electric field at any point in the tetrahedron element is expressed as:

[0015]

[0016] in, represents the numerical solution of the electric field, (x, y, z) represents the position coordinates, e i represents the coefficient of the basis function, n is the number of basis functions, represents a second-order vector stack basis function.

[0017] Furthermore, in step D, the error field energy of the tetrahedron element is expressed as:

[0018]

[0019] Among them, α erepresents the error field energy, m is the number of volume integration points of the tetrahedral element, p is the total number of volume integration points and surface integration points of the tetrahedral element, Z0 is the wave impedance in vacuum, k0 represents the wave number of electromagnetic waves in vacuum, and R represents the distance between two integration points; Represents the residual current, including the internal residual current and surface residual current of the tetrahedral unit; ρ i ,ρ j Represents the residual charge, including the internal residual charge and surface residual charge of the tetrahedral unit.

[0020] Furthermore, in step D, the internal residual current of the tetrahedron unit is:

[0021]

[0022] in, represents the internal residual current, n is the number of basis functions, represents the gradient operator, ω is the phase velocity of electromagnetic waves, j is the imaginary unit, e i represents the coefficient of the basis function, μ0 is the magnetic permeability of vacuum, ε r 、μ r are the relative permittivity and relative permeability of the material to which the tetrahedral unit belongs, k represents the wave number of the electromagnetic wave, represents the second-order vector stacked basis function;

[0023] The internal residual charge of the tetrahedral unit is:

[0024]

[0025] Among them, ρ v represents the internal residual charge, and ε represents the dielectric constant of the material to which the tetrahedral unit belongs;

[0026] The surface residual current and surface residual charge of the tetrahedron element are:

[0027]

[0028] Among them, ρ s is the residual charge on the interface, is the surface residual current of the interface; is the unit external normal vector of the interface, ε1 and ε2 are the dielectric constants of the tetrahedral units on both sides of the interface, and is the electric field distribution of the tetrahedral units on both sides of the interface, and is the magnetic field distribution of the tetrahedral units on both sides of the interface.

[0029] Furthermore, in step F, for the unit to be encrypted, the encryption size ratio is:

[0030]

[0031] Among them, γ e is the encryption size ratio of the unit to be encrypted, α e is the error field energy of the unit to be encrypted, α min is the minimum value of the error field energy among all tetrahedral elements to be encrypted, α avg is the average of the error field energies of all tetrahedral elements.

[0032] Based on the above technical solution, the beneficial effects of the present invention are:

[0033] The present invention provides a grid adaptive encryption method based on error field energy. First, a target antenna is modeled, corresponding excitation and boundary conditions are introduced, adaptive frequency points and solution frequency bands are determined, and an electromagnetic simulation model is established. Then, a tetrahedral grid is used to perform initial partitioning of the computational domain and finite element electromagnetic simulation calculations to obtain the electric field at each unit node of the tetrahedral grid. The energy corresponding to the error field inside each unit and on the interface between adjacent units is calculated, and a posteriori error estimation is performed. Finally, a grid encryption strategy is calculated based on the posteriori error, including encryption units and encryption sizes. After encryption, simulation calculations are performed again, and the above process is repeated until the solution meets the accuracy requirements.

[0034] In summary, the present invention performs error estimation by calculating the energy of the error field on the interface between each tetrahedral unit and the adjacent units, which serves as an indication for adaptive mesh encryption. The present invention takes into account the error corresponding to the discontinuity of the normal derivative at the unit interface, and has high simulation accuracy for the antenna model. At the same time, the engineering implementation is relatively simple and easy to apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the process of the grid adaptive encryption method based on error field energy in the present invention.

[0036] Figure 2 This is an electromagnetic simulation model diagram of the target antenna structure in an embodiment of the present invention.

[0037] Figure 3 2 is a comparison diagram of the mesh distribution before and after the mesh adaptive encryption method in an embodiment of the present invention, where (a) is the tetrahedral mesh before adaptive encryption, and (b) is the tetrahedral mesh after adaptive encryption. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and beneficial effects of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0039] This embodiment provides a grid adaptive encryption method based on error field energy, the process of which is as follows: Figure 1 As shown, taking a dipole antenna as an example, the specific steps include:

[0040] A. Perform finite element modeling on the target antenna structure, introduce excitation and boundary conditions, set adaptive frequency points, and establish an electromagnetic simulation model, such as Figure 2 As shown;

[0041] B. Perform tetrahedral meshing on the electromagnetic simulation model of the target antenna structure and globally number the points, edges, and faces on each discretized tetrahedral unit. Simultaneously, perform local numbering within the tetrahedral unit to integrate and associate the global mesh with the unit.

[0042] C. Using the second-order vector stacked basis function, the finite element method is used to obtain the numerical solution of the electric field on the tetrahedral grid and the numerical solution of the electric field at any point in the tetrahedral unit. Expressed as:

[0043]

[0044] Among them, (x, y, z) represents the position coordinates, e i Indicates the coefficients of the corresponding basis functions, n is the number of basis functions, represents the corresponding second-order vector stacked basis function; it should be noted that electromagnetic simulation based on the finite element method is a well-known technology and will not be described in detail here;

[0045] D. performing a posteriori error estimation based on the electric field numerical solution of each tetrahedral unit obtained in step C to obtain the error field energy of each tetrahedral unit;

[0046] In high-frequency electromagnetic field problems, the electric field distribution is theoretically The vector wave equation should be fully satisfied:

[0047]

[0048] in, represents the gradient operator, μ and ε represent the magnetic permeability and dielectric constant of the material respectively, ω is the phase velocity of electromagnetic wave, ω=2πf, j is the imaginary unit, is the excitation current source;

[0049] In high-frequency antenna simulation problems, there is no external excitation except for the port. Therefore, in any non-port unit, the right-hand side of equation (2) should be 0, that is, the electric field distribution satisfy:

[0050]

[0051] Due to the existence of numerical errors, substituting the finite element numerical solution into the above formula will not fully satisfy the above equation, but there will be a residual term Right now:

[0052]

[0053] Considering the residual term on the right side as an excitation, the numerical error can be understood as the residual current in the unit As the error field excited by the error source, the numerical solution is the error field The superposition with the real physical field is expressed as:

[0054]

[0055] According to the subtraction of equation (2) and equation (5), and because the value of magnetic permeability μ is usually much less than 1, the equation is appropriately scaled to avoid μ as a divisor. The relationship between the residual current at any position in the tetrahedral unit and the finite element solution at that position can be obtained, which is expressed as:

[0056]

[0057] Among them, k represents the wave number of electromagnetic wave, k 2 =ω 2 με, μ0 is the magnetic permeability of vacuum, ε r 、μ r are the relative permittivity and relative permeability of the material to which the tetrahedral element belongs respectively; finally, the calculation expression of the residual current at any position in the tetrahedral element can be obtained as follows:

[0058]

[0059] Analogous to the wave equation, the high-frequency vector electric field should also satisfy the electric field divergence equation:

[0060]

[0061] Where ρ is the excitation charge source;

[0062] In the high-frequency antenna simulation problem, there is no external charge source; therefore, the right-hand side of (8) should be 0. By analogy with the idea of ​​the wave equation, substituting the numerical solution, there will also be a residual term R generated by the residual charge. ρ :

[0063]

[0064] Then the residual charge ρ v and the corresponding error field satisfy:

[0065]

[0066] Similarly, the calculation expression for the residual charge at any position in the tetrahedral unit can be obtained as follows:

[0067]

[0068] At the interface of the internal tetrahedral elements, the electromagnetic field should satisfy the following boundary conditions:

[0069]

[0070] in, is the unit external normal vector of the interface, ε1 and ε2 are the dielectric constants of the tetrahedral units on both sides of the interface, and is the electric field distribution of the tetrahedral units on both sides of the interface, and is the magnetic field distribution of the tetrahedral units on both sides of the interface, ρ s is the residual charge on the interface, is the surface residual current of the interface;

[0071] Since there is no surface charge and surface current inside the calculation area, the electromagnetic field should be continuous; therefore, the electric field and magnetic field obtained by numerical solution are substituted into the above formula, and the calculated surface residual charge ρ s With residual current It is the error charge source and error current source on the interface;

[0072] According to the Green's function approximation, the error field of the point charge source / current source at any position in the tetrahedron unit can be expressed as:

[0073]

[0074] Where R is the distance from the field calculation position to the source position, Ω is the unit area; the error field in the tetrahedron unit is obtained by integration calculation The energy α e for:

[0075]

[0076] The numerical solution and the corresponding residual charge / residual current exist at multiple discrete points within a cell and on its interface. Therefore, it is necessary to calculate the error field energy of the entire cell through numerical integration. The numerical integration focuses on the error energy within the cell, and the error on the interface is used as a correction. Therefore, the following format is used for approximate calculation:

[0077]

[0078] Where m is the number of volume points of the tetrahedral element, n is the total number of volume points and area points of the tetrahedral element; Z0 is the wave impedance in vacuum, which is obtained by sorting the dielectric constant and permeability: k0 represents the wave number of the electromagnetic wave in vacuum; R represents the distance between the two integration points. The distance from the field calculation position to the source position is the distance between the two integration points in the numerical integration calculation;

[0079] E. Calculate the error field energy of all tetrahedral elements and sort them from largest to smallest. Set a percentage threshold and select the elements with the largest errors. If the accumulated errors reach the percentage threshold of the total error, mark them as elements to be encrypted.

[0080] F. Calculate the encryption size ratio of each unit to be encrypted and re-divide the tetrahedral mesh;

[0081] For the encryption unit e, the encryption size ratio is:

[0082]

[0083] Among them, α min is the minimum value of the error field energy of all units to be encrypted;

[0084] At the same time, in order to avoid excessive mesh encryption and excessive local element encryption, the maximum encryption size ratio needs to be limited to:

[0085]

[0086] Among them, α avg is the average value of the error field energy of all tetrahedral elements;

[0087] F. Repeat steps C to E until the finite element electromagnetic simulation results meet the accuracy requirements. The tetrahedral mesh before and after adaptive encryption is as follows: Figure 3 As shown in the figure, it can be seen that the present invention can divide the area with greater error field energy in the antenna simulation area into denser grids based on the electromagnetic simulation calculation results.

[0088] It can be seen from the above embodiments that the present invention first obtains the electric field solution on the initial grid, and performs error estimation based on the energy excited by the error source inside the unit and on the interface, comprehensively considering the error inside the unit and the error of the discontinuous field solution at the interface, and has high adaptive accuracy; moreover, only a single tetrahedron and its adjacent units are considered in the error estimation, the calculation amount is small, and engineering applications are easy to implement.

[0089] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A grid adaptive encryption method based on error field energy, characterized in that: The following steps are involved: A. Conduct finite element modeling of the target antenna structure, introduce excitation and boundary conditions, set adaptive frequency points, and establish an electromagnetic simulation model; B. Perform tetrahedral meshing on the electromagnetic simulation model of the target antenna structure and globally number the points, edges, and faces on each discretized tetrahedral unit, while also performing local numbering within the tetrahedral unit. C. Using the second-order vector stacked basis function and the finite element method, the numerical solution of the electric field on the tetrahedral grid is obtained; D. Perform a posteriori error estimation based on the numerical solution of the electric field of the tetrahedral unit to obtain the error field energy of each tetrahedral unit; E. Sort all tetrahedral elements in descending order of error field energy, set a percentage threshold, select tetrahedral elements in descending order of error field energy until the cumulative error reaches the percentage threshold of the total error, and mark the selected tetrahedral elements as elements to be encrypted; F. Calculate the encryption size ratio of each unit to be encrypted and re-divide the tetrahedral mesh; F. Repeat steps C to E until the finite element electromagnetic simulation results meet the preset goals.

2. The grid adaptive encryption method based on error field energy according to claim 1, characterized in that: In step C, the numerical solution of the electric field at any point in the tetrahedron element is expressed as: in, represents the numerical solution of the electric field, (x, y, z) represents the position coordinates, e i represents the coefficient of the basis function, n is the number of basis functions, represents a second-order vector stack basis function.

3. The grid adaptive encryption method based on error field energy according to claim 1, characterized in that: In step D, the error field energy of the tetrahedral element is expressed as: Among them, α e represents the error field energy, m is the number of volume integration points of the tetrahedral element, p is the total number of volume integration points and surface integration points of the tetrahedral element, Z0 is the wave impedance in vacuum, k0 represents the wave number of electromagnetic waves in vacuum, and R represents the distance between two integration points; Represents the residual current, including the internal residual current and surface residual current of the tetrahedral unit; ρ i ,ρ j Represents the residual charge, including the internal residual charge and surface residual charge of the tetrahedral unit.

4. The grid adaptive encryption method based on error field energy according to claim 3 is characterized in that: In step D, the internal residual current of the tetrahedron unit is: in, represents the internal residual current, n is the number of basis functions, represents the gradient operator, ω is the phase velocity of electromagnetic waves, j is the imaginary unit, e i represents the coefficient of the basis function, μ0 is the magnetic permeability of vacuum, ε r 、μ r are the relative permittivity and relative permeability of the material to which the tetrahedral unit belongs, k represents the wave number of the electromagnetic wave, represents the second-order vector stacked basis function; The internal residual charge of the tetrahedral unit is: Among them, ρ v represents the internal residual charge, and ε represents the dielectric constant of the material to which the tetrahedral unit belongs; The surface residual current and surface residual charge of the tetrahedron element are: Among them, ρ s is the residual charge on the interface, is the surface residual current of the interface; is the unit external normal vector of the interface, ε1 and ε2 are the dielectric constants of the tetrahedral units on both sides of the interface, and is the electric field distribution of the tetrahedral units on both sides of the interface, and is the magnetic field distribution of the tetrahedral units on both sides of the interface.

5. The grid adaptive encryption method based on error field energy according to claim 1, characterized in that: In step F, for the unit to be encrypted, the encryption size ratio is: Among them, γ e is the encryption size ratio of the unit to be encrypted, α e is the error field energy of the unit to be encrypted, α min is the minimum value of the error field energy in all units to be encrypted, α avg is the average of the error field energies of all tetrahedral elements.

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