Integral equation grid adaptive encryption method based on non-conformal grid current discontinuity estimation

Abstract

The invention belongs to an electromagnetic simulation technology, and provides an integral equation grid adaptive encryption method based on non-conformal grid current discontinuity estimation, which is used for efficiently obtaining a high-precision simulation result. The method comprises the following steps: firstly, using a conformal or non-conformal triangular mesh discrete model surface, defining a MultiBranch-RWG primary function on a discrete mesh unit, establishing an electric field integral equation, and solving to obtain surface current distribution; then, according to the surface current distribution, a current discontinuity error estimation method is utilized to calculate and obtain a current discontinuity error of each grid unit; and finally, traversing current discontinuity errors of all grid units, when the current discontinuity error of any grid unit is greater than a preset threshold value, executing adaptive encryption, and executing iteration by taking the adaptively encrypted grid as input. Otherwise, outputting the grid information. According to the method, higher precision can be realized with lower calculation cost, grid generation is more flexible, and the method is more suitable for complex targets.

Description

Technical Field

[0001] The invention belongs to electromagnetic simulation technology, and specifically provides an integral equation grid adaptive encryption method based on non-conformal grid current discontinuity estimation. Background Art

[0002] In computational electromagnetics, the rapid and accurate analysis of conductor targets depends on many factors, and the quality of the grid is one of the key factors. Generally, denser grids can achieve better accuracy, but they also bring higher computational burden. The grid adaptive encryption technology hopes to strike a balance between grid density and computational cost. The core of the grid adaptive encryption technology is the error estimator, which can determine which grid units have larger errors. Among the existing error estimators, current discontinuity estimation is an error estimation method with low computational cost and high computational accuracy, but the existing technology is only applicable to conformal grids, such as the literature: SK Kim and AF Peterson, "Evaluation of Local Error Estimators for the RWG-Based EFIE," in IEEE Transactions on Antennas and Propagation, vol. 66, no. 2, pp. 819-826, Feb. 2018. When analyzing multi-scale models, the generation of conformal grids is more difficult, and the unknown quantities generated are often much more than non-conformal grids. Therefore, the present invention provides an integral equation grid adaptive encryption method based on non-conformal grid current discontinuity estimation for multi-scale models. Summary of the invention

[0003] The object of the present invention is to provide an integral equation mesh adaptive encryption method based on non-conformal grid current discontinuity estimation, which is used to efficiently obtain high-precision simulation results and achieve the highest possible calculation accuracy at the lowest possible calculation cost.

[0004] To achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for adaptively refining an integral equation grid based on non-conformal grid current discontinuity estimation, characterized by comprising the following steps:

[0006] Step 1. Discretize the model surface using conformal or non-conformal triangle meshes;

[0007] Step 2. Define the MultiBranch-RWG basis function on the discretized grid cells, establish the electric field integral equation, and solve it to obtain the current coefficient, and then calculate the surface current distribution from the current coefficient;

[0008] Step 3. According to the surface current distribution, the current discontinuity error of each grid unit is calculated using the current discontinuity error estimation method;

[0009] Step 4. Traverse the current discontinuity errors of all grid cells. When the current discontinuity error of any grid cell is greater than the preset threshold, perform adaptive encryption, and use the adaptively encrypted grid as input, return to step 2 for iteration; otherwise, output the grid information.

[0010] Furthermore, the specific process of step 2 is:

[0011] The surface current J of the equivalent surface is discretized using the MultiBranch-RWG basis function as follows: Among them, a n is the current coefficient, f n is the MultiBranch-RWG basis function, N is the total number of basis functions, n = 1, 2, ... N; the electric field integral equation established according to the discrete form of the surface current J is:

[0012] [Z mn ][J n ]=[b m ]

[0013]

[0014] Where r is the field point, r′ is the source point, G(r,r′) represents the Green’s function, S n is the MultiBranch-RWG basis function f n The domain of S m is the MultiBranch-RWG basis function f m The domain of E inc is the incident electric field, k is the wave number, ω is the incident wave angular frequency, μ 0 is the free space permeability, j is the imaginary unit;

[0015] The electric field integral equation obtained by discretization is solved iteratively to obtain the current coefficient {a n} 1≤n≤N , and then the surface current distribution of the equivalent surface is obtained.

[0016] Furthermore, the specific process of step 3 is as follows:

[0017] Calculate the current discontinuity error of the ith unit:

[0018]

[0019] Among them, Error i represents the current discontinuity error of the i-th unit, ε(i,m) represents the current discontinuity error of the mth edge of the ith unit, represents the maximum value of the tangential component of the surface current density at the midpoints of all mesh edges, A i represents the area of ​​the i-th unit.

[0020] Furthermore, in step 3, the current discontinuity error calculation process of each edge in the unit is:

[0021] The MultiBranch-RWG basis function corresponding to the mth edge of the i-th unit is f (i ,m ) , if the mth edge of the ith unit is f (i,m) The side of the equilateral triangle, then ε (i,m) It is expressed as:

[0022]

[0023] in, represents the unit vector tangent to the mth side of the ith unit, Q (i,m) represents the MultiBranch-RWG basis function f (i,m) The number of negative triangles, r q represents the MultiBranch-RWG basis function f (i,m) The midpoint of the overlapping edge of the qth negative triangle, Represents r q The current calculated based on the i-th unit, Represents r q The current calculated based on the qth negative triangle;

[0024] If the mth edge of the ith unit is f (i,m) The negative triangle side, then ε (i,m) It is expressed as:

[0025]

[0026] in, Represents r q The current calculated based on the i-th unit, Represents r q The current calculated based on the equilateral triangle.

[0027] Furthermore, in step 4, the specific process of adaptive encryption is: traversing the current discontinuity errors of all grid cells, selecting the top 30% of grid cells with the largest errors, and performing midpoint encryption on each selected grid.

[0028] Furthermore, in step 4, the specific process of midpoint encryption is: connecting the midpoints of the three sides of the triangle unit to be encrypted to each other, and dividing the triangle unit to be encrypted into four equal triangle units.

[0029] Based on the above technical solution, the beneficial effects of the present invention are:

[0030] The present invention provides an integral equation mesh adaptive encryption method based on non-conformal grid current discontinuity estimation, which is used to efficiently obtain high-precision simulation results; the computational cost of this method is much lower than the traditional mesh adaptive encryption method based on residual estimation, and compared with the traditional integral equation mesh adaptive encryption method based on conformal grid current discontinuity estimation, its mesh generation is more flexible and more suitable for complex targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is the initial grid map of the aircraft model in the embodiment of the present invention.

[0032] Figure 2 This is the final grid map after adaptive encryption is completed in the embodiment of the present invention.

[0033] Figure 3 It is a grid error diagram of each iteration in the adaptive encryption process in an embodiment of the present invention.

[0034] Figure 4 It is a scattering near-field diagram of each iteration in the adaptive encryption process in an embodiment of the present invention and a scattering near-field diagram of a reference result.

[0035] Figure 5 It is a schematic diagram of the principle of mesh unit encryption in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] 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.

[0037] This embodiment provides an integral equation mesh adaptive encryption method based on non-conformal mesh current discontinuity estimation, taking electromagnetic scattering of an aircraft model as an example, comprising the following steps:

[0038] Step 1. Discretize the model surface using conformal or non-conformal triangle meshes;

[0039] Step 2. Define the MultiBranch-RWG basis function on the discretized grid cells, establish the electric field integral equation, and solve it to obtain the current coefficient, and then calculate the surface current distribution from the current coefficient; the specific process is:

[0040] Traverse each edge of all triangular meshes to determine whether there are two triangular edges that completely overlap or one triangular edge just completely contains several other triangular edges; if two triangular edges completely overlap, define the RWG basis function in the two triangles sharing the edge; if one triangular edge just completely contains several other triangular edges, define the MultiBranch-RWG basis function in these triangles, the triangle corresponding to the former is a positive triangle, and the triangle corresponding to the latter is a negative triangle; in fact, the RWG basis function is a special case of the MultiBranch-RWG basis function when there is only one negative unit, so in the following, the meaning of the MultiBranch-RWG basis function includes the RWG basis function;

[0041] According to the MultiBranch-RWG basis function, the electric field integral equation of the current coefficient to be solved is established, which is:

[0042] The surface current J of the equivalent surface is discretized using the MultiBranch-RWG basis function as follows: Among them, a n is the current coefficient, f n is the MultiBranch-RWG basis function, N is the total number of basis functions, n = 1, 2, ... N; the electric field integral equation established according to the discrete form of the surface current J is:

[0043] [Z mn ][J n ]=[b m ]

[0044]

[0045] Where r is the field point, r′ is the source point, G(r,r′) represents the Green’s function, S n is the MultiBranch-RWG basis function f n The domain of S m is the MultiBranch-RWG basis function f m The domain of ; k is the wave number, “·” represents vector dot product, “▽·” and “▽′·” both represent gradient operators (the superscript “'” is only used to distinguish the operating object); E inc is the incident electric field, ω is the incident wave angular frequency, μ 0 is the free space permeability, ε 0 is the free space conductivity, j is the imaginary unit;

[0046] The electric field integral equation obtained by discretization is solved iteratively to obtain the current coefficient {a n} 1≤n≤N , and then the surface current distribution of the equivalent surface is obtained;

[0047] Step 3. According to the surface current distribution, the current discontinuity error of each grid unit is calculated using the current discontinuity error estimation method; the specific process is:

[0048] Taking the calculation of the current discontinuity error of the i-th unit as an example, the current discontinuity error is expressed as:

[0049]

[0050] Among them, Error i represents the current discontinuity error of the i-th unit, ε (i,m) represents the current discontinuity error of the mth edge of the ith unit, represents the maximum value of the tangential component of the surface current density at the midpoints of all mesh edges, A i represents the area of ​​the i-th unit;

[0051] Furthermore, the MultiBranch-RWG basis function corresponding to the mth edge of the i-th unit is f (i ,m ) , if the mth edge of the ith unit is f (i,m) The side of the equilateral triangle, then ε (i,m) It is expressed as:

[0052]

[0053] in, represents the unit vector tangent to the mth side of the ith unit, Q (i,m) represents the MultiBranch-RWG basis function f (i,m) The number of negative triangles (if it corresponds to the RWG basis function, then Q (i,m) =1), r q represents the MultiBranch-RWG basis function f (i,m) The midpoint of the overlapping edge of the qth negative triangle, Represents r q The current calculated based on the i-th unit, Represents r q The current calculated based on the qth negative triangle;

[0054] If the mth edge of the ith unit is f (i,m) The negative triangle side, then ε (i,m) It is expressed as:

[0055]

[0056] in, Represents r qThe current calculated based on the i-th unit, Represents r q The current calculated based on the equilateral triangle.

[0057] In the present invention, the MultiBranch-RWG basis function is used to only ensure the normal continuity of the current at the common edge, but not to enforce the property of tangential continuity and the strong current discontinuity at the place where the current changes rapidly on the surface of the object. The discontinuity error is used as an indicator to indicate whether the grid needs to be encrypted;

[0058] Step 4. Traverse the current discontinuity errors of all grid cells. When the current discontinuity error of any grid cell is greater than a preset threshold, perform adaptive encryption, and use the adaptively encrypted grid as input, and return to step 2 for iteration; otherwise, output the grid information;

[0059] The specific process of the adaptive encryption is: traversing the current discontinuity errors of all grid cells, selecting the top 30% of the grid cells with the largest errors, and performing midpoint encryption on each selected grid;

[0060] The specific process of midpoint encryption is: connect the midpoints of the three sides of the triangle unit to be encrypted, and divide the triangle unit to be encrypted into four triangle units. Figure 5 shown.

[0061] In more detail, in this embodiment, the initial mesh of the metal aircraft model is as follows: Figure 1 As shown in the figure, the aircraft is 17.9m long, 12m wide, and 5.7m high. The calculation frequency is 300MHz, the initial grid cell size is about 0.2λ, and the error threshold of the grid adaptive encryption process is set to 5×10 -4 ; According to the mesh information, MultiBranch-RWG basis functions are defined on the discretized triangular mesh. The total number of basis functions on the initial mesh is 8301; the mesh adaptive encryption is terminated after 4 iterations. The mesh error diagram of each iteration during the adaptive encryption process is shown in Figure 3 As shown, the final grid is as follows Figure 2 As shown, the total number of unknown quantities is 128586. The calculation result of the reference grid with a unit size of 0.0375λ is used as a comparative example. The number of unknown quantities of the reference grid is 531264. To prove the effectiveness of the present invention, the scattering near-field calculation formula is used to calculate Figure 2 The scattered near field at the red rectangle in the middle, the scattered near field calculated by this embodiment and the comparative example are as follows Figure 4As shown in the figure, it can be seen that the scattered near field calculated by the final grid adaptively encrypted in the present invention is almost the same as the scattered near field calculated by the reference grid, but their unknown quantities differ by nearly 3 times, which proves that the integral equation grid adaptive encryption method based on non-conformal grid current discontinuity estimation proposed in the present invention can achieve higher accuracy with fewer unknown quantities.

[0062] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for adaptive mesh refinement of integral equations based on non-conformal mesh current discontinuity estimation, characterized in that: The following steps are involved: Step 1. Discretize the model surface using conformal or non-conformal triangle meshes; Step 2. Define the MultiBranch-RWG basis function on the discretized grid cells, establish the electric field integral equation, and solve it to obtain the current coefficient, and then calculate the surface current distribution from the current coefficient; Step 3. According to the surface current distribution, the current discontinuity error of each grid unit is calculated using the current discontinuity error estimation method; Step 4. Traverse the current discontinuity errors of all grid cells. When the current discontinuity error of any grid cell is greater than the preset threshold, perform adaptive encryption, and use the adaptively encrypted grid as input, return to step 2 for iteration; otherwise, output the grid information.

2. The method for adaptive mesh encryption of integral equations based on non-conformal mesh current discontinuity estimation according to claim 1, characterized in that: The specific process of step 2 is: The surface current J of the equivalent surface is discretized using the MultiBranch-RWG basis function as follows: Among them, a n is the current coefficient, f n is the MultiBranch-RWG basis function, N is the total number of basis functions, n = 1, 2, ... N; the electric field integral equation established according to the discrete form of the surface current J is: [Z mn ][J n ]=[b m ] Where r is the field point, r′ is the source point, G(r,r′) represents the Green’s function, S n is the MultiBranch-RWG basis function f n The domain of S m is the MultiBranch-RWG basis function f m The domain of E inc is the incident electric field, k is the wave number, ω is the incident wave angular frequency, μ0 is the free space permeability, and j is the imaginary unit; The electric field integral equation obtained by discretization is solved iteratively to obtain the current coefficient {a n } 1≤n≤N , and then the surface current distribution of the equivalent surface is obtained.

3. The method for adaptive mesh encryption of integral equations based on non-conformal mesh current discontinuity estimation according to claim 1, characterized in that: The specific process of step 3 is: Calculate the current discontinuity error of the ith unit: Among them, Error i represents the current discontinuity error of the i-th unit, ε (i,m) represents the current discontinuity error of the mth edge of the ith unit, represents the maximum value of the tangential component of the surface current density at the midpoints of all mesh edges, A i represents the area of ​​the i-th unit.

4. The method for adaptive mesh encryption of integral equations based on non-conformal mesh current discontinuity estimation according to claim 3, characterized in that: In step 3, the current discontinuity error calculation process of each edge in the unit is: The MultiBranch-RWG basis function corresponding to the mth edge of the i-th unit is f (i ,m ) , if the mth edge of the ith unit is f (i,m) The side of the equilateral triangle, then ε (i,m) It is expressed as: in, represents the unit vector tangent to the mth side of the ith unit, Q (i,m) represents the MultiBranch-RWG basis function f (i,m) The number of negative triangles, r q represents the MultiBranch-RWG basis function f (i,m) The midpoint of the common side of the qth negative triangle, Represents r q The current calculated based on the i-th unit, Represents r q The current calculated based on the qth negative triangle; If the mth edge of the ith unit is f (i,m) The negative triangle side, then ε (i,m) It is expressed as: in, Represents r q The current calculated based on the i-th unit, Represents r q The current calculated based on the equilateral triangle.

5. The method for adaptive mesh encryption of integral equations based on non-conformal mesh current discontinuity estimation according to claim 1, characterized in that: In step 4, the specific process of adaptive encryption is: traverse the current discontinuity errors of all grid cells, select the first 30% of the grid cells with the largest errors, and perform midpoint encryption on each selected grid.

6. The method for adaptive mesh encryption of integral equations based on non-conformal mesh current discontinuity estimation according to claim 5, characterized in that: In step 4, the specific process of midpoint encryption is: connecting the midpoints of the three sides of the triangle unit to be encrypted to each other, and dividing the triangle unit to be encrypted into four equal triangle units.

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