FDTD conformal mesh generation method suitable for complex model

Abstract

An FDTD conformal mesh generation method suitable for a complex model comprises the steps that (1) a real physical model of an FDTD electromagnetic target is obtained, and electromagnetic simulation software is used for exporting the real physical model as an STL model; 2) reading key data of all triangular surface elements in the STL model, and generating rays for geometric boundary detection on the STL model; 3) determining intersection points of all the rays and all the triangular surface elements based on a ray tracing algorithm, and determining incident points and emergent points corresponding to all the rays through dot products of normal vectors of the rays and normal vectors of the triangular surface elements; and 4) based on the incidence points and the emergence points of all rays, performing FDTD conformal mesh generation on a real physical model by using a conformal parameter-based target model conformal mesh generation method. The method is suitable for a complex model in any shape, can quickly and accurately generate a hexahedral mesh required by FDTD calculation, and has general applicability.

Description

An FDTD conformal mesh generation method suitable for complex models Technical Field

[0001] This invention relates to the fields of electromagnetic compatibility and electromagnetic computation technology, and specifically to an FDTD conformal mesh generation method suitable for complex models. Background Technology

[0002] The Finite-Difference Time-Domain (FDTD) method, as one of the core methods in the field of numerical electromagnetic field computation, has been widely applied in antenna design, microwave device simulation, electromagnetic compatibility analysis, and optical device optimization due to its advantages of full-wave time-domain analysis and ease of handling complex boundary conditions. This method primarily utilizes the idea of ​​central difference to discretize Maxwell's curl equations, obtaining a set of equations that reflect the electric field in a given space. ,magnetic field The time-domain iterative formula for the changing situation. The essence of this method is to perform numerical calculations by discretizing the continuous electromagnetic field space. Its smallest spatial unit is the Yee cell, in which the electric and magnetic fields are staggered. Each magnetic field component is surrounded by four electric field components, and each electric field component is also surrounded by four magnetic field components. The FDTD mesh generation technique converts the real model into the Yee cell form required by the FDTD algorithm. However, since the Yee cell is a standard hexahedral structure, it cannot perfectly fit complex models, especially for structures such as inclined planes or curved surfaces, thus introducing a stepped approximation error. Therefore, it is necessary to improve the FDTD mesh generation for complex electromagnetic models.

[0003] In the practical application of the FDTD method, a key step is how to quickly and accurately convert the physical model of the target into a hexahedral discrete mesh suitable for FDTD electromagnetic calculations. Existing FDTD mesh generation methods typically use a stepped approximation to fit complex geometric boundaries, that is, by stitching together rectangular mesh cells to approximate the curved surfaces, inclined planes, or irregular edges of the model. This approach leads to stepped approximation errors, and to reduce these errors, the mesh cell size needs to be significantly reduced, which results in an exponential increase in computational resource consumption.

[0004] To achieve FDTD mesh modeling for complex target models, various FDTD mesh modeling methods have been developed in the industry. Among them, some scholars have proposed a ray tracing algorithm based on ray intersection judgment. This method generates an FDTD mesh by generating rays below the model and performing intersection judgments with the target model. Subsequently, scholars have proposed various optimization algorithms based on this method. A representative example is the mesh modeling optimization method based on bounding box and octree algorithms, which can significantly reduce the number of intersection judgments between rays and triangular elements, accelerating the generation speed of the target mesh. Other scholars have proposed an FDTD mesh modeling method based on random filling. This method first creates uniformly distributed points on the target model and maps these points onto the FDTD mesh, thereby generating the surface mesh of the target model. The internal mesh is generated inside the surface mesh. This method has higher generation efficiency when handling more complex models.

[0005] The mesh modeling methods described above all generate non-conformal meshes with a standard hexahedral shape. To address the stepped approximation error problem of non-conformal meshes, conformal meshes need to be generated. Currently, various FDTD conformal meshing techniques have been developed. Among them, the volume averaging method and the surface filling estimation method are relatively representative and common. The volume averaging method calculates the material coefficients of the conformal mesh by weighting the proportion of the volume of all filling materials within the mesh. The surface filling estimation method estimates the filling volume of various materials within the mesh based on the material filling area on the six faces of the hexahedral mesh. The volume averaging method can be directly calculated based on the FDTD algorithm, while the surface filling estimation method requires modification of the FDTD iterative formula during calculation.

[0006] While FDTD mesh modeling methods and conformal techniques are mature, they still have limitations. In mesh modeling, because the electromagnetic components on an FDTD mesh are discretely distributed, and adjacent meshes share electric field components on adjacent edges and magnetic field components on surfaces, traditional FDTD modeling methods introduce errors when accurately constructing the electromagnetic components within the target model. Furthermore, because the location of electromagnetic components cannot be accurately described, conformal calculations can lead to inaccurate material parameter representations in the conformal mesh, resulting in significant errors in the conformal calculations. Summary of the Invention

[0007] The purpose of this invention is to provide an FDTD conformal mesh generation method suitable for complex models, comprising the following steps:

[0008] 1) Obtain the real physical model of the FDTD electromagnetic target, and use electromagnetic simulation software to export the real physical model as an STL model.

[0009] 2) Read the key data of all triangular facets in the STL model and generate rays on the STL model for geometric boundary detection.

[0010] The key data of the triangular element includes the vertices and normal vectors of the triangular element.

[0011] 3) Based on the ray tracing algorithm, determine the intersection points of all rays with all triangular elements, and determine the entry and exit points of all rays by taking the dot product of the normal vector of the ray and the normal vector of the triangular element.

[0012] 4) Based on the entry and exit points of all rays, the FDTD conformal mesh generation method based on the target model conformal mesh generation method based on conformal parameters is used to perform conformal mesh generation on the real physical model.

[0013] Furthermore, the electromagnetic simulation software includes CST Studio Suite.

[0014] Furthermore, the step of generating rays for geometric boundary detection on the STL model is as follows:

[0015] S1 constructs a spatial rectangular coordinate system on the STL model.

[0016] S2 determines the minimum and maximum values ​​of the vertex coordinates of all triangular elements in the coordinate axes based on the key data of all triangular elements in the STL model.

[0017] S3 generates the starting plane of the ray 2D mesh based on the minimum value of the vertex coordinates of all triangular elements in the coordinate axes, as shown below:

[0018] (1)

[0019] In the formula, The function represents rounding down. These represent the starting points of the rays incident along the positive X, Y, and Z axes, respectively. , , These represent the minimum values ​​of the vertex coordinates of all triangular facets along the X, Y, and Z axes, respectively. This represents the spacing between the starting plane of the ray 2D mesh and the mesh of the STL model. These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively.

[0020] S4 generates the starting points of the electric field component rays and the magnetic field component rays based on the minimum and maximum values ​​of the vertex coordinates of all triangular facets in the coordinate axes.

[0021] Furthermore, the starting point of the electric field component ray is shown below:

[0022] (2)

[0023] In the formula, , , These represent the coordinates of the starting points of the electric field components incident along the positive X, Y, and Z axes, respectively. , , These represent the grid spacing along the X, Y, and Z axes, respectively. The function represents rounding up. , , These represent the minimum values ​​of the vertex coordinates of all triangular facets along the X, Y, and Z axes, respectively. , , These represent the maximum values ​​of the vertex coordinates of all triangular elements along the X, Y, and Z axes, respectively. These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively.

[0024] The starting point of the magnetic field component ray is shown below:

[0025] (3)

[0026] In the formula, , , These represent the coordinates of the starting points of the magnetic field components incident along the positive directions of the X, Y, and Z axes, respectively.

[0027] Furthermore, the steps for determining the intersection points of all rays and all triangular elements based on the ray tracing algorithm are as follows:

[0028] A1 defines the ray parameter equation. As shown below:

[0029] (4)

[0030] In the formula, Indicates the starting position of the ray. The normal vector of the ray. This represents the distance from the starting point of the ray to any point on the ray.

[0031] A2 determines the coordinates of any point on the plane containing the triangular element. As shown below:

[0032] (5)

[0033] In the formula, , , This represents the three vertices of a triangular element. , This is a limiting factor.

[0034] A3 is based on the ray parameter equation. and coordinates The solution for the intersection of the ray and the triangular element is as follows:

[0035] (6)

[0036] Let parameters ,parameter ,parameter Applying Cramer's rule and the mixed product formula, the solution formula can be rewritten as follows:

[0037] (7)

[0038] In the formula, express.

[0039] A4 determines whether the coordinates of the intersection point after the solution are located inside the triangular element. If so, the intersection point of the ray and the triangular element and the distance from the starting point of the ray to the triangular element are obtained.

[0040] The formula for determining whether the intersection point's coordinates lie within the triangular element is as follows:

[0041] (8).

[0042] Furthermore, if the dot product of the normal vector of the ray and the normal vector of the triangular element is less than 0, then the intersection point is the injection point.

[0043] If the dot product of the normal vector of the ray and the normal vector of the triangular element is greater than 0, then the intersection point is the emission point.

[0044] Furthermore, the steps for performing FDTD conformal mesh generation on the real physical model are as follows:

[0045] B1 defines the grid values ​​for the injection and exit points, as shown below:

[0046] (9)

[0047] In the formula, This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This represents the smallest scalar that satisfies the grid values. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions. This represents the distance from the starting point of the ray to the point of entry. This represents the distance from the starting point of the ray to the point of emission.

[0048] B2 defines conformal parameters. As shown below:

[0049] (10)

[0050] In the formula, r represents the intersection index. When r is odd, it represents the injection point; when r is even, it represents the injection point. This represents the distance from the starting point of the ray to the r-th intersection point. This represents the grid value at the r-th intersection point of the FDTD electromagnetic target.

[0051] Among them, the conformal parameters at the intersection point The conformal parameter between the injection point and the injection point is 0, and the other conformal parameters are 1.

[0052] B3 is based on the distance parameter from the ray's origin to the intersection point. The starting point and number of generated electric field components.

[0053] Based on the distance parameter from the ray's origin to its intersection and conformal parameters The starting point and quantity of the generated magnetic field components.

[0054] Furthermore, the starting point and number of the electric field components are as follows:

[0055] (11)

[0056] In the formula, It refers to the minimum value of the vertex coordinates of all triangular elements in the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions.

[0057] Furthermore, the starting point and number of the magnetic field components are as follows:

[0058] (12)

[0059] In the formula, It refers to the minimum value of the vertex coordinates of all triangular elements in the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions. This represents the conformal parameter of the injection point. This represents the conformal parameter of the injection point.

[0060] Furthermore, after performing FDTD conformal mesh generation on the real physical model, FDTD electromagnetic coupling calculations are performed.

[0061] The FDTD electromagnetic coupling calculation includes conformal FDTD calculation and ordinary FDTD calculation.

[0062] When performing conformal FDTD calculations, the conformal area of ​​the FDTD electromagnetic target surface mesh is calculated as follows:

[0063] (13)

[0064] In the formula, These represent the conformal parameters of the electromagnetic components on the four edges of the FDTD mesh. Represents the conformal area.

[0065] The technical effects of this invention are undeniable. This invention proposes an FDTD conformal mesh generation method suitable for complex models. This method is based on the actual physical model of the target, and... , , Rays are generated for different electromagnetic components in three different directions, and their intersection with the target model is determined. Based on the intersection results, a conformal parameter is defined at each electromagnetic component in the computational space to describe the positional relationship between that component and the target model, thus identifying whether the electromagnetic component is located outside, inside, or on the surface of the target model. Based on the electromagnetic component data of the target model's surface, commonality calculations can be performed. This method can accurately determine the position of electromagnetic components, improve mesh generation accuracy, and avoid the generation of surface step approximation errors.

[0066] The conformal FDTD mesh generation method for complex models proposed in this invention is a method that extracts model data based on the triangular facet structure of the real model, while considering the discretization of each parameter variable in the Yee cell. It performs ray intersection judgment from different directions for each electromagnetic component, thereby accurately generating the conformal FDTD mesh of the model. Since adjacent Yee cells share the electric field components on the edges and the magnetic field components on the faces, simply representing them using mesh position and number is insufficient. The position and number of electromagnetic parameters can lead to errors. Therefore, this invention proposes to perform ray intersection judgment in three directions for each electromagnetic parameter and generate a conformal mesh, which can avoid errors caused by differences in the electric and magnetic field components and the number of meshes. For complex model surface structures, to reduce step approximation errors, this method introduces conformal mesh technology. Conformal meshes break free from the constraints of the standard hexahedral structure and can better fit the complex model surface structure, reducing step approximation errors. When generating the conformal FDTD mesh, this method records the conformal parameters of each mesh and calculates the conformal area of ​​each mesh for conformal FDTD calculation. Compared with ordinary FDTD calculation, it can significantly reduce the step approximation errors caused by the irregularity of the model surface, thereby greatly improving simulation accuracy and enhancing the reliability and applicability of the FDTD method.

[0067] This invention is based on the actual physical model of the target model and uses a ray tracing algorithm to determine the required mesh locations for the target model. Rays are generated from three directions for each of the six electromagnetic components in the FDTD mesh, and their intersection with the triangular facets representing the target model is determined, thus accurately generating an FDTD mesh with discrete characteristics.

[0068] This invention introduces conformal parameters and conformal area It can quickly and accurately identify the number of meshes that need to be generated and the number of meshes that need to be computed conformally.

[0069] This invention is applicable to complex models of arbitrary shapes and can quickly and accurately generate the hexahedral mesh required for FDTD calculations, thus having universal applicability. Attached Figure Description

[0070] Figure 1 is a flowchart of the present invention;

[0071] Figure 2 is a schematic diagram of the ray plane; Figure 2(a) is a schematic diagram of the starting plane of the ray two-dimensional grid and the FDTD grid; Figure 2(b) is a schematic diagram of the electromagnetic components on the FDTD grid;

[0072] Figure 3 is a schematic diagram of the FDTD mesh model;

[0073] Figure 4 is a schematic diagram of the rays;

[0074] Figure 5 shows a schematic diagram of the intersection between the target model and the ray;

[0075] Figure 6 shows the conformal parameters of the surface mesh of the target model. ;

[0076] Figure 7 shows the conformal area of ​​the surface mesh of the target model; Figure 7(a) shows... A schematic diagram of the conformal area; Figure 7(b) shows... A schematic diagram of the conformal area; Figure 7(c) is... Schematic diagram of conformal area;

[0077] Figure 8 is a schematic diagram of a spherical metal cavity; Figure 8(a) is a schematic diagram of a real model of a spherical metal cavity; Figure 8(b) is a schematic diagram of an FDTD mesh model of a spherical metal cavity.

[0078] Figure 9 shows the spherical metal cavity. , Components; Figure 9(a) shows the spherical metal cavity. Component schematic diagram; Figure 9(b) shows the spherical metal cavity. Component diagram;

[0079] Figure 10 shows the shielding effectiveness of the spherical metal cavity;

[0080] Figure 11 is a schematic diagram of a four-slot U-shaped aircraft wiring channel; Figure 11(a) is a schematic diagram of a real model of a four-slot U-shaped aircraft wiring channel; Figure 11(b) is a schematic diagram of an FDTD mesh model of a four-slot U-shaped aircraft wiring channel.

[0081] Figure 12 shows the shielding effectiveness of the four-slot U-shaped aircraft wiring duct; Figure 12(a) shows the shielding effectiveness at different positions in the side slot; Figure 12(b) shows the shielding effectiveness at different positions in the side slot. Detailed Implementation

[0082] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0083] Example 1:

[0084] Referring to Figures 1 to 12, an FDTD conformal mesh generation method suitable for complex models includes the following steps:

[0085] 1) Obtain the real physical model of the FDTD electromagnetic target, and use electromagnetic simulation software to export the real physical model as an STL model.

[0086] 2) Read the key data of all triangular facets in the STL model and generate rays on the STL model for geometric boundary detection.

[0087] The key data of the triangular element includes the vertices and normal vectors of the triangular element.

[0088] 3) Based on the ray tracing algorithm, determine the intersection points of all rays with all triangular elements, and determine the entry and exit points of all rays by taking the dot product of the normal vector of the ray and the normal vector of the triangular element.

[0089] 4) Based on the entry and exit points of all rays, the FDTD conformal mesh generation method based on the target model conformal mesh generation method based on conformal parameters is used to perform conformal mesh generation on the real physical model.

[0090] Example 2:

[0091] An FDTD conformal mesh generation method suitable for complex models is described in Example 1. Furthermore, the electromagnetic simulation software includes CST Studio Suite.

[0092] Example 3:

[0093] An FDTD conformal mesh generation method suitable for complex models, the main technical contents of which are described in any one of Examples 1 and 2, further wherein the step of generating rays for geometric boundary detection on the STL model is as follows:

[0094] S1 constructs a spatial rectangular coordinate system on the STL model.

[0095] S2 determines the minimum and maximum values ​​of the vertex coordinates of all triangular elements in the coordinate axes based on the key data of all triangular elements in the STL model.

[0096] S3 generates the starting plane of the ray 2D mesh based on the minimum value of the vertex coordinates of all triangular elements in the coordinate axes, as shown below:

[0097] (1)

[0098] In the formula, The function represents rounding down. These represent the starting points of the rays incident along the positive X, Y, and Z axes, respectively. , , These represent the minimum values ​​of the vertex coordinates of all triangular facets along the X, Y, and Z axes, respectively. This represents the spacing between the starting plane of the ray 2D mesh and the mesh of the STL model. These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively.

[0099] S4 generates the starting points of the electric field component rays and the magnetic field component rays based on the minimum and maximum values ​​of the vertex coordinates of all triangular facets in the coordinate axes.

[0100] Example 4:

[0101] An FDTD conformal mesh generation method suitable for complex models, the main technical contents of which are described in any one of Examples 1 to 3, further wherein the starting point of the electric field component ray is as follows:

[0102] (2)

[0103] In the formula, , , These represent the coordinates of the starting points of the electric field components incident along the positive X, Y, and Z axes, respectively. , , These represent the grid spacing along the X, Y, and Z axes, respectively. The function represents rounding up. , , These represent the minimum values ​​of the vertex coordinates of all triangular facets along the X, Y, and Z axes, respectively. , , These represent the maximum values ​​of the vertex coordinates of all triangular elements along the X, Y, and Z axes, respectively. These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively.

[0104] The starting point of the magnetic field component ray is shown below:

[0105] (3)

[0106] In the formula, , , These represent the coordinates of the starting points of the magnetic field components incident along the positive directions of the X, Y, and Z axes, respectively.

[0107] Example 5:

[0108] A conformal mesh generation method for complex models using FDTD is provided, the main technical contents of which are described in any one of Examples 1 to 4. Further, the step of determining the intersection points of all rays and all triangular elements based on the ray tracing algorithm is as follows:

[0109] A1 defines the ray parameter equation. As shown below:

[0110] (4)

[0111] In the formula, Indicates the starting position of the ray. The normal vector of the ray. This represents the distance from the starting point of the ray to any point on the ray.

[0112] A2 determines the coordinates of any point on the plane containing the triangular element. As shown below:

[0113] (5)

[0114] In the formula, , , This represents the three vertices of a triangular element. , This is a limiting factor.

[0115] A3 is based on the ray parameter equation. and coordinates The solution for the intersection of the ray and the triangular element is as follows:

[0116] (6)

[0117] Let parameters ,parameter ,parameter Applying Cramer's rule and the mixed product formula, the solution formula can be rewritten as follows:

[0118] (7)

[0119] In the formula, express.

[0120] A4 determines whether the coordinates of the intersection point after the solution are located inside the triangular element. If so, the intersection point of the ray and the triangular element and the distance from the starting point of the ray to the triangular element are obtained.

[0121] The formula for determining whether the intersection point's coordinates lie within the triangular element is as follows:

[0122] (8).

[0123] Example 6:

[0124] An FDTD conformal mesh generation method suitable for complex models is described in any one of Examples 1 to 5. Further, if the dot product of the normal vector of the ray and the normal vector of the triangular element is less than 0, then the intersection point is the injection point.

[0125] If the dot product of the normal vector of the ray and the normal vector of the triangular element is greater than 0, then the intersection point is the emission point.

[0126] Example 7:

[0127] An FDTD conformal mesh generation method suitable for complex models is described in any one of Examples 1 to 6. Further, the steps for performing FDTD conformal mesh generation on the real physical model are as follows:

[0128] B1 defines the grid values ​​for the injection and exit points, as shown below:

[0129] (9)

[0130] In the formula, This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This represents the smallest scalar that satisfies the grid values. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions. This represents the distance from the starting point of the ray to the point of entry. This represents the distance from the starting point of the ray to the point of emission.

[0131] B2 defines conformal parameters. As shown below:

[0132] (10)

[0133] In the formula, r represents the intersection index. When r is odd, it represents the injection point; when r is even, it represents the injection point. This represents the distance from the starting point of the ray to the r-th intersection point. This represents the grid value at the r-th intersection point of the FDTD electromagnetic target.

[0134] Among them, the conformal parameters at the intersection point The conformal parameter between the injection point and the injection point is 0, and the other conformal parameters are 1.

[0135] B3 is based on the distance parameter from the ray's origin to the intersection point. The starting point and number of generated electric field components.

[0136] Based on the distance parameter from the ray's origin to its intersection and conformal parameters The starting point and quantity of the generated magnetic field components.

[0137] Example 8:

[0138] An FDTD conformal mesh generation method suitable for complex models, the main technical contents of which are described in any one of Examples 1 to 7, and further, the starting point and number of the electric field components are as follows:

[0139] (11)

[0140] In the formula, It refers to the minimum value of the vertex coordinates of all triangular elements in the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions.

[0141] Example 9:

[0142] An FDTD conformal mesh generation method suitable for complex models, the main technical contents of which are described in any one of Examples 1 to 8, and further, the starting point and number of the magnetic field components are as follows:

[0143] (12)

[0144] In the formula, It refers to the minimum value of the vertex coordinates of all triangular elements in the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating the FDTD grid. This indicates the value of the ejection point grid at which the FDTD electromagnetic target finishes generating the FDTD grid. This refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions. Refers to the X, Y, and Z directions. This represents the conformal parameter of the injection point. This represents the conformal parameter of the injection point.

[0145] Example 10:

[0146] An FDTD conformal mesh generation method suitable for complex models is provided. The main technical contents are described in any one of Examples 1 to 9. Further, after performing FDTD conformal mesh generation on the real physical model, FDTD electromagnetic coupling calculation is performed.

[0147] The FDTD electromagnetic coupling calculation includes conformal FDTD calculation and ordinary FDTD calculation.

[0148] When performing conformal FDTD calculations, the conformal area of ​​the FDTD electromagnetic target surface mesh is calculated as follows:

[0149] (13)

[0150] In the formula, These represent the conformal parameters of the electromagnetic components on the four edges of the FDTD mesh. Represents the conformal area.

[0151] Example 11:

[0152] Referring to Figures 1 to 12, an FDTD conformal mesh generation method suitable for complex models is presented, the main technical contents of which include:

[0153] First, commercial software such as CST is used to export the model of the real complex electromagnetic target as an STL model file in the form of triangular facets. Then, the model data such as the vertices and normal vectors of the triangular facets in the STL model file are read, and the six variables required for the time-domain iteration of the FDTD algorithm are calculated in three directions around the model. Rays are generated at the distribution locations of the rays; then, based on the ray tracing algorithm, the intersection between all rays and all triangular elements is determined; the intersection points are obtained at the intersections of rays and triangular elements, and the angle between the ray direction and the normal vector of the triangular element is used to determine a set of entry and exit points. FDTD conformal meshes are generated between the entry and exit points; if the surface of the real model and the surface of the generated conformal FDTD mesh do not coincide, and their spacing is within one mesh length, the difference between the surface of the real model and the surface of the generated conformal FDTD mesh is recorded as the conformal parameter of that point, and the number of meshes required between the entry and exit points is determined based on the value of the conformal parameter; finally, conformal FDTD electromagnetic coupling calculations can be performed using the generated model mesh data and the conformal parameter.

[0154] Example 12:

[0155] Referring to Figures 1 to 12, an FDTD conformal mesh generation method suitable for complex models is presented, the main technical contents of which include:

[0156] First, the real physical model is preprocessed using electromagnetic simulation software and exported as an STL format model file containing triangular facet structures. This file can completely preserve the geometric contour information of the model. Second, key data of the triangular facets in the STL file, including vertex coordinates and facet normals, are read, and the model is then analyzed in three-dimensional space. , , In three directions, the electric field of the solution is required during the time-domain iteration of the FDTD algorithm. With magnetic field The spatial distribution locations of the six field quantities are used to generate rays for geometric boundary detection. Next, a ray tracing algorithm is used to determine the intersection of each generated ray with a triangular element of the model. Intersection points are calculated at these points, and the angle between the ray propagation direction and the triangular element's normal vector is analyzed to distinguish the entry point and exit point of the ray. A preliminary FDTD conformal mesh is then generated between these two points, using them as boundaries. Since the actual model surface and the generated FDTD conformal mesh surface are not completely coincident, and the distance between them is controlled within a single mesh size, the deviation values ​​between the model surface and the mesh surface at corresponding locations are recorded and defined as conformal parameters. Based on the specific values ​​of the conformal parameters, the number of mesh elements required between the entry and exit points is dynamically determined to ensure the mesh's fit accuracy with the model boundary. Finally, the generated model mesh data and the conformal parameters at each location are integrated as input conditions to perform conformal FDTD time-domain electromagnetic coupling calculations, achieving accurate simulation of the electromagnetic properties of the complex model.

[0157] This method can be used to generate conformal FDTD meshes for complex models.

[0158] (1) Mesh generation method for complex models based on ray tracing algorithm

[0159] 1) Target model data reading

[0160] The CST electromagnetic simulation software was used to perform geometric modeling on the real physical model, and an ASCII STL file was exported to ensure that the geometric contour information of the triangular facets was completely preserved. The information read from the STL file is shown in Table 1. The first line of the file provides the file path and filename. Triangular facet information is organized into units called "facets," each consisting of 7 lines of data. After `facetnormal` are the unit normal vector coordinates pointing outwards from the solid, and the three lines after `outer loop` are the coordinates of the three vertices of the triangular facet, arranged counter-clockwise along the direction of the normal vector pointing outwards from the solid. Based on the information of each triangular facet in the STL file, the normal vector and vertex coordinates of the triangular facets were read sequentially.

[0161] Table 1 STL file format

[0162]

[0163] 2) Ray generation

[0164] The mesh ray plane can be configured with different starting points based on the incident direction of the ray. If the ray is incident along the positive X-axis, then the plane containing the ray's starting point is perpendicular to the X-axis, and all ray normal vectors on this plane... This can be denoted as (1,0,0); if the ray is incident along the positive Y-axis, then the plane containing the ray's origin is perpendicular to the Y-axis, and the normal vector of each ray... If the ray is incident along the positive Z-axis, then the plane containing the ray's origin is perpendicular to the Z-axis, and the normal vector of the ray is (0,1,0). The value is (0,0,1).

[0165] Because the positions of electromagnetic components in the FDTD mesh are staggered, and adjacent meshes share electromagnetic components on adjacent edges and faces, in order to accurately identify the number of generated electromagnetic components, [further details are needed]. Different electromagnetic components generate corresponding rays.

[0166] On the starting plane of the ray 2D mesh, it is only necessary to generate rays within a finite space. Taking a plane as an example, in to Between For spacing, to Between Generate a two-dimensional mesh with spacing.

[0167] exist The rays generated on the plane are shown in Figure 2. A two-dimensional mesh plane is generated below the target model, and rays are generated at the center point of each mesh. The component rays, as shown by the green rays in the figure; generate rays at each vertex of the grid. The component of the ray, as shown by the red ray in the figure. plane and The generation of rays in a plane is similar to The rules for ray generation on a plane, in On the plane The component generates rays at the center point of the grid on the plane starting from the ray 2D grid, for... The component generates rays at the grid vertices; On the plane The component generates rays at the center point of the grid on the plane starting from the ray 2D grid, for... The component generates rays at the grid vertices.

[0168] The specific rules for ray generation are as follows:

[0169] After reading the triangular facet information of the target model from the STL file, record the minimum and maximum values ​​of its vertex coordinates along the coordinate axes, denoted as . , In a Cartesian coordinate system, a two-dimensional ray mesh starting plane is generated around the target model, as shown in formula (1).

[0170] (1)

[0171] In the formula, The function represents rounding down, that is, rounding to the lower surface of the mesh containing the boundary of the target model. This indicates that the starting plane of the ray 2D mesh is located several meshes below the target model, to avoid the starting point of the ray coinciding with the model boundary. This indicates the side length of the generated FDTD mesh.

[0172] Therefore, the formula for the starting point of the electric field component rays generated on the three planes is shown in formula (2).

[0173] (2)

[0174] The formula for the starting point of the magnetic field component rays generated on the three planes is shown in formula (3).

[0175] (3)

[0176] In the formula, The function represents rounding up. , , They respectively indicate that they need to be The number of rays obtained in a given direction.

[0177] An FDTD mesh is generated above the starting plane of the ray 2D mesh, so as to... Taking a ray generated from a plane as an example, its relationship with the ray is shown in Figure 3. Figure 3(a) shows that in An FDTD grid is generated above the starting plane of a ray 2D grid on a plane. Rays emanating from the vertices of the 2D grid pass through the edges of the FDTD grid, and rays emanating from the center point of the 2D grid pass through the center point of the FDTD grid. Figure 3(b) shows the positions of the electric and magnetic field components on a hexahedral grid, which intersect with different ray positions.

[0178] 3) Determining the intersection of a ray and a triangular facet

[0179] The three elements of a ray—the ray origin, the ray direction, and the translation distance—are defined by parametric equations as shown in formula (4).

[0180] (4)

[0181] In the formula, Indicates the starting position of the ray. The normal vector of the ray. This is a scalar representing the distance between the starting point and a point on the ray, or it can be considered as the distance moved along the ray's direction from the starting point. As shown in Figure 4, by selecting different... The value can be viewed as a ray moving from the starting point along the direction of the ray's normal vector. distance.

[0182] The coordinates of any point on the plane containing the triangular element are shown in formula (5).

[0183] (5)

[0184] In the formula, , , This represents the three vertices of the triangular element, defined by constraint coefficients. , The value of can be used to determine the point. The position of the point on the plane containing the triangular element. If it is located inside a triangular element, the following conditions must be met:

[0185] (6)

[0186] After obtaining the equations of the ray and the plane of the triangular element, the intersection point of the ray and the triangular element can be solved using formula (7). Solving formula (7) is equivalent to solving for the parameters. , , , where the parameters This represents the distance from the ray's origin to the intersection of the ray and the triangular element, while the parameter... , Then it needs to satisfy formula (6). If it does not satisfy, it means that the intersection point is outside the triangular element.

[0187] (7)

[0188] Substituting formulas (4) and (5) into formula (7), we can obtain formula (8).

[0189] (8)

[0190] To solve formula (8), let , , Applying Cramer's rule, formula (8) can be transformed into:

[0191] (9)

[0192] According to the formula for the mixed product Formula (9) can be rewritten as:

[0193] (10)

[0194] The intersection point of the ray and the triangular element can be solved using formula (10). and the distance from the starting point of the ray to the intersection point In the process of determining ray intersection, the parameters are first determined. , Does it satisfy formula (6)? If it does, then prove that the ray intersects with the triangular element, and then solve for the solution. The value is used to calculate the distance from the ray's origin to the triangular element.

[0195] (2) Target model conformal mesh generation method based on conformal parameters

[0196] The intersection points between a ray and the target model can be divided into entry points and exit points. The mesh between the entry and exit points is the mesh inside the target model. Whether an intersection point is an entry or exit point can be determined by the dot product of the ray's normal vector and the normal vector of the triangular element; a dot product less than 0 indicates an entry point, and a dot product greater than 0 indicates an exit point. Entry and exit points exist in pairs. If the target model is complex, there may be multiple pairs of entry and exit points, as shown in Figure 5. The cross-sectional view represents the intersection points. and , and The grid between them is the grid inside the target model.

[0197] 1) Determine the number of grids generated

[0198] Each ray intersects a triangular element with a parameter. , representing the distance from the intersection point to the starting point of the ray. Using parameters It is possible to calculate which grid point, starting from the ray origin plane, is defined as the target model FDTD grid; this only requires comparing parameters. The size can be the same as any number of meshes. However, since the surface of the target model may not perfectly coincide with the surface of the FDTD mesh, the error is within one mesh size; and the intersection points are divided into entry and exit points, with different mesh definition rules. Taking the intersection point obtained by judging the intersection of the ray generated by the plane and the triangular facet as an example, the mesh values ​​of the injection point and the injection point are as shown in formula (11).

[0199] (11)

[0200] In the formula This indicates that starting from the plane of the ray origin, it is necessary to... After one grid, start generating the grid. This means that the mesh of the target model only needs to be generated up to the [number]th [number]. After generating one grid, that's it. A total of [number] grids need to be generated between the injection point and the injection point. Each grid.

[0201] 2) Generate conformal parameters

[0202] The mesh between the injection point and the injection point belongs to the mesh inside the target model. However, the surface of the target model and the FDTD mesh surface may not coincide, as shown in Figure 6. The outer surface of the surface mesh is not inside the target model; therefore, the magnetic field components on the outer surface do not belong to the target model. Thus, a conformal parameter is introduced to represent the difference between the outer surface of the target surface mesh and the outer surface of the target model, used to determine whether the magnetic field components on the outer surface of the target model surface mesh belong to the target model. The conformal parameter is defined as... The calculation formula is shown in formula (12).

[0203] (12)

[0204] In the formula, It can be obtained from formula (11). The range of values ​​is .

[0205] At each intersection The conformal parameters can be obtained at this point. Through a pair of entry and exit points Value and The value indicates the number of grids that need to be generated.

[0206] Formula (12) is only used to calculate the conformal parameters of the mesh at the intersection point. Otherwise, it defines the conformal parameters of other meshes between the injection point and the exit point. The conformal parameters of the mesh in the remaining computational space .

[0207] 3) Generate electromagnetic components of the target model

[0208] For the electric field components, it is only necessary to use the parameters The required quantity can be determined, and the determination rule is shown in formula (13); however, for the magnetic field component, the parameters need to be used simultaneously. and The judgment rule is shown in formula (14).

[0209] (13)

[0210] In the formula, , These represent the number of grid points for the injection point and the injection point, respectively, obtained from formula (11).

[0211] (14)

[0212] In the formula, and The value of is used to determine the starting point and the number of generated magnetic field components, and is obtained from formula (12). , Then, these represent the number of grids for the injection point and the injection point obtained by formula (11), respectively.

[0213] The above content, from formula (11) to formula (14), introduces... The mesh generation rules between the intersections of rays generated from a plane include electric field components. and magnetic field components The generation of the first plane is similar; the generation rules for the other two planes are the same, only requiring the following... Transform into , That's all.

[0214] 4) Calculate the conformal area

[0215] When performing conformal FDTD iterations, it is also necessary to calculate the conformal area of ​​the target model's surface mesh. Since multiple media exist within the target model's surface mesh, only conformal processing of the target model's surface mesh is required, and the conformal area needs to be calculated. The conformal area is the area of ​​the surface mesh occupied by the external media of the target model. The FDTD mesh is a hexahedral mesh, requiring calculation of the area of ​​different media on each face. Using a... Taking a two-dimensional FDTD mesh surface as an example, as shown in Figure 7, each of the four edges of this surface is composed of two... Components and two Each electromagnetic component has a conformal parameter. Its value range is within Between. Based on the different values ​​of the four conformal parameters, the conformal area of ​​the mesh can be calculated. The four conformal parameters are sorted from smallest to largest and defined as follows: , , , The formula for calculating the conformal area is shown in formula (15).

[0216] (15)

[0217] Only meshes with calculated conformal area require conformal FDTD calculation, while meshes without calculated conformal area only require ordinary FDTD calculation.

[0218] Example 13:

[0219] A conformal mesh generation method for FDTD suitable for complex models is described in Example 12. Further, consider a spherical metal cavity as shown in Figure 8, excited by an external plane wave. This spherical metal cavity is an ideal conductor with an outer radius of R = 50 mm and an inner radius of r = 40 mm. A [missing information - likely a surface marking] is formed on its surface. A rectangular single aperture is constructed using PEC as its material. An incident plane wave, a Gaussian pulse, is directed directly into the aperture. In the conformal FDTD simulation, the mesh size is selected... The time step is set to ,in It is the speed of light in free space. The shielding effectiveness is tested by selecting the center point of a spherical metal cavity.

[0220] Split spherical metal cavity , The components are shown in Figure 9, where each The component is followed by a conformal parameter , used to substitute into formula (15) to calculate the conformal area, and The conformal parameters of the components are mainly used to determine the number of magnetic field components generated, so they do not need to be output.

[0221] Finally, the shielding effectiveness of the spherical metal cavity obtained by substituting the generated conformal FDTD mesh into the conformal FDTD calculation is given in Figure 10, and compared with CST.

[0222] Consider now the four-slot U-shaped aircraft cable tray shown in Figure 11, whose dimensions are... Set its material to PEC. Select the FDTD mesh size. The time step is set to ,in It is the speed of light in free space. An external plane wave in the form of Gaussian wave excitation is incident directly on the opening of the cable tray. Six points at different locations within the cable tray are selected as monitoring points to evaluate the shielding effectiveness of the four-slot U-shaped aircraft cable tray, as shown in Figure 12.

Claims

1. An FDTD conformal mesh generation method suitable for complex models, characterized in that, Includes the following steps: 1) Obtain the real physical model of the FDTD electromagnetic target, and use electromagnetic simulation software to export the real physical model as an STL model; 2) Read the key data of all triangular facets in the STL model and generate rays for geometric boundary detection on the STL model; the key data of the triangular facets include the vertices and normal vectors of the triangular facets; 3) Determine the intersection points of all rays with all triangular facets based on the ray tracing algorithm, and determine the entry and exit points of all rays by the dot product of the normal vectors of the rays and the normal vectors of the triangular facets; 4) Based on the entry and exit points of all rays, perform FDTD conformal mesh generation on the real physical model using the conformal mesh generation method of the target model based on conformal parameters.

2. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, The electromagnetic simulation software includes CST Studio Suite.

3. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, The steps for generating rays for geometric boundary detection on the STL model are as follows: S1 Construct a spatial Cartesian coordinate system on the STL model; S2 Based on the key data of all triangular facets in the STL model, determine the minimum and maximum values ​​of the vertex coordinates of all triangular facets in the coordinate axes; S3 Based on the minimum value of the vertex coordinates of all triangular facets in the coordinate axes, generate the starting plane of the ray 2D mesh, as shown below: (1) In the formula, The function represents rounding down; These represent the starting points of the rays incident along the positive X, Y, and Z axes, respectively. 、 、 These represent the minimum values ​​of the vertex coordinates of all triangular elements along the X, Y, and Z axes, respectively. This represents the spacing between the starting plane of the ray 2D mesh and the mesh of the STL model; These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively; S4 generates the starting points of the electric field component ray and the magnetic field component ray based on the minimum and maximum values ​​of the vertex coordinates of all triangular elements in the coordinate axes.

4. The FDTD conformal mesh generation method for complex models according to claim 3, characterized in that, The starting point of the electric field component ray is shown below: (2) In the formula, 、 、 These represent the coordinates of the starting points of the electric field components incident along the positive X, Y, and Z axes, respectively. 、 、 These represent the grid spacing along the X, Y, and Z axes, respectively. The function represents rounding up; 、 、 These represent the minimum values ​​of the vertex coordinates of all triangular elements along the X, Y, and Z axes, respectively. 、 、 These represent the maximum values ​​of the vertex coordinates of all triangular elements along the X, Y, and Z axes, respectively. These represent the side lengths of the generated FDTD mesh in the X, Y, and Z directions, respectively; the starting points of the magnetic field component rays are shown below: (3) In the formula, 、 、 These represent the coordinates of the starting points of the magnetic field components incident along the positive directions of the X, Y, and Z axes, respectively.

5. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, The steps for determining the intersection points of all rays and all triangular elements based on the ray tracing algorithm are as follows: A1 Define the ray parametric equations. As shown below: (4) In the formula, Indicates the starting position of the ray. This represents the normal vector of the ray. A1 represents the distance from the starting point of the ray to any point on the ray; A2 determines the coordinates of any point on the plane containing the triangular element. As shown below: (5) In the formula, 、 、 Represents the three vertices of a triangular element; 、 The limiting coefficient; A3 is based on the ray parameter equation. and coordinates The solution for the intersection of the ray and the triangular element is as follows: (6) Let the parameter ,parameter ,parameter Applying Cramer's rule and the mixed product formula, the solution formula can be rewritten as follows: (7) A4 determines whether the coordinates of the intersection point after solving are located within the triangular element. If so, the intersection point of the ray and the triangular element and the distance from the starting point of the ray to the triangular element are obtained. The formula for determining whether the coordinates of the intersection point are located within the triangular element is as follows: （8）。 6. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, If the dot product of the normal vector of the ray and the normal vector of the triangular element is less than 0, then the intersection point is the injection point; if the dot product of the normal vector of the ray and the normal vector of the triangular element is greater than 0, then the intersection point is the injection point.

7. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, The steps for performing FDTD conformal mesh generation on the real physical model are as follows: B1 defines the mesh values ​​for the injection point and the injection point, as shown below: In equation (9), This indicates the injection point grid value at which the FDTD electromagnetic target begins generating its FDTD grid; This indicates the grid value at the exit point where the FDTD electromagnetic target finishes generating its grid. Represents the smallest scalar that satisfies the grid values; Refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions; Refers to the X, Y, and Z directions; This represents the distance from the starting point of the ray to the point of entry. B2 represents the distance from the ray's origin to its exit point; B2 defines the conformal parameter. As shown below: (10) In the formula, r represents the intersection index. When r is odd, it represents the injection point. When r is even, it represents the injection point. This represents the distance from the starting point of the ray to the r-th intersection point; This represents the mesh value at the r-th intersection point of the FDTD electromagnetic target; where the conformal parameter at the intersection point is... The conformal parameter between the entry and exit points is set to 0, while all other conformal parameters are set to 1; B3 is based on the distance parameter from the ray's origin to the intersection point. The origin and number of generated electric field components; based on the distance parameter from the ray origin to the intersection point. and conformal parameters The starting point and quantity of the generated magnetic field components.

8. The FDTD conformal mesh generation method for complex models according to claim 7, characterized in that, The starting point and number of the electric field components are as follows: In formula (11), This refers to the minimum value of the vertex coordinates of all triangular facets along the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating its FDTD grid; This indicates the grid value at the exit point where the FDTD electromagnetic target finishes generating its grid. Refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions; Refers to the X, Y, and Z directions.

9. The FDTD conformal mesh generation method for complex models according to claim 7, characterized in that, The starting point and number of the magnetic field components are as follows: In equation (12), This refers to the minimum value of the vertex coordinates of all triangular facets along the X, Y, and Z axes. This indicates the injection point grid value at which the FDTD electromagnetic target begins generating its FDTD grid; This indicates the grid value at the exit point where the FDTD electromagnetic target finishes generating its grid. Refers to the side lengths of the generated FDTD mesh in the X, Y, and Z directions; Refers to the X, Y, and Z directions; The conformal parameter represents the injection point; This represents the conformal parameter of the injection point.

10. The FDTD conformal mesh generation method for complex models according to claim 1, characterized in that, After performing FDTD conformal mesh generation on the real physical model, FDTD electromagnetic coupling calculations are performed. These calculations include conformal FDTD calculations and standard FDTD calculations. During the conformal FDTD calculation, the conformal area of ​​the FDTD electromagnetic target surface mesh is calculated, as shown below: In equation (13), These represent the conformal parameters of the electromagnetic components on the four edges of the FDTD mesh, respectively. Represents the conformal area.

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