RCS solving method of uniaxial anisotropic medium based on moment method

Abstract

The invention provides an RCS (radar cross section) solving method of a uniaxial anisotropic medium based on a moment method. The method comprises the following steps of: modeling a uniaxial anisotropic scatterer or a target model to be simulated in COMSOL; the surface of the scatterer is subjected to triangular mesh generation, and the size of a mesh is determined according to the wavelengths of electromagnetic waves inside and outside the scatterer; after the parameters of the scatterer and the background medium thereof are set, the grid is imported into the moment method for solving, and compared with a finite element method for solving the problem, the background medium of electromagnetic wave radiation and the interior of the scatterer do not need to be subjected to grid subdivision, and the degree of freedom only exists on the surface of the scatterer; the degree of freedom and memory used for solving the integral equation are far smaller than those used by a finite element method, and the method shows excellent calculation efficiency and calculation precision in actual examples.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic field modeling and simulation, and in particular relates to a method for solving RCS of a uniaxial anisotropic medium based on the method of moments. Background Art

[0002] Accurate electromagnetic simulation plays a vital role in fields such as wireless communications, metamaterial design, geophysical exploration, and biodetection. In recent years, the wide range of applications of various anisotropic media has attracted the attention of many researchers. For example, liquid crystals have been widely used in communications, resonators, and sensors; ferrite materials are widely used in many devices such as memory chips, transformers, filters, circulators, and phase shifters. With the emergence of new materials, anisotropic media have also found widespread applications in metamaterials, antenna designs, and geophysical imaging.

[0003] Anisotropic materials have been extensively used in integrated circuit design. As integrated circuit manufacturing processes shrink to the nanometer scale and advance toward heterogeneous integration, the limitations of traditional isotropic dielectrics in high-frequency signal transmission, electromagnetic compatibility, and thermal management are becoming increasingly prominent. Especially above the GHz band, silicon-based dielectrics, due to dielectric loss and dispersion, limit signal latency and bandwidth. Crosstalk caused by lateral electromagnetic field coupling in high-density wiring significantly impacts device reliability. Electromagnetic radiation and modal dispersion from vertical interconnects in three-dimensional integration hinder performance improvements. Localized hot spots exacerbate the risk of device failure. Existing solutions, such as metal shielding layers or optimized wiring structures, suffer from high costs and complex processes, making them incapable of meeting the high-performance, low-power, and multifunctional integration requirements of next-generation integrated circuits. To address this issue, a new approach, leveraging the directional electromagnetic response of uniaxial anisotropic dielectrics, can be used to freely tailor electromagnetic properties by introducing uniaxial dielectric layers in key IC regions (such as signal lines, antennas, and interconnect layers). The uniaxial anisotropic medium can be realized through materials such as liquid crystal, ferrite, nanostructure or superlattice. Its dielectric constant and magnetic permeability are orderly arranged along a specific direction (such as the z-axis), and the parameters can be dynamically controlled by applying an external electric field, magnetic field or stress field. In specific implementations, the use of a dielectric layer can significantly reduce high-frequency transmission line losses (such as improving the S parameters of microstrip lines by more than 30%) and suppress the diffusion of lateral electromagnetic fields to reduce crosstalk (reduced by 50% compared to traditional designs). At the same time, electromagnetic isolation channels can be constructed in three-dimensional integration to support high-density interconnection. In the field of storage, the orderly arrangement of the magnetic moments of ferrite media can be used for high-speed, low-power MRAM. In the field of computing, combining memristors with anisotropic insulating layers can construct brain-like neuromorphic circuits. In photonic integration, lithium niobate or chalcogenide glass media can achieve optical waveguide polarization state control through electro-optical / thermo-optical effects, which can be used for high-speed optical modulators (speeds up to 100GHz). In addition, thermally anisotropic materials such as graphene or hexagonal boron nitride can be used as substrates or packaging layers to build efficient heat dissipation paths along the vertical direction (thermal conductivity increased by 2 times), thereby alleviating the FinFET gate leakage current problem.

[0004] When solving electromagnetic scattering problems, both the finite element method (FEM) and the finite-difference time-domain (FDTD) method (FDTD) require meshing of the background medium, which typically results in a high demand for computer memory and computational time. The FEM divides the solution domain into multiple finite elements, each with its own unique geometry and nodes. This requires meshing the entire background medium and object, which not only increases the number of meshes but also leads to complex boundary conditions and high memory requirements. Furthermore, the FEM solution requires assembling and solving a large system of linear equations, further increasing computational time. To improve computational efficiency, researchers have developed various optimization techniques, such as adaptive meshing and multigrid techniques, but these methods still require significant computational resources. The FDTD method, on the other hand, discretizes space into a rectangular grid (Yee grid) on Cartesian coordinates and iteratively updates the electric and magnetic fields in time. This method eliminates the need for meshing the object itself and instead employs a structured meshing of the entire solution space. Despite this, the FDTD method still requires processing a large number of mesh nodes, especially for complex geometries or high frequencies, resulting in high computational and memory requirements. As for the moment method, due to the introduction of Green's function, it only needs to mesh the surface of the uniaxial anisotropic medium object, which greatly reduces the scale of the problem solution and improves the solution efficiency.

[0005] Secondly, for the moment method, it only needs to divide the scatterer into two-dimensional surface meshes. Compared with the three-dimensional meshes of other numerical algorithms, it is essentially a reduced-order method, which reduces the order of magnitude of the problem. After introducing the Green's function in uniaxial anisotropic media, the surface integral equation in the uniaxial anisotropic medium can be listed to characterize the field source relationship corresponding to the surface of the object. Since the Green's function can characterize the field source relationship of objects with the optical axis facing any direction, and the dielectric constant and magnetic permeability are both anisotropic media, this greatly broadens the scope of application of the integral equation, making it extremely universal in solving uniaxial anisotropic media problems. RCS is an important data that characterizes the scattering characteristics of an object. In integrated circuit design, especially antenna design, its far-field RCS is an important reference indicator for engineering designers to understand the antenna radiation capability.

[0006] In view of this, it is very meaningful to propose a RCS solution method for uniaxial anisotropic media based on the method of moments. Summary of the Invention

[0007] This invention provides a method for calculating the RCS of uniaxial anisotropic media based on the method of moments. This method can accurately and rapidly determine the current and magnetic flux on the surface of uniaxial anisotropic media. The algorithm also accurately calculates the RCS in the far field. Compared to the established finite element electromagnetic simulation software COMSOL, this invention offers significant advantages in computational efficiency and memory consumption, and has broad application prospects.

[0008] In a first aspect, the present invention proposes a method for solving the RCS of a uniaxial anisotropic medium based on the method of moments, the method comprising the following steps:

[0009] Model the scatterer to be simulated in COMSOL;

[0010] Meshing the surface of the scatterer, determining the wavelength of the electromagnetic wave of the uniaxial anisotropic medium, determining the sampling rate of the grid according to the size of the wavelength, and meshing the surface of the scatterer;

[0011] The mesh is imported into the moment method for solution. The PMCHWT algorithm constructs integral equations based on the internal and external aspects of the object and uses the moment method to directly solve the surface current and magnetic current of the uniaxial anisotropic medium. In the algorithm post-processing, the RCS position point information is calculated as needed, and the corresponding scattered field information is calculated through the Green's function to finally obtain the RCS.

[0012] More preferably, the model is first modeled and meshed in COMSOL software and its information is exported, and the PMCHWT algorithm is used to perform moment method solution and RCS simulation.

[0013] Further preferably, when modeling in COMSOL, the directionality of the optical axis of the scatterer is taken into consideration, and the vector direction thereof is determined by the coordinate system used when modeling the object.

[0014] Further preferably, after completing the modeling in COMSOL, the wavelength of the electromagnetic wave in the corresponding area is determined according to the medium parameters inside and outside the scatterer, and the grid size is determined by ensuring the sampling rate of the grid according to the smaller wavelength value of the two areas, and further grid division is performed.

[0015] Further preferably, the same set of triangular grids is used inside and outside the scatterer to ensure that the equivalent current and equivalent magnetic current inside and outside can correspond to each other, thereby reducing the amount of calculation and improving the calculation accuracy.

[0016] Further preferably, the triangular mesh result after meshing is exported, which includes the node numbers of the triangular mesh and the three-dimensional coordinate information corresponding to the numbers.

[0017] Further preferably, the grid is imported into the PMCHWT algorithm, and after the model medium parameter information is set, the algorithm reads the corresponding model information to perform electromagnetic simulation and solve

[0018] The relevant settings include: setting the polarization direction and propagation direction of the excitation plane wave, the electromagnetic parameter information of the scatterer and background medium, the simulation frequency, and the location information of the RCS field receiving point.

[0019] Secondly, the present invention adopts a method for solving RCS of uniaxial anisotropic media based on the method of moments, which mainly includes:

[0020] The integral equation method-of-moments solver used in the present invention is a solution process for three-dimensional problems. It can directly list surface integral equations based on the uniaxial anisotropic media inside and outside the object, and construct an integral equation that characterizes the relationship between the surface current and surface magnetic current on the outer surface of the uniaxial anisotropic object. After calculating the corresponding surface current and surface magnetic current, the electric field in the far-field region of the scatterer is obtained based on the field-type Green's function in three-dimensional space, thereby further calculating the RCS information.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] Compared with the finite element method and the finite difference time domain method, the moment method equation is mainly constructed based on the surface integral equation. In essence, it only needs to mesh the surface of the object, reducing the degree of freedom of the background medium in the equation, greatly reducing the scale of the solution. Since the integral equation automatically meets the radiation boundary conditions, and RCS often needs to solve the information of the far-field, it does not need to set up a very large solution area. Compared with the finite element method, its simulation setting is simple and intuitive, and the solution calculation amount is small. The present invention can be used to analyze the electromagnetic field RCS problem of uniaxial anisotropic objects in space, and can be applied to military target detection and EDA simulation design; compared with common finite element RCS simulation software, it has very obvious advantages in computing efficiency and computing resource consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and, together with the description, serve to explain the principles of the present invention. Other embodiments and many of the expected advantages of the embodiments will be readily apparent as they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with respect to each other. Like reference numerals designate corresponding similar parts.

[0024] Figure 1 Schematic diagram of a flow chart of a method for solving RCS of a uniaxial anisotropic medium based on the method of moments according to an embodiment of the present invention;

[0025] Figure 2 Schematic diagram of a simulation structure of a method for solving RCS of a uniaxial anisotropic medium based on the method of moments according to an embodiment of the present invention;

[0026] Figure 3 This is an example of calculating the RCS of a uniaxial anisotropic dielectric sphere in free space, using plane wave incident excitation. The RCS on the XOZ plane is calculated and compared with HFSS.

[0027] Figure 4 Based on Figure 2 The model is simulated using HFSS and moment method to obtain the RCS result diagram at the receiving point; DETAILED DESCRIPTION

[0028] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are illustrated by illustrative specific embodiments in which the present invention may be practiced. To this end, directional terms, such as "top," "bottom," "left," "right," "up," "down," etc., are used with reference to the orientation of the figures being described. Because the components of the embodiments may be positioned in several different orientations, directional terms are used for illustrative purposes and are in no way limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0029] Figure 1 The embodiment of the present invention discloses a method for solving RCS of uniaxial anisotropic media based on the method of moments, such as Figure 1 As shown, the method includes the following steps:

[0030] S1. First, use COMSOL to model the uniaxial anisotropic scatterer to be simulated and mesh its surface.

[0031] S2. When meshing a uniaxial anisotropic object, it is necessary to pay attention to the electromagnetic parameters of the uniaxial anisotropic medium to determine the mesh size to ensure the accuracy of the numerical results. Then, the mesh file after meshing is exported. For example, Figure 3 As shown, the medium of the sphere is

[0032]

[0033] Its optical axis is along and At a frequency of 30MHz, since the wavelength in anisotropic media is related to its propagation direction, the medium is divided according to the direction parallel to the optical axis and perpendicular to the optical axis, which can be expressed as

[0034] ∈ rs,|| =3,∈ rs,⊥ =2,μ rs,|| =2,μ rs,⊥ =0.8

[0035] It can be concluded that the wavelength in the direction parallel to the optical axis is 4.08m. At the same time, in the direction of the shortest wavelength of the medium, in order to ensure that the grid sampling rate is greater than 10PPW (Points Per Wavelength), a grid size smaller than 0.408m should be used for segmentation. Finally, the segmented grid file is exported.

[0036] S3. Import the grid into the PMCHWT algorithm and use the moment method to solve it. Set the parameters of the plane wave electromagnetic excitation, background medium and field receiving point to complete the accurate solution of the surface current and surface magnetic current of the uniaxial anisotropic medium object. Then introduce the field type's dyadic Green's function to achieve efficient and accurate electromagnetic calculations for the electric field strength and RCS at any position in the background.

[0037] In this embodiment, the incident direction of the plane wave is (1,0,0), its polarization direction is (0,0,1), and the receiving field points are set on the XOZ plane to calculate its far-field result distribution. For the uniaxial anisotropic medium sphere, its center position is set at (0,0,0)m and its radius is set to 3m. The model settings in HFSS and PMCHWT algorithms are the same; the difference is that since two algorithms are used to calculate the model respectively, they are based on different grids. For HFSS, it is based on the finite element method and uses a tetrahedral grid, while for the moment method solution process of the surface integral equation, it uses a triangular grid. In particular, for HFSS, it is necessary to use a perfectly matched layer to perform spatial truncation of the three-dimensional region of calculation and obtain the far-field result through far-field equivalence. For the PMCHWT algorithm, due to the introduction of the Green's function of the uniaxial anisotropic medium, the radiation boundary conditions of the calculation region are automatically satisfied. It does not require special treatment of the calculation boundary, which has a natural advantage in solving RCS problems. After solving the PMCHWT equation using the moment method, the equivalent current and equivalent magnetic current on the outer surface of the uniaxial anisotropic medium can be obtained. The field-type Green's function is then used to calculate the electric field at any position in the far field and solve the RCS.

[0038] Furthermore, in the use of HFSS and SDIE to complete the Figure 2The RCS results of the uniaxial anisotropic medium model shown in Figure 4 As shown in the figure, a comparison of the RCS values of the two stations in the dB domain is presented. The results show a close agreement between the two methods. Further quantification of the error in the calculation results shows that for the electric field calculation, the relative error is 0.13%, validating the accuracy of the proposed algorithm. A further comparison of the computational resources consumed and efficiency is shown in Table 1. The equations solved by HFSS have hundreds of times the degrees of freedom of the SIE method, and correspondingly, its memory consumption is ten times that of the SIE method. Furthermore, in terms of CPU time consumed, the SIE algorithm only takes about a quarter of the time of HFSS to complete the solution. The SIE algorithm has significant advantages over HFSS in solving RCS problems for uniaxial anisotropic dielectric objects, using less computer memory and shorter CPU computation time, while achieving results of comparable accuracy to HFSS. This algorithm has great application value in multiphysics simulation, antenna design, EDA circuit design, military target detection, and other applications.

[0039] Software / Method Degrees of freedom (unknown quantity) CPU time Memory consumption HFSS 131822 13s 1.36GB SIE 1134 3.3s 94.6MB

[0040] Table 1

[0041] The present invention proposes a pre-processing method for solving the RCS of uniaxial anisotropic media based on the method of moments. The uniaxial anisotropic medium scatterer to be simulated and its model are built in COMSOL. The wavelength of the electromagnetic wave in the uniaxial anisotropic medium is calculated according to the optical axis direction, dielectric constant and permeability parameters in the uniaxial anisotropic medium, and the size of the grid is determined according to the wavelength.

[0042] Secondly, the present invention introduces the method of moments algorithm into the far-field RCS solution of uniaxial anisotropic medium objects. Compared with the mature electromagnetic field simulation software HFSS based on the finite element algorithm, the algorithm proposed by the present invention has extremely obvious advantages in computing efficiency and computing resource consumption while obtaining results similar to HFSS. This shows that the present invention can greatly reduce the early pre-research time cost in multi-physics field simulation calculations and EDA, shorten the R&D cycle, and greatly help to improve the scientific research and R&D efficiency of the industry.

[0043] The above description is merely an illustration of the preferred embodiments of the present invention and the technical principles employed. Those skilled in the art should understand that the scope of the invention is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in the present invention.

Claims

1. A method for solving RCS of uniaxial anisotropic media based on the method of moments, characterized in that: The method comprises the following steps: Model the scatterer to be simulated in COMSOL; Mesh the surface of the scatterer to determine the wavelength of the electromagnetic wave of the uniaxial anisotropic medium, and determine the size of the mesh according to the wavelength; The mesh is imported into the moment method for solution. The PMCHWT algorithm constructs integral equations based on the internal and external structure of the object, and uses the moment method to solve the surface current and magnetic current of the uniaxial anisotropic medium. In the algorithm post-processing, the position point information of the RCS is calculated, and the corresponding scattering field size is calculated through the Green's function to finally obtain the RCS.

2. The RCS solution method for uniaxial anisotropic media based on the method of moments according to claim 1 is characterized in that: First, model and mesh the model in COMSOL software and export the information.

3. The RCS solution method for uniaxial anisotropic media based on the method of moments according to claim 2, characterized in that: When modeling in COMSOL, the vector direction of the scatterer's optical axis is determined by the coordinate system used when modeling the object.

4. The RCS solution method for uniaxial anisotropic media based on the method of moments according to claim 3 is characterized in that: After completing the modeling in COMSOL, the wavelength of the electromagnetic wave in the corresponding area is determined based on the medium parameters inside and outside the scatterer. Based on the smaller wavelength value between the two areas, the size of the face triangle mesh is determined by ensuring the mesh sampling rate, and the mesh is generated using the COMSOL mesher.

5. The RCS solution method for uniaxial anisotropic media based on the method of moments according to claim 4 is characterized in that: The same set of triangle meshes is used for both the interior and exterior of the scattering.

6. The RCS solution method for uniaxial anisotropic media based on the method of moments according to claim 5, characterized in that: The triangular mesh includes node numbers of the triangular mesh and three-dimensional coordinate information corresponding to the numbers.

7. According to the RCS solution method of uniaxial anisotropic medium based on the moment method in claim 6, the triangular mesh is imported into the PMCHWT algorithm. After the model medium parameter information is set, the algorithm reads the corresponding model information to perform electromagnetic simulation and solve The relevant settings include: Set the polarization direction and propagation direction of the excitation plane wave, the electromagnetic parameter information of the scatterer and background medium, the simulation frequency, and the location information of the RCS field receiving point.

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