Method for rapidly calculating green function of uniaxial anisotropic layered medium based on DCIM and electromagnetic simulation system

Abstract

The invention provides a DCIM-based method for rapidly calculating a green function of a uniaxial anisotropic layered medium and an electromagnetic simulation system. The method comprises the following steps: modeling a uniaxial anisotropic layered medium to be simulated; determining a uniaxial anisotropic dielectric material of each layer, and assigning transverse parameters and longitudinal parameters; determining longitudinal coordinates of field point and source point distribution required to be solved, fitting a uniaxial anisotropic medium Green function spectral domain expression under the field source distribution by using a DCIM method, and solving an analytical expression in a spatial domain by using Somerfeld identical equation properties; solving the size of the electromagnetic field on the plane according to the fitted analytical expression; compared with a direct numerical integration method or a finite element method numerical solution using the Green function, the method has the advantages that the airspace analytical expression corresponding to the field source distributed on the plane is directly fitted, so that the solution of the airspace Green function is greatly accelerated, and the calculation efficiency and the calculation precision are both good in an actual example.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic field modeling and simulation, and particularly relates to a method for fast calculation of a Green function of a uniaxial anisotropic layered medium based on DCIM and an electromagnetic simulation system. BACKGROUND

[0002] With the improvement of the integration of integrated circuits and the development of microwave devices towards high frequency, uniaxial anisotropic layered media are widely used in printed circuit boards (PCB), high-density interconnection (HDI), metamaterial devices and other scenarios. The key feature of such media is that there is a significant difference in electromagnetic parameters (permittivity, permeability, conductivity) between the transverse (x, y direction) and the longitudinal (z direction), which can realize signal integrity optimization, interference suppression and other functions by directional regulation of electromagnetic wave propagation characteristics.

[0003] In a uniaxial anisotropic layered medium, the key to solving the electromagnetic field is the calculation of the Green function. The traditional methods mainly include: 1. Direct numerical integration method: the Green function is obtained by numerically solving Sommerfeld integral, but the integral converges slowly and the calculation is time-consuming, especially when multiple field points are solved, the efficiency is extremely low; 2. Finite element method (such as COMSOL): the entire calculation domain (including the background medium) needs to be meshed, which has large degrees of freedom and high memory consumption, and is difficult to adapt to large-scale problems; 3. Method of moments: although it does not need to mesh the background medium, in the uniaxial anisotropic scene, the spectral domain expression of the Green function is complex, still relies on numerical integration, and the efficiency is improved limitedly.

[0004] In the prior art, the discrete complex image method (DCIM) has been used for fast calculation of the Green function of the isotropic layered medium, but it does not consider the difference in longitudinal wave number between TE and TM waves in the uniaxial anisotropic medium, and cannot be directly applied.

[0005] Therefore, for the uniaxial anisotropic layered medium, there is an urgent need for a high-efficiency and high-precision Green function calculation method. SUMMARY

[0006] The application aims to solve the problems of low calculation efficiency, insufficient precision and large resource consumption of the Green function in the uniaxial anisotropic layered medium, and provides a method for fast calculation of the Green function of the uniaxial anisotropic layered medium based on DCIM and an electromagnetic simulation system, which realizes fast solving of the electromagnetic field.

[0007] In a first aspect, the application provides a method for fast calculation of the Green function of the uniaxial anisotropic layered medium based on DCIM, which comprises the following steps: S1: modeling a uniaxial anisotropic layered medium to be simulated, including the thickness and position of each layer of medium, and further determining the transverse parameter information and the longitudinal parameter information of the uniaxial anisotropic medium material; S2: determining the longitudinal coordinates of the field point and the source point distribution required to be solved, and deriving a spectral domain expression of the uniaxial anisotropic medium Green function, which needs to reflect the longitudinal wavenumber difference between TE wave and TM wave; S3: fitting the spectral domain expression using the DCIM method, and performing spectral domain fitting by the generalized function bundle GPOF method with equivalent longitudinal wavenumber as the independent variable to obtain a spectral domain fitting result; S4: converting the spectral domain fitting result into an analytical expression in the spatial domain by using the properties of Sommerfeld's constant equation; and S5: solving the electromagnetic field size on the plane according to the analytical expression in the spatial domain combined with the position information of the field point and the source point.

[0008] The method does not require mesh partitioning, greatly improves the efficiency of electromagnetic field solving in a uniaxial anisotropic layered medium, has high precision, and significantly reduces the consumption of computing resources.

[0009] Preferably, in S2, the longitudinal wavenumber of the TE wave and the longitudinal wavenumber of the TM wave are calculated by the transverse and longitudinal electromagnetic parameters of the uniaxial anisotropic medium, wherein the transverse parameters correspond to the x and y directions, and the longitudinal parameters correspond to the z direction.

[0010] By distinguishing the transverse (x, y direction) and longitudinal (z direction) electromagnetic parameters, the longitudinal wavenumbers of TE wave and TM wave are accurately calculated, the wavenumber coupling problem in the uniaxial anisotropic medium is solved, accurate basic data are provided for subsequent spectral domain fitting, and the accuracy of the Green function calculation is further guaranteed.

[0011] Preferably, in S3, the equivalent longitudinal wavenumber is the longitudinal wavenumber of the TE wave or the longitudinal wavenumber of the TM wave, and the spectral domain Green function is decomposed into the cumulative form of multiple exponential terms when fitting by the generalized function bundle GPOF method, and the fitting error is not more than 1%.

[0012] This preferred scheme obtains the equivalent longitudinal wavenumber by the longitudinal wavenumber of the TE wave or the TM wave, decomposes the spectral domain Green function into the cumulative form of exponential terms by the GPOF method, and controls the fitting error within 1%, which not only adapts to the wavenumber characteristics of the uniaxial anisotropic medium, but also guarantees the spectral domain fitting accuracy, laying a foundation for the efficiency and accuracy of subsequent spatial domain conversion.

[0013] Preferably, in S4, the conversion process of the Sommerfeld constant equation converts the transverse wavenumber integral in the spectral domain into a function form based on the transverse distance between the field point and the source point in the spatial domain.

[0014] The preferred scheme converts the integral operation in the spectral domain with transverse wave number as the variable into a function form in the spatial domain only dependent on the transverse distance between the field point and the source point by Sommerfeld identity, avoids the complexity of direct numerical integration, significantly improves the calculation efficiency, and retains the analytical solution characteristics to guarantee the accuracy, and adapts to the spatial field solving demand of uniaxial anisotropic medium.

[0015] Preferably, the solving of the electromagnetic field size in S5 includes the components of the electric field and the magnetic field in x, y, and z directions, and the polarization direction information of the excitation source needs to be input during calculation.

[0016] The preferred scheme clearly defines that the solving of the electromagnetic field covers the electric field and the magnetic field components in x, y, and z directions, and the polarization direction information of the excitation source needs to be input, which not only guarantees the completeness of the field distribution description, but also adapts to different excitation scenarios through the polarization direction parameter, improves the applicability of the method to complex electromagnetic problems, and ensures that the solving result is consistent with the actual excitation characteristics.

[0017] Preferably, the uniaxial anisotropic layered medium in S1 includes at least two layers of medium, and the transverse dielectric constant, the transverse magnetic permeability, the longitudinal dielectric constant, and the longitudinal magnetic permeability of each layer of medium are different.

[0018] The preferred scheme clearly defines that the uniaxial anisotropic layered medium needs to include at least two layers, and the dielectric constant and the magnetic permeability in the transverse and longitudinal directions of each layer are different, accurately defines the structural characteristics of the applicable object, distinguishes from the isotropic medium, and excludes the simple scenario of single-layer structure, ensures that the method is specifically used to solve the Green function calculation problem of the multilayer uniaxial anisotropic medium, and strengthens the specificity and applicability of the technical scheme.

[0019] Preferably, it further includes a verification step of the calculation result: S6: comparing the solved electromagnetic field size with the result of the direct numerical integration method or the finite element method to ensure that the relative error is not more than 3%. The method of the present application can greatly improve the efficiency while maintaining high accuracy, providing reliability guarantee for engineering application.

[0020] In the second aspect, the embodiments of the present application provide a computer readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the method described in any of the implementations of the first aspect.

[0021] In the third aspect, the embodiments of the present application provide an electromagnetic simulation system based on the method of any one of the first aspect, which includes: The layered model construction module is configured to model a single-axis anisotropic layered medium to be simulated, including thickness and position of each layer of medium, and further determine transverse parameter information and longitudinal parameter information of the single-axis anisotropic medium material; The Green function processing module is configured to determine longitudinal coordinates of a field point and a source point distribution required to be solved, derive a spectral domain expression of a Green function of the single-axis anisotropic medium, the spectral domain expression needs to embody a longitudinal wavenumber difference between TE waves and TM waves, use a DCIM method to fit the spectral domain expression, perform spectral domain fitting by using a generalized function bundle GPOF method with an equivalent longitudinal wavenumber as an independent variable, and obtain a spectral domain fitting result; and convert the spectral domain fitting result into an analytical expression in a spatial domain by using a property of a Sommerfeld constant equation. The electromagnetic field calculation module is configured to solve electromagnetic field sizes on a plane according to the analytical expression in the spatial domain and in combination with position information of the field point and the source point.

[0022] Preferably, the system is applicable to PCB board simulation in integrated circuits, microwave device design, electromagnetic field analysis of photonic devices, and geophysical exploration scenarios.

[0023] The modules of the system cooperate, maintain high precision of an analytical solution, reduce resource consumption through a fast calculation method, and are applicable to PCB design, microwave device simulation and other scenarios.

[0024] Compared with the prior art, the beneficial results of the present application are as follows: Compared with a traditional direct numerical integration method, the DCIM method actually gives an analytical corresponding relationship of a planar structure, for any field source distribution in the planar structure, the structure can be obtained through analytical calculation. Compared with a finite element method, the DCIM method does not need to perform mesh division on a problem model and involves a large number of degrees of freedom solving processes. For the DCIM method, it is usually used for solving layered isotropic medium, but is not applied to solving layered single-axis anisotropic medium problems. The present application extends the DCIM method to a layered single-axis anisotropic medium model, and realizes fast calculation of an electromagnetic field. BRIEF DESCRIPTION OF DRAWINGS

[0025] The accompanying drawings are included to provide a further understanding of embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate the embodiments and, together with the description, serve to explain the principles of the present application. Other embodiments and many of the intended advantages of the present application will be readily appreciated as the same becomes better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding similar parts.

[0026] Figure 1This is a flowchart illustrating the method for rapid calculation of the Green's function of a uniaxial anisotropic layered medium based on DCIM, as described in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of the simulation structure of Embodiment 1 of the present invention; Figure 3 This is a schematic diagram illustrating the determination of the electromagnetic field on the receiving plane in Embodiment 1 of the present invention; Figure 4 Embodiment 1 of the present invention is based on Figure 3 The electric field results obtained from the model are illustrated, and compared with the results of the traditional Green's function direct numerical integration method and the simulation results of the finite element method-based simulation software COMSOL. Figure 1 ; Figure 5 Embodiment 1 of the present invention is based on Figure 3 The magnetic field results obtained from the model are illustrated and compared with those obtained by the traditional Green's function direct numerical integration method and the simulation results of the finite element method-based simulation software COMSOL. Figure 2 ; Figure 6 This is a schematic diagram of the architecture of the electromagnetic simulation system in Embodiment 2 of the present invention. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0028] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0029] With the rapid development of integrated circuit technology, various circuit structures and materials are widely used in circuit design and manufacturing, including uniaxial anisotropic dielectric materials. One of the core values ​​of layered uniaxial anisotropic structures in circuit design lies in their ability to directionally control key physical parameters of materials, such as conductivity and dielectric constant, through spatial dimension, thereby significantly improving signal integrity and suppressing interference. This structure is particularly crucial in modern multilayer printed circuit board (PCB) and high-density interconnect (HDI) designs.

[0030] In addition, the layered uniaxial anisotropic structure exhibits its extraordinary ability in actively manipulating the electromagnetic wave propagation behavior, making it an important cornerstone for microwave engineering, terahertz technology and photonic device design. This ability is usually achieved by periodically constructing metal-dielectric alternating thin film stacks, etching structures (such as slot lines) to form frequency selective surfaces (FSS), or artificial electromagnetic super materials.

[0031] A typical application example is a single-screen cross-slot anisotropic frequency selective surface structure, which can ingeniously convert linearly polarized waves (such as commonly used horizontal or vertical polarization in satellite communication) into very pure circularly polarized waves (left-handed or right-handed) when incident, and has a significant bandwidth advantage. Experimental results show that the 3 dB axial ratio bandwidth can be increased by up to 24 times compared to traditional designs, providing high-performance anti-interference filtering and polarization diversity functions for satellite communication links.

[0032] Furthermore, through the coordinated design and gradient change of the multi-layer film orientation, high-efficiency polarization conversion can be achieved, such as converting nearly 100% of the incident TE wave energy into TM wave, or constructing a broadband polarization rotator. These characteristics provide new physical basis and engineering implementation approach for designing new type of reconfigurable antennas (changing antenna radiation pattern and polarization by dynamically controlling the bias state of anisotropic units), high-efficiency polarization separator, low-profile electromagnetic wave absorber, and even exploring electromagnetic stealth technology, significantly improving the spectrum utilization and anti-interference capability of modern wireless communication systems.

[0033] Therefore, the embodiment of the present application proposes a method for fast calculation of uniaxial anisotropic layered medium Green's function based on DCIM and an electromagnetic simulation system, which can accurately and quickly solve the Green's function and electromagnetic field of the planar structure in the uniaxial anisotropic layered medium. Compared with the traditional direct numerical integration method and the multi-physical field commercial software COMSOL based on the finite element method, the present application has obvious advantages in calculation efficiency and memory resource consumption, and has broad application prospects.

[0034] Embodiment 1: In a first aspect, the embodiment of the present application discloses a method for fast calculation of uniaxial anisotropic layered medium Green's function based on DCIM, as shown in the method comprises the following steps: Figure 1 S1: modeling the uniaxial anisotropic layered medium to be simulated, including the thickness and position of each layer of medium, and further determining the transverse parameter information and longitudinal parameter information of the uniaxial anisotropic medium material; Specifically, the uniaxial anisotropic layered medium includes at least two layers of medium, and the transverse dielectric constant, transverse magnetic permeability, longitudinal dielectric constant and longitudinal magnetic permeability of each layer of medium are different.

[0035] ​The simulation structure diagram of the present invention is as follows: Figure 2 and 3 As shown in Table 1, taking a four-layer uniaxial anisotropic layered medium as an example, the specific model parameters are as follows: Table 1 Figure 3 Medium parameter table of the corresponding model

[0036] As shown in Table 1 above, in this example, the parameters of each layer of medium are divided into transverse parameters ( and Direction) and longitudinal parameters ( (Direction), usually for directional layered medium, its and The medium parameters of the direction and The directions are different, as shown in the medium tensor matrix in Table 1.

[0037] S2: Determine the longitudinal coordinates of the field point and source point distribution to be solved, and derive the spectral domain expression of the Green's function for the uniaxial anisotropic medium. The spectral domain expression must reflect the longitudinal wavenumber difference between the TE wave and the TM wave. Specifically, in this embodiment, an electric dipole is used as the excitation source, with a position of (0, 0, -2 m) and a polarization direction vector of (1, 1, 1). The operating frequency is f = 30 MHz (corresponding to the free space wavenumber). ).

[0038] Field point distribution: Solve for the electromagnetic field distribution in the z=-3 m plane, with field point coordinates (x, y, -3 m), where x∈[-2 m, 2 m], y∈[-2 m, 2 m], and a total of 64 uniformly distributed field points (interval 0.5 m).

[0039] The longitudinal wavenumbers of TE and TM waves are calculated using the transverse and longitudinal electromagnetic parameters of a uniaxial anisotropic medium, where the transverse parameters correspond to the x and y directions and the longitudinal parameters correspond to the z direction.

[0040] S3: The spectral domain expression is fitted using the DCIM method, and the spectral domain is fitted using the generalized function bundle GPOF method with the equivalent longitudinal wavenumber as the independent variable to obtain the spectral domain fitting result; In one specific embodiment, the longitudinal wavenumbers of the TE wave and TM wave are calculated as follows: TE wave longitudinal wavenumber: ; TM wave longitudinal wavenumber: ; in, respectively the relative transverse permeability, the relative longitudinal permeability of the medium, respectively the relative transverse permittivity, the relative longitudinal permittivity of the medium, is the transverse wave number, is the free space wave, is the angular frequency, respectively the permeability, the permittivity of vacuum).

[0041] Specifically, the equivalent longitudinal wave number is the TE wave longitudinal wave number or the TM wave longitudinal wave number, the spectral domain Green function is decomposed into an accumulation form of multiple exponential terms when the GPOF method is fitted, and the fitting error is not more than 1%. In specific embodiments, the equivalent longitudinal wave number can be flexibly selected in the following forms: Single wave number: directly using the TE wave longitudinal wave number or the TM wave longitudinal wave number ; Vacuum wave number approximation: for weak anisotropic medium, the longitudinal wave number in vacuum can be directly used .

[0042] The equivalent longitudinal wave number is fitted by the GPOF as follows:

[0043] Taking the equivalent longitudinal wave number as the longitudinal wave number in vacuum , the spectral domain Green function is fitted by the GPOF method: Sampling range ; Fitting form: is the fitting coefficient, N is the number of exponential terms of fitting, and N is determined by the GPOF algorithm.

[0044] In this embodiment, N is 15, and the fitting error is less than or equal to 1% to meet the engineering precision requirement.

[0045] In this embodiment, by flexibly selecting the equivalent longitudinal wave number and combining the GPOF fitting, the complex spectral domain Green function is converted into an exponential term accumulation form which is easy to calculate under the premise of ensuring the precision (error less than or equal to 1%), and the solving efficiency of electromagnetic field in uniaxial anisotropic layered medium is significantly improved.

[0046] It should be noted that in actual use, both TE wave and TM wave can be used to equivalently represent the electromagnetic field in uniaxial anisotropic medium , and no distinction is made, for example, the wave number in vacuum ​​It is a simplified strategy to use the vacuum wavenumber as the equivalent longitudinal wavenumber, which is only feasible in the scenario of weak anisotropy and low accuracy requirement. For the simulation of strictly uniaxial anisotropic medium, the TE or TM longitudinal wavenumber containing medium parameters is still used as the equivalent wavenumber to ensure the physical authenticity of the calculation.

[0047] S4: Convert the spectral-domain fitting result into an analytical expression in the spatial domain by using the property of Sommerfeld's identity; The conversion process of Sommerfeld's identity converts the transverse wavenumber integral in the spectral domain into a function form based on the transverse distance between the field point and the source point in the spatial domain.

[0048] In one specific embodiment, the present application completes the conversion from the spectral domain to the spatial domain by Sommerfeld's identity, realizes the accurate mapping of the spectral-domain Green's function fitting result to the analytical form in the spatial domain for two types of Sommerfeld integrals containing 0th and 1st order Bessel functions, and the specific process is as follows: 1) For the Sommerfeld integral containing the 0th order Bessel function: ; 2) For the Sommerfeld integral containing the 1st order Bessel function: ; The present application uses the above two types of Sommerfeld integrals, wherein , convert the spectral-domain fitting result into the spatial domain: The transverse distance ((x, y, z) is the field point coordinate, (x', y', z') is the source point coordinate); For the above two types of Sommerfeld's identity, the spatial-domain Green's function is respectively: 1) For the 0th order Bessel function: ; 2) For the 1st order Bessel function: ; Wherein is the fitting coefficient.

[0049] In the isotropic medium scenario, the present application directly uses the longitudinal wavenumber in vacuum as the equivalent longitudinal wavenumber, and completes the conversion from the spectral domain to the spatial domain by Sommerfeld's identity.

[0050] The steps S2-S4 are core steps of the present application, because in the uniaxial anisotropic medium, the longitudinal wave numbers of the TE wave and TM wave are different Unlike the need to assume an equivalent longitudinal wave number when fitting, in the present application, the assumption is that the spectral-domain analytical expression to be fitted is based on the free-space wave number The defined wave number And all the sampling parameters in the fitting process are given by the relevant definition of the parameter. After completing the spectral-domain sampling, the analytical expression in the form of exponential term accumulation in the spectral domain is obtained by the GPOF (generalized function bundle) method, and the analytical expression in the spatial domain is obtained by the property of the Sommerfeld constant equation.

[0051] Spectral-domain modeling: In view of the difference between the longitudinal wave numbers k z of the TE wave and TM wave in the uniaxial anisotropic medium, the free-space wave number k z,0 is used as the equivalent longitudinal wave number to unify the independent variable of the spectral-domain analytical expression; GPOF fitting: Based on k z,0 100 sample points are collected in the sampling range [0, 200 rad / m], the spectral-domain Green function is decomposed into 15 exponential term accumulation forms, and the fitting error is ≤1%; Spatial-domain conversion: By the above two types of Sommerfeld constant equations, the spectral-domain exponential terms are mapped into spatial-domain analytical terms one by one, and finally the spatial-domain Green function depending on the lateral distance and the spatial distance r is formed, realizing the efficient conversion from “spectral-domain integration” to “spatial-domain summation”.

[0052] Through this process, the present application retains the electromagnetic characteristics of the uniaxial anisotropic medium while avoiding the calculation bottleneck of the traditional numerical integration, and provides an analytical tool for fast solving of the electromagnetic field.

[0053] S5: According to the analytical expression in the spatial domain, the electromagnetic field size on the plane is solved in combination with the position information of the field point and the source point.

[0054] The solving of the electromagnetic field size includes the components of the electric field and the magnetic field in the x, y, and z directions, and the polarization direction information of the excitation source needs to be input during the calculation. According to the polarization direction of the excitation point source and the calculated field-type Green function, the corresponding electromagnetic field result is obtained, and the related settings include: the layer thickness and layer position information of the layered medium model, the electromagnetic parameter information of the uniaxial anisotropic medium, the simulation frequency, the position information of the electromagnetic excitation source and the field receiving point.

[0055] In one specific embodiment, field component calculation: according to the spatial-domain Green function, the polarization direction of the electric dipole excitation is combined to calculate the electric field and magnetic field components, formula as follows: , are electric, magnetic dyadic Green's functions respectively, is current density.

[0056] Result output: output 64 field point electromagnetic field component values, in the form of a table or three-dimensional distribution graph (such as electric field E x real part, imaginary part).

[0057] As preferred, it also includes a verification step of the calculation result: S6: compare the electromagnetic field size obtained by solving with the result of direct numerical integration method or finite element method, ensure that the relative error is not more than 3%.

[0058] Accuracy verification: compare the calculation result of the embodiment method of the application with the direct numerical integration method (solve Sommerfeld integral), the relative error of each component of the electric field is less than or equal to 0.19%, the relative error of each component of the magnetic field is less than or equal to 0.11%, which meets the requirement of error less than or equal to 3%.

[0059] Efficiency verification: the embodiment method of the application takes 0.021 s to solve 64 field points, and the memory occupation is 69.3 MB; the traditional finite element method (COMSOL) takes 879.59 s to solve the same problem, and the memory occupation is 206.04 GB, the efficiency is improved by about 41885 times, and the memory consumption is reduced by about 3045 times.

[0060] Specifically, since the fitted space Green's function is essentially a function relationship between the transverse distance between the excitation source and the field point, it can represent the Green's function on the same horizontal plane. The fitted Green's function actually gives an analytical form for the plane distribution of the field source relationship, realizing the fast solving of electromagnetic field.

[0061] In this embodiment, the polarization direction of the electric dipole source is (1, 1, 1), which is placed at the position (0, 0, -2) m, and 64 receiving points are uniformly placed on the plane (X, Y, -3) m, where m. In the COMSOL model, the same model needs to be modeled in three dimensions. Since COMSOL uses finite element method for simulation, perfect matched layer (PML) needs to be applied to the model to simulate the transversely infinite layered medium model, and the medium parameters of PML are also set to uniaxial anisotropic medium material, and consistent with the medium parameters of the medium layer. In this embodiment, the thickness of PML is set to 5 m. After completing the parameter modeling of each layer, the entire layered medium model is divided using tetrahedral mesh for solving calculation.

[0062] Further, using the DCIM method proposed in the present application and the direct numerical integration method for Sommerfeld integral, the solution for the uniaxial anisotropic medium model shown in Figure 3 The electric field and magnetic field calculation results are shown in Figure 4 and Figure 5 The results of the real and imaginary parts of the electric field and magnetic field in three directions are given. From the results, the calculation results of the three are very consistent. Further, the calculation result error is quantified. Taking the results given by the direct numerical solution as a benchmark, for the calculation result of the electric field, the relative error of COMSOL is 2.29%, while the relative error of the field strength result obtained by the fast calculation method of the planar structure Green function in the uniaxial anisotropic layered medium based on the DCIM method proposed in the present application is 0.19%. For the calculation result of the magnetic field, the relative error of COMSOL is 2.15%, while the relative error of the magnetic field result calculated by the method proposed in the present application is 0.11%, which verifies the calculation accuracy of the algorithm proposed in the present application.

[0063] Further comparison shows that the consumed calculation resources and calculation efficiency of the two are shown in Table 2 below. Since the direct numerical integration method and the DCIM method are essentially based on the Green function method to calculate the electromagnetic field, they do not need grid discretization, so the two do not produce grid degrees of freedom. For the COMSOL software, it is based on the finite element method for solving, and the solving matrix degree of freedom in the whole process is 29479332. Corresponding to the large-scale degree of freedom solving process of COMSOL, it consumed 879.59 s of time and 206.04 GB of memory to solve the problem.

[0064] For the Green function method, the direct numerical solution consumed 11.92 s of CPU time and 108.7 MB of memory to solve the problem. The DCIM method consumed 0.021 s of CPU time and 69.3 MB of memory to solve the problem. From the method proposed in the present application, the direct numerical integration method consumed nearly 568 times of time to complete the solution. For the mature finite element commercial simulation software COMSOL, it consumed nearly 41885 times of time and 3045 times of memory consumption to complete the solution.

[0065] Table 2 Comparison of calculation resources and calculation efficiency

[0066] From the results, the method has great advantages in solving the electromagnetic field of the planar structure of the layered uniaxial anisotropic medium in time and memory consumption, and the same accuracy can be obtained with less calculation time and computer memory.

[0067] And the planar structure and the layered uniaxial anisotropic medium material are widely used in the structure design of modern integrated circuits and PCBs, and the algorithm can quickly calculate the electric field and magnetic field on the patch structure, which has great application value in the application fields such as multi-physical field simulation, military target detection, antenna design and EDA circuit design.

[0068] The application provides a fast calculation method of a planar structure Green function in a uniaxial anisotropic layered medium based on DCIM, models the uniaxial anisotropic layered medium to be simulated, includes the thickness of each layer, the position of each layer and the uniaxial anisotropic medium material of each layer, assigns values to the transverse parameters and the longitudinal parameters, then determines the longitudinal coordinates of the field points and the source point distribution required to be solved, fits the spectral domain expression of the uniaxial anisotropic medium Green function under the source distribution by using the DCIM method, and completes the spectral domain fitting of the electromagnetic field Green function.

[0069] In addition, it should be noted that in Figure 2 , Figure 3 and Figure 4 , the definitions of the parameters are as follows: : represents different layer numbers, from the uppermost layer (the number is N) to the lowermost layer (the number is 1), and is used to identify each medium layer.

[0070] : represents the dielectric constant tensor of the nth layer, represents the magnetic permeability tensor of the Nth layer. In actual application, if the medium is isotropic, the dielectric constant and the magnetic permeability can be simplified as scalars.

[0071] : represents the position coordinate of the interface between the mth layer and the m+1th layer in the z-axis direction. For example, is the interface position between layer 1 and layer 2, is the interface position between layer m-1 and layer m.

[0072] f = 30 MHz: represents that the frequency of the electromagnetic wave is 30 MHz.

[0073] Source: the red dot represents the source point of the electromagnetic wave, and the coordinate is (0, 0, -2) m, which means that the source point is located at x=0, y=0, z=-2 m.

[0074] Receiver: The blue quadrilateral represents the receiver plane, which is located at Z = -3 m, indicating the receiver's position coordinate in the z-axis direction is -3 m.

[0075] Layer1-Layer4: Represent different media layers, each with its corresponding permittivity and permeability , as well as the position coordinates of the layer interfaces . For example, Layer1 has a permittivity and permeability of , with an upper layer interface position of m.

[0076] Numerical: Numerical solution, in this invention refers to the calculation method of Sommerfeld integral using piecewise spectral domain numerical integration.

[0077] DCIM: Discrete Complex Image Method, a fast method for calculating layered media Green's function.

[0078] COMSOL: COMSOL Multiphysics software, a multi-physics simulation software used to simulate and analyze various physical phenomena.

[0079] Observation point: Observation point, represents the observation points set at different positions in space, used to measure the components of electromagnetic field.

[0080] real(Ex)[V / m]: Real part of the electric field x component, unit is volt per meter (V / m).

[0081] imag(Ex)[V / m]: Imaginary part of the electric field x component, unit is volt per meter (V / m).

[0082] real(Ey)[V / m]: Real part of the electric field y component, unit is volt per meter (V / m).

[0083] imag(Ey)[V / m]: Imaginary part of the electric field y component, unit is volt per meter (V / m).

[0084] real(Ez)[V / m]: Real part of the electric field z component, unit is volt per meter (V / m).

[0085] imag(Ez)[V / m]: Imaginary part of the electric field z component, unit is volt per meter (V / m).

[0086] real(Hx)[A / m]: Real part of the magnetic field x component, unit is ampere per meter (A / m).

[0087] imag(Hx) [A / m]: Imaginary part of the x-component of the magnetic field in Ampere per meter (A / m).

[0088] real(Hy) [A / m]: Real part of the y-component of the magnetic field in Ampere per meter (A / m).

[0089] imag(Hy) [A / m]: Imaginary part of the y-component of the magnetic field in Ampere per meter (A / m).

[0090] real(Hz) [A / m]: Real part of the z-component of the magnetic field in Ampere per meter (A / m).

[0091] imag(Hz) [A / m]: Imaginary part of the z-component of the magnetic field in Ampere per meter (A / m).

[0092] The Green function calculation method of the uniaxial anisotropic medium based on DCIM adopted by the embodiment of the application is essentially an approximate fitting method, and is aimed at solving the electromagnetic field problem of the planar structure of the layered medium. The GPOF method is used to realize the fitting of the spectral domain Green function of the layered medium, and the analytical correspondence relationship between the spatial domain expression and the spectral domain expression is constructed by using the properties of the Sommerfeld identity. Since the fitted one-dimensional function is about the transverse distance between the excitation source and the receiving point, the fast solution of the Green function of the corresponding field source can be realized.

[0093] Further referring to Figure 6 , as an implementation of the method shown in the above figures, the application provides an embodiment of an electromagnetic simulation system, which corresponds to the method embodiment shown in Figure 1 , and the electromagnetic simulation system can be specifically applied to various electronic devices.

[0094] Embodiment 2: In a second aspect, the embodiment of the application further discloses an electromagnetic simulation system, which is realized by using the method according to any one of the first aspect, and the system further comprises a layered model construction module 61, a Green function processing module 62 and an electromagnetic field calculation module 63.

[0095] In a specific embodiment, the layered model construction module 61 is used to model the uniaxial anisotropic layered medium to be simulated, including the thickness and position of each layer of medium, and further determining the transverse parameter information and the longitudinal parameter information of the uniaxial anisotropic medium material. The Green function processing module 62 is configured to determine the longitudinal coordinates of the field points and the source points distribution required to be solved, derive a spectral domain expression of the Green function of the uniaxial anisotropic medium, wherein the spectral domain expression needs to reflect the difference in the longitudinal wavenumber between the TE wave and the TM wave; use the DCIM method to fit the spectral domain expression, perform spectral domain fitting by using the generalized function bundle GPOF method with the equivalent longitudinal wavenumber as the independent variable, and obtain a spectral domain fitting result; and convert the spectral domain fitting result into an analytical expression in the spatial domain by using the property of the Sommerfeld identity. The electromagnetic field calculation module 63 is configured to solve the electromagnetic field size on the plane according to the analytical expression in the spatial domain and in combination with the position information of the field points and the source points.

[0096] Preferably, the system is applicable to PCB board simulation in integrated circuits, microwave device design, electromagnetic field analysis of photonic devices, and geophysical exploration scenarios.

[0097] The simulation of the PCB board in the integrated circuit (such as the analysis of the signal transmission characteristics of the uniaxial anisotropic substrate), the design of the microwave device (such as the optimization of the radiation characteristics of the antenna based on the anisotropic medium), the electromagnetic field solving of the photonic device (such as the mode analysis of the uniaxial anisotropic waveguide), and the electromagnetic field response simulation in the geophysical exploration (such as the inversion of the resource distribution by using the electromagnetic characteristics of the underground layered anisotropic geological structure). The system can precisely adapt to the anisotropic characteristics of the medium in different fields by virtue of the efficient solving capability of the Green function of the uniaxial anisotropic layered medium, and provides high-precision and high-efficiency simulation support for various electromagnetic problem analysis, which significantly widens the application boundary of the technology.

[0098] The functions of the above modules correspond to the methods, and thus will not be described herein.

[0099] The spectral domain approximate fitting result in the uniaxial anisotropic medium is solved by using the property of the Sommerfeld identity, and the analytical expression in the spatial domain corresponding to the spectral domain approximate fitting result is solved. The electric field and the magnetic field on the plane structure are calculated by using the analytical expression in the spatial domain. Compared with the traditional spectral domain Green function direct numerical integration method and the finite element method of the numerical simulation software COMOL, the present application has obvious advantages in the calculation time and the calculation resource consumption, which indicates that the present application can greatly reduce the pre-research time cost in the multi-physical field simulation calculation and the integrated circuit simulation design, shorten the circuit design and development cycle, and greatly help and promote the efficiency of the scientific research and the research and development in the industry.

[0100] In particular, the processes described above with reference to the flowcharts can be implemented as a computer software program in accordance with embodiments of the present disclosure. For example, embodiments of the present disclosure include a computer program product comprising a computer program carried on a computer readable medium, the computer program comprising program code for executing the methods illustrated by the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication section, and / or installed from a detachable medium. When the computer program is executed by a central processing unit (CPU) and a graphics processor (GPU), the above-described functions defined in the methods of the present disclosure are executed.

[0101] It should be noted that the computer readable medium described in the present disclosure can be a computer readable signal medium or a computer readable storage medium or any combination of the two. The computer readable medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor device, device or means, or any combination of the above. More specific examples of the computer readable medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, the computer readable medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution device, device or means. In the present disclosure, the computer readable signal medium can include a data signal carried in a baseband or as a part of a carrier wave, which carries computer readable program code. Such a propagated data signal can take many forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer readable signal medium can also be any computer readable medium other than the computer readable medium that can send, propagate or transmit the program for use by or in conjunction with an instruction execution device, device or means. The program code contained on the computer readable medium can be transmitted by any suitable medium, including but not limited to wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0102] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0103] The flow diagrams and the block diagrams in the drawings are illustrations of architectures, functionalities, and operations of possible implementations of apparatuses, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flow diagrams or block diagrams can represent a module, a procedure, or a part of code, which comprises one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently or in the reverse order, depending on the functionality involved. It is also noted that each block of the block diagrams and / or flow diagrams and combinations of blocks in the block diagrams and / or flow diagrams can be implemented by dedicated hardware-based apparatuses or by a combination of dedicated hardware-based apparatuses and computer instructions.

[0104] The modules described in the embodiments of the present application can be implemented by software, or by hardware. The described modules can also be arranged in a processor.

[0105] As another aspect, the present application also provides a computer readable medium, which can be included in the electronic device described in the above embodiments, or can exist separately without being assembled into the electronic device. The above computer readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods and steps described in the first aspect of the embodiments of the present application.

[0106] The above description is only the preferred embodiment of the present application and the explanation of the applied technical principles. It should be understood by those skilled in the art that the inventive scope of the present application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or their equivalent features without departing from the above inventive concept. For example, the technical solutions formed by the mutual replacement of the above features and the technical features disclosed in the present application (but not limited to) with similar functions.

Claims

1. A method for fast computation of Green's function of DCIM based uniaxial anisotropic layered media, characterized in that, The method comprises the following steps: S1: modeling the uniaxial anisotropic layered medium to be simulated, including the thickness and position of each layer of medium, and further determining the transverse parameter information and longitudinal parameter information of the uniaxial anisotropic medium material; S2: determining the longitudinal coordinates of the field point and source point distribution to be solved, and deriving the spectral domain expression of the uniaxial anisotropic medium Green function, which needs to reflect the longitudinal wavenumber difference between TE wave and TM wave; S3: fitting the spectral domain expression using the DCIM method, and performing spectral domain fitting by the generalized function bundle GPOF method with equivalent longitudinal wavenumber as the independent variable to obtain the spectral domain fitting result; S4: converting the spectral domain fitting result into an analytical expression in the spatial domain by using the properties of Sommerfeld's constant equation; and S5: solving the electromagnetic field size on the plane according to the analytical expression in the spatial domain combined with the position information of the field point and source point.

2. The method of fast computation of the Green's function for DCIM based uniaxial anisotropic layered media according to claim 1, wherein, In S2, the longitudinal wavenumber of the TE wave and the longitudinal wavenumber of the TM wave are calculated by the transverse and longitudinal electromagnetic parameters of the uniaxial anisotropic medium, wherein the transverse parameters correspond to the x and y directions, and the longitudinal parameters correspond to the z direction.

3. The method of fast computation of the Green's function for DCIM based uniaxial anisotropic layered media according to claim 1, wherein, In S3, the equivalent longitudinal wavenumber is the longitudinal wavenumber of the TE wave or the longitudinal wavenumber of the TM wave, and the generalized function bundle GPOF method decomposes the spectral domain Green function into the cumulative form of multiple exponential terms, and the fitting error is not more than 1%.

4. The method of fast calculation of the Green's function for DCIM based uniaxial anisotropic layered media according to claim 1, wherein, In S4, the conversion process of the Sommerfeld constant equation converts the transverse wavenumber integration in the spectral domain into a function form based on the transverse distance between the field point and the source point in the spatial domain.

5. The method of fast computation of the Green's function for DCIM based uniaxial anisotropic layered media of claim 1, wherein, In S5, the solving of the electromagnetic field size includes the components of the electric field and the magnetic field in the x, y, and z directions, and the polarization direction information of the excitation source needs to be input during calculation.

6. The method of fast computation of the Green's function for DCIM based uniaxial anisotropic layered media of claim 1, wherein, In S1, the uniaxial anisotropic layered medium comprises at least two layers of medium, and the transverse dielectric constant, transverse magnetic permeability, longitudinal dielectric constant, and longitudinal magnetic permeability of each layer of medium are different.

7. The method of fast computation of Green's function for DCIM based uniaxial anisotropic layered media of claim 1, wherein, It also includes a verification step for the calculation result: S6: comparing the solved electromagnetic field size with the results of the direct numerical integration method or the finite element method to ensure that the relative error is not more than 3%.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to realize the method as claimed in any one of claims 1 to 7.

9. An electromagnetic simulation system based on the method of any one of claims 1-7, characterized by It comprises: a layered model construction module for modeling the uniaxial anisotropic layered medium to be simulated, including the thickness and position of each layer of medium, and further determining the transverse parameter information and longitudinal parameter information of the uniaxial anisotropic medium material; a Green function processing module for determining the longitudinal coordinates of the field point and source point distribution to be solved, deriving the spectral domain expression of the uniaxial anisotropic medium Green function, which needs to reflect the longitudinal wavenumber difference between TE wave and TM wave; fitting the spectral domain expression using the DCIM method, and performing spectral domain fitting by the generalized function bundle GPOF method with equivalent longitudinal wavenumber as the independent variable to obtain the spectral domain fitting result; and converting the spectral domain fitting result into an analytical expression in the spatial domain by using the properties of Sommerfeld's constant equation; An electromagnetic field calculation module is configured to solve the electromagnetic field size on the plane according to the analytical expression in the space domain, in combination with the position information of the field point and the source point.

10. The electromagnetic simulation system of claim 9, wherein, The system is suitable for PCB board simulation in integrated circuits, microwave device design, electromagnetic field analysis of photonic devices, and geophysical exploration scenarios.

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