Electromagnetic wave compact time domain fine integration method based on artificial anisotropy parameter

Abstract

The application provides an electromagnetic wave compact time domain fine integration method based on an artificial anisotropy parameter, which comprises the following steps: obtaining a waveguide with a long straight constant structure, and performing mesh division through a rectangular mesh; introducing an artificial anisotropy parameter to obtain a control equation of an electromagnetic wave in a rectangular mesh area; obtaining a numerical dispersion equation through Fourier analysis to obtain a numerical dispersion equation of the electromagnetic wave in the rectangular mesh area; defining a normalized numerical phase velocity value, and preliminarily selecting the artificial anisotropy parameter to obtain a preliminary value of the artificial anisotropy parameter; calculating an optimal value of the artificial anisotropy parameter according to the preliminary value and the numerical dispersion equation of the electromagnetic wave in the rectangular mesh area; and obtaining an electromagnetic field quantity iterative solving formula according to the optimal value and the control equation to perform iterative solving, so as to obtain the electromagnetic field quantity of the electromagnetic wave in the rectangular mesh area. The application can reduce the number of mesh divisions and the memory requirement, and can improve the calculation efficiency and the calculation precision.

Description

Technical Field

[0001] This application relates to the field of computational electromagnetics, and in particular to a method and apparatus for tight time-domain fine integration of electromagnetic waves based on artificial anisotropic parameters. Background Technology

[0002] The compact scheme time-domain fine integration method for electromagnetic waves is mainly applied to electromagnetic field problems with long, straight, invariant structures. By introducing a wave propagation factor to reflect the propagation characteristics of the long, straight, invariant direction, it can reduce the dimensionality of three-dimensional problems to two-dimensional problems, thereby reducing the number of meshes. Furthermore, in practical engineering simulations, the compact scheme time-domain fine integration method often encounters simulation requirements with elongated structures, such as non-uniform gratings, lossy transmission lines, and photonic crystal fibers. For these problems, using a traditional square mesh usually results in a large number of meshes. While a suitable rectangular mesh can be used for spatial discretization, the use of a rectangular mesh inevitably affects the numerical dispersion error of the compact scheme time-domain fine integration method. This impact manifests in two main ways: firstly, it significantly increases the numerical dispersion error; secondly, it makes the numerical dispersion curve asymmetrical, meaning the propagation speed of the electromagnetic wave along the x-axis and y-axis becomes different, exhibiting significant numerical anisotropy. These effects can lead to unacceptable deviations in the calculation results. Summary of the Invention

[0003] This application aims to at least partially address one of the technical problems in the related art.

[0004] Therefore, the first objective of this application is to propose a compact time-domain fine integration method for electromagnetic waves based on artificial anisotropic parameters. This method solves the technical problems of existing methods that use square spatial grids to solve electromagnetic field problems with narrow structures, resulting in a large number of grid subdivisions, high memory requirements, and low computational efficiency. Furthermore, it addresses the numerical dispersion problem that exists when existing methods use rectangular grids to solve electromagnetic field problems with narrow structures. By introducing artificial anisotropic parameters to adjust the numerical dispersion error, the number of grid subdivisions can be significantly reduced, memory requirements can be reduced, and computational efficiency can be improved. It can also effectively correct the anisotropic numerical dispersion error introduced by rectangular grids, ensuring computational accuracy.

[0005] The second objective of this application is to propose a compact time-domain fine integration device for electromagnetic waves based on artificial anisotropic parameters.

[0006] The third objective of this application is to propose a computer device.

[0007] The fourth objective of this application is to provide a non-transitory computer-readable storage medium.

[0008] To achieve the above objectives, the first aspect of this application proposes a compact time-domain fine integration method for electromagnetic waves based on artificial anisotropic parameters, comprising: obtaining a waveguide with a long, straight, invariant structure, and meshing the cross-section of the waveguide using a rectangular grid, wherein the electromagnetic waves within the rectangular grid region satisfy the curl equation of Maxwell's equations; transforming the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the governing equation of the electromagnetic waves within the rectangular grid region; obtaining the numerical dispersion equation through Fourier analysis based on the governing equation, and transforming the numerical dispersion equation according to the shape and parameter information of the rectangular grid to obtain the numerical dispersion equation of the electromagnetic waves within the rectangular grid region. The process involves defining a normalized numerical phase velocity value and, based on the numerical dispersion equation of electromagnetic waves within a rectangular grid region, initially selecting artificial anisotropic parameters to obtain their initial values. Based on these initial values, the optimal normalized numerical phase velocity value is calculated. Then, based on the optimal value and the numerical dispersion equation of electromagnetic waves within the rectangular grid region, the preferred values ​​of the artificial anisotropic parameters are calculated. Finally, based on the preferred values ​​and the governing equation of electromagnetic waves within the rectangular grid region, an iterative solution formula for the electromagnetic field quantity is obtained. This formula is then used to iteratively solve the problem and obtain the electromagnetic field quantity of electromagnetic waves within the rectangular grid region.

[0009] Optionally, in one embodiment of this application, the curl equation of Maxwell's equations is transformed by introducing artificial anisotropy parameters to obtain the governing equations for electromagnetic waves within a rectangular grid region, including:

[0010] The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region.

[0011] The governing equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0012]

[0013]

[0014] Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε zε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

[0015] Optionally, in one embodiment of this application, the numerical dispersion equation is expressed as:

[0016]

[0017]

[0018]

[0019]

[0020] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, and ε x ε y and ε z are the relative permittivity in the x, y, and z directions, respectively. and These are the numerical wave propagation constants in the x and y directions, respectively;

[0021] The numerical dispersion equation for electromagnetic waves within a rectangular grid region is expressed as:

[0022]

[0023]

[0024] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, α is the wave propagation angle, A is the normalized numerical phase velocity, R is the spatial grid resolution, Z is the shape information of the rectangular grid, and β... z Let ε be the wave propagation constant in the z-direction. x ε y and ε z denoted as , and respectively as the relative permittivity in the x, y, and z directions.

[0025] Optionally, in one embodiment of this application, a normalized numerical phase velocity value is defined, and artificial anisotropy parameters are initially selected based on the numerical dispersion equation of electromagnetic waves within a rectangular grid region to obtain initial values ​​for the artificial anisotropy parameters, including:

[0026] Define the normalized numerical phase velocity value as 1;

[0027] By assigning wave propagation angles of 0 degrees and 90 degrees respectively, the numerical dispersion equations of electromagnetic waves within the rectangular grid region are obtained.

[0028] Based on the normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the initial values ​​of the artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method.

[0029] The numerical dispersion equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0030]

[0031]

[0032] Where c0 is the speed of light in vacuum, Δt is the time step, l is a pre-selected positive integer, Z is the shape information of the rectangular grid, A is the normalized numerical phase velocity, R is the spatial grid resolution, and β z Let ε be the wave propagation constant in the z-direction. x ε y denoted as and , respectively, as the relative permittivity in the x and y directions.

[0033] Optionally, in one embodiment of this application, an optimal normalized numerical phase velocity value is calculated based on the initial selected value of the artificial anisotropy parameter, and an preferred value of the artificial anisotropy parameter is calculated based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of the electromagnetic wave within the rectangular grid region, including:

[0034] The initial values ​​of the artificial anisotropy parameters are substituted into the numerical dispersion equation of electromagnetic waves within the rectangular grid region, and the maximum normalized numerical phase velocity value is obtained by solving the equation.

[0035] The optimal normalized numerical phase velocity value is calculated using the formula for calculating the optimal normalized numerical phase velocity based on the maximum normalized numerical phase velocity value.

[0036] Based on the optimal normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the optimal values ​​of artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method.

[0037] The optimal normalized numerical phase velocity calculation formula is expressed as follows:

[0038]

[0039] Among them, A opt Represented as the optimal normalized numerical phase velocity value, A max It is represented as the maximum normalized numerical phase velocity value.

[0040] Optionally, in one embodiment of this application, based on the preferred values ​​of the artificial anisotropy parameters and the governing equations of electromagnetic waves within the rectangular grid region, an iterative solution formula for the electromagnetic field quantities is obtained, including:

[0041] The governing equations of electromagnetic waves within the rectangular grid region are processed to obtain a set of ordinary differential equations;

[0042] Based on the theory of ordinary differential equations, the Gaussian integral formula is constructed using two-point interpolation, and the iterative solution formula for electromagnetic field quantities is obtained.

[0043] To achieve the above objectives, a second aspect of this application provides an electromagnetic wave compact time-domain fine integration device based on artificial anisotropic parameters, comprising:

[0044] The mesh generation module is used to obtain waveguides with long, straight, invariant structures and to mesh the cross-section of the waveguides using rectangular meshes.

[0045] The governing equation construction module is used to transform the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the governing equations of electromagnetic waves within a rectangular grid region.

[0046] The numerical dispersion equation construction module is used to obtain the numerical dispersion equation through Fourier analysis based on the governing equation, and to transform the numerical dispersion equation based on the shape and parameter information of the rectangular grid to obtain the numerical dispersion equation of electromagnetic waves within the rectangular grid region.

[0047] The artificial anisotropic parameter initial selection module is used to define the normalized numerical phase velocity value and, based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, to perform initial selection of the artificial anisotropic parameters and obtain the initial values ​​of the artificial anisotropic parameters.

[0048] The artificial anisotropy parameter optimization module is used to calculate the optimal normalized numerical phase velocity value based on the initial selection value of the artificial anisotropy parameter, and to calculate the optimized value of the artificial anisotropy parameter based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of electromagnetic waves in the rectangular grid area.

[0049] The iterative solution module is used to obtain the iterative solution formula for electromagnetic field quantities based on the preferred values ​​of artificial anisotropy parameters and the governing equations of electromagnetic waves within the rectangular grid region. The electromagnetic field quantities within the rectangular grid region are obtained by iteratively solving the electromagnetic field quantity using the iterative solution formula.

[0050] Optionally, in one embodiment of this application, the governing equation construction module is specifically used for:

[0051] The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region.

[0052] The governing equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0053]

[0054]

[0055] Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

[0056] To achieve the above objectives, a third aspect of this application provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the electromagnetic wave compact time-domain fine integration method based on artificial anisotropic parameters described in the above embodiments.

[0057] To achieve the above objectives, a fourth aspect of this application provides a non-transitory computer-readable storage medium that, when instructions in the storage medium are executed by a processor, can perform a tight time-domain fine integration method for electromagnetic waves based on artificial anisotropic parameters.

[0058] The electromagnetic wave compact time-domain fine integration method, apparatus, computer equipment, and non-transitory computer-readable storage medium based on artificial anisotropic parameters of this application solve the technical problems of existing methods that use square spatial grids to solve electromagnetic field problems with narrow structures, resulting in a large number of grid subdivisions, high memory requirements, and low computational efficiency. It also solves the numerical dispersion problem that exists when existing methods use rectangular grids to solve electromagnetic field problems with narrow structures. By introducing artificial anisotropic parameters to adjust the numerical dispersion error, the number of grid subdivisions can be significantly reduced, memory requirements can be reduced, and computational efficiency can be improved. It can also effectively correct the anisotropic numerical dispersion error introduced by rectangular grids and ensure computational accuracy.

[0059] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0060] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0061] Figure 1 A flowchart of a method for tight time-domain fine integration of electromagnetic waves based on artificial anisotropic parameters, provided in Embodiment 1 of this application;

[0062] Figure 2 Another flowchart of the electromagnetic wave compact time-domain fine integration method based on artificial anisotropic parameters according to an embodiment of this application;

[0063] Figure 3 This is an example of the numerical phase velocity versus propagation direction curves of the rectangular mesh compact format time-domain fine integration method and the artificial anisotropic parameter rectangular mesh time-domain fine integration method under initial parameters in this application embodiment;

[0064] Figure 4 This is an example diagram showing the variation of numerical phase velocity with propagation direction for the time-domain fine integration method of the rectangular mesh compact format and the time-domain fine integration method of the artificial anisotropic parameter rectangular mesh under preferred parameters according to embodiments of this application.

[0065] Figure 5 This is an example graph showing the variation of the normalized numerical phase velocity with Courant's constant in an embodiment of this application;

[0066] Figure 6 This is a schematic diagram of the structure of an electromagnetic wave compact time-domain fine integration device based on artificial anisotropic parameters, provided in Embodiment 2 of this application. Detailed Implementation

[0067] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0068] Currently, when using the compact scheme time-domain fine integration method to solve electromagnetic field problems with narrow structures, traditional square meshes can be used for spatial discretization. However, this method results in a large number of meshes, leading to high memory requirements and low computational efficiency. Alternatively, rectangular meshes of appropriate proportions can be used to discretize the problem based on its structure. However, there are currently no corresponding modifications to the compact scheme time-domain fine integration method, which requires tolerance to large numerical dispersion errors, potentially resulting in unacceptable deviations in the calculation results.

[0069] Therefore, this application addresses the numerical dispersion problem in the electromagnetic wave compact scheme time-domain fine integration method when using a rectangular mesh for computation. By introducing artificial anisotropic parameters, the numerical dispersion error of the algorithm is adjusted. This reduces the numerical dispersion error on the one hand, and eliminates the spatial anisotropic error introduced by the rectangular mesh on the other. A compact scheme time-domain fine integration method for electromagnetic waves based on an artificial anisotropic parameter rectangular mesh is established. Simulation based on the artificial anisotropic parameters maintains the advantages of low memory requirements and high computational efficiency brought by the rectangular mesh, while significantly reducing the numerical dispersion error introduced by the rectangular mesh.

[0070] The following description, with reference to the accompanying drawings, describes an embodiment of the electromagnetic wave compact time-domain fine integration method and apparatus based on artificial anisotropic parameters.

[0071] Figure 1 This is a flowchart illustrating a method for tight time-domain fine integration of electromagnetic waves based on artificial anisotropic parameters, as provided in Embodiment 1 of this application.

[0072] like Figure 1 As shown, the electromagnetic wave compact time-domain fine integration method based on artificial anisotropic parameters includes the following steps:

[0073] Step 101: Obtain a waveguide with a long, straight, invariant structure, and mesh the cross-section of the waveguide using a rectangular grid. The electromagnetic waves within the rectangular grid region satisfy the curl equation of Maxwell's equations.

[0074] Step 102: By introducing artificial anisotropy parameters, the curl equation of Maxwell's equations is transformed to obtain the governing equations of electromagnetic waves within the rectangular grid region.

[0075] Step 103: Based on the governing equations, obtain the numerical dispersion equations through Fourier analysis, and transform the numerical dispersion equations according to the shape and parameter information of the rectangular grid to obtain the numerical dispersion equations of electromagnetic waves within the rectangular grid region.

[0076] Step 104: Define the normalized numerical phase velocity value, and based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, perform preliminary selection of artificial anisotropic parameters to obtain the preliminary values ​​of artificial anisotropic parameters.

[0077] Step 105: Based on the initial selection of the artificial anisotropy parameters, calculate the optimal normalized numerical phase velocity value, and based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of electromagnetic waves within the rectangular grid region, calculate the preferred value of the artificial anisotropy parameters.

[0078] Step 106: Based on the preferred values ​​of the artificial anisotropy parameters and the governing equations of electromagnetic waves within the rectangular grid region, the iterative solution formula for electromagnetic field quantities is obtained. The electromagnetic field quantities of electromagnetic waves within the rectangular grid region are obtained by iteratively solving the electromagnetic field quantity solution formula.

[0079] This application's embodiment of the electromagnetic wave compact time-domain fine integration method based on artificial anisotropic parameters obtains a waveguide with a long, straight, invariant structure and meshes its cross-section using a rectangular grid. Within the rectangular grid region, the electromagnetic waves satisfy the curl equation of Maxwell's equations. By introducing artificial anisotropic parameters to transform the curl equation of Maxwell's equations, the governing equations for the electromagnetic waves within the rectangular grid region are obtained. Based on the governing equations, a numerical dispersion equation is obtained through Fourier analysis. This numerical dispersion equation is then transformed based on the shape and parameter information of the rectangular grid to obtain the numerical dispersion equation for the electromagnetic waves within the rectangular grid region. A normalized number is defined. The phase velocity value is calculated, and based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, the artificial anisotropy parameters are initially selected to obtain the initial values ​​of the artificial anisotropy parameters. Based on the initial values ​​of the artificial anisotropy parameters, the optimal normalized numerical phase velocity value is calculated, and based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of electromagnetic waves within the rectangular grid region, the optimal values ​​of the artificial anisotropy parameters are calculated. Based on the optimal values ​​of the artificial anisotropy parameters and the governing equation of electromagnetic waves within the rectangular grid region, the iterative solution formula for the electromagnetic field quantity is obtained, and the electromagnetic field quantity of electromagnetic waves within the rectangular grid region is obtained by iteratively solving the electromagnetic field quantity using the iterative solution formula. Therefore, this method can solve the technical problems of existing methods that use square spatial grids to solve electromagnetic field problems with narrow and elongated structures, resulting in a large number of grid subdivisions, high memory requirements, and low computational efficiency. It also solves the numerical dispersion problem that exists when existing methods use rectangular grids to solve electromagnetic field problems with narrow and elongated structures. By introducing artificial anisotropy parameters to adjust the numerical dispersion error, the number of grid subdivisions can be significantly reduced, memory requirements can be reduced, and computational efficiency can be improved. In addition, it can effectively correct the anisotropic numerical dispersion error introduced by rectangular grids and ensure computational accuracy.

[0080] The time-domain fine integration method for electromagnetic wave compact schemes based on artificial anisotropic parameter rectangular meshes in this application mainly includes the following steps: rectangular mesh partitioning, construction of governing equations, derivation of numerical stability and numerical dispersion relations, initial selection of artificial anisotropic parameters, optimal selection of artificial anisotropic parameters, and iterative solution.

[0081] In this embodiment of the application, for electromagnetic field problems with a long, straight, invariant structure in the propagation direction, according to the characteristics of the structure to be solved, a suitable rectangular grid can be selected to divide the cross-section into spatial grids. In the rectangular grid region after division, the electromagnetic wave satisfies the curl equation of Maxwell's equations.

[0082] Furthermore, in this embodiment, by introducing artificial anisotropy parameters to transform the curl equation of Maxwell's equations, the governing equations for electromagnetic waves within a rectangular grid region are obtained, including:

[0083] The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region.

[0084] The governing equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0085]

[0086]

[0087] Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

[0088] For electromagnetic field problems with invariant length and width, assume that its structure is invariant along the +z direction, and that electromagnetic waves propagate in the waveguide along the +z direction according to the wave propagation constant β. z The electric and magnetic field components then propagate along the +z direction, and can be written in the forms shown in equations (1) and (2):

[0089]

[0090]

[0091] Where E and H are the electric field intensity vector and the magnetic field intensity vector, respectively, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z These are the magnetic field intensity components in the x, y, and z directions, respectively, e x ey and e z Let β be the unit vectors in the x, y, and z directions, respectively. z The +z direction is determined according to the wave propagation constant.

[0092] Differentiating z with respect to equations (1) and (2) respectively, we can obtain... Right now

[0093] Consider introducing an artificial anisotropic medium with a relative permittivity tensor of ε. r =diag(ε x ,ε y ,ε z ), where ε x ε y and ε z Let μ be the relative permittivity in the x, y, and z directions, respectively, and let μ be the relative permeability tensor. r =diag(μ x ,μ y ,μ z ), where μ x μ y and μ z Let μ be the relative permeability in the x, y, and z directions, respectively. To reduce complexity and control variables, let μ be... r =ε r Therefore, the curl equation of Maxwell's equations based on the compact time-domain fine integration method using an artificial anisotropic parameter rectangular mesh is shown in equations (3)-(8):

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε yand ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

[0101] Furthermore, in the embodiments of this application, the numerical dispersion equation is expressed as:

[0102]

[0103]

[0104]

[0105]

[0106] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, and ε x ε y and ε z are the relative permittivity in the x, y, and z directions, respectively. and These are the numerical wave propagation constants in the x and y directions, respectively;

[0107] The numerical dispersion equation for electromagnetic waves within a rectangular grid region is expressed as:

[0108]

[0109]

[0110] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, α is the wave propagation angle, A is the normalized numerical phase velocity, R is the spatial grid resolution, Z is the shape information of the rectangular grid, and β... z Let ε be the wave propagation constant in the z-direction. x ε y and ε z denoted as , and respectively as the relative permittivity in the x, y, and z directions.

[0111] Based on the Fourier analysis method, substituting a set of plane wave solutions into the discrete iterative form of the governing equations, and simplifying, we can obtain the numerical dispersion equation of the electromagnetic wave compact scheme time-domain fine integration method based on an artificial anisotropic parameter rectangular grid:

[0112]

[0113] In the formula:

[0114]

[0115]

[0116]

[0117] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, and ε x ε y and ε z are the relative permittivity in the x, y, and z directions, respectively. and are the numerical wave propagation constants in the x and y directions, respectively.

[0118] This application defines parameters such as the aspect ratio of the rectangular mesh, the spatial mesh resolution, and the normalized numerical phase velocity to transform the numerical dispersion equation.

[0119] Define parameter Z to reflect the shape information of the rectangular grid, that is, the aspect ratio of the rectangular grid. Assume that the long side of the rectangular grid is in the x direction and the short side is in the y direction, as shown in equation (13):

[0120]

[0121] The spatial grid resolution R is defined as the number of grid cells per wavelength in the x-direction, i.e.:

[0122]

[0123] Where, λ T =c0 / f is the transverse wavelength in vacuum (note that it is not the numerical wavelength in the grid), and c0 is the speed of light in vacuum.

[0124] Define the Courant constant S as:

[0125]

[0126] Where c0 is the speed of light in a vacuum, and Δt is the time step.

[0127] Define the normalized numerical phase velocity as:

[0128]

[0129] in, c is the numerical wave speed, and c0 is the speed of light in a vacuum.

[0130] Therefore, in the numerical dispersion equation,

[0131]

[0132]

[0133]

[0134] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, S is Courant's constant, and R is the spatial grid resolution. and These are the numerical wave propagation constants in the x and y directions, respectively. α is the transverse numerical wavenumber, A is the wave propagation angle, Z is the normalized numerical phase velocity, and Z is the shape information of the rectangular grid.

[0135] Substituting equations (17)-(19) into equations (9) and (10) respectively, the numerical dispersion equation can be rewritten as:

[0136]

[0137]

[0138] Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, α is the wave propagation angle, A is the normalized numerical phase velocity, R is the spatial grid resolution, Z is the shape information of the rectangular grid, and β... z Let ε be the wave propagation constant in the z-direction. x ε y and ε z denoted as , and respectively as the relative permittivity in the x, y, and z directions.

[0139] Furthermore, in this embodiment, a normalized numerical phase velocity value is defined, and based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, the artificial anisotropy parameters are initially selected to obtain the initial values ​​of the artificial anisotropy parameters, including:

[0140] Define the normalized numerical phase velocity value as 1;

[0141] By assigning wave propagation angles of 0 degrees and 90 degrees respectively, the numerical dispersion equations of electromagnetic waves within the rectangular grid region are obtained.

[0142] Based on the normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the initial values ​​of the artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method.

[0143] The numerical dispersion equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0144]

[0145]

[0146] Where c0 is the speed of light in vacuum, Δt is the time step, l is a pre-selected positive integer, Z is the shape information of the rectangular grid, A is the normalized numerical phase velocity, R is the spatial grid resolution, and β z Let ε be the wave propagation constant in the z-direction. x ε y denoted as and , respectively, as the relative permittivity in the x and y directions.

[0147] The initial selection of artificial anisotropy parameters is to determine the ε parameter that results in a normalized numerical phase velocity of A = 1 when α = 0° and α = 90°. x ε y and ε z .

[0148] Since the compact scheme algorithm compresses the 3D spatial mesh into a 2D compact spatial mesh along the z-direction, i.e., it does not perform differencing in the z-direction, therefore, the parameter ε z It can be set to ε z =1.

[0149] Let α = 0°, then equation (21) can be transformed into:

[0150]

[0151] Let α = 90°, then equation (21) can be transformed into:

[0152]

[0153] Let A = 1, and by combining equations (22) and (23), the parameter ε can be obtained by applying the Newton-Raphson iterative method to solve the system of equations. x and ε y The initial selection value.

[0154] Further, in this embodiment, based on the initial selected values ​​of the artificial anisotropy parameters, the optimal normalized numerical phase velocity value is calculated, and based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of the electromagnetic wave within the rectangular grid region, the preferred values ​​of the artificial anisotropy parameters are calculated, including:

[0155] The initial values ​​of the artificial anisotropy parameters are substituted into the numerical dispersion equation of electromagnetic waves within the rectangular grid region, and the maximum normalized numerical phase velocity value is obtained by solving the equation.

[0156] The optimal normalized numerical phase velocity value is calculated using the formula for calculating the optimal normalized numerical phase velocity based on the maximum normalized numerical phase velocity value.

[0157] Based on the optimal normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the optimal values ​​of artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method.

[0158] The optimal normalized numerical phase velocity calculation formula is expressed as follows:

[0159]

[0160] Among them, A opt Represented as the optimal normalized numerical phase velocity value, A max It is represented as the maximum normalized numerical phase velocity value.

[0161] By initially selecting the anisotropic parameters, the numerical dispersion characteristics of the time-domain fine integration method based on artificial anisotropic rectangular meshes have been greatly improved, but there is still room for improvement. The maximum normalized numerical phase velocity A can be obtained from the initial parameter selection. max The maximum normalized numerical phase velocity A can be obtained by substituting the initial values ​​of the artificial anisotropy parameters into equations (20) and (21). max .

[0162] Define the optimal normalized numerical phase velocity A opt for:

[0163]

[0164] Let A=A opt By combining equations (22) and (23) and applying the Newton-Raphson iterative method to solve the system of equations, the parameter ε can be obtained. x and ε y The preferred value.

[0165] Furthermore, in this embodiment of the application, based on the preferred values ​​of the artificial anisotropy parameters and the governing equations of the electromagnetic waves within the rectangular grid region, an iterative solution formula for the electromagnetic field quantities is obtained, including:

[0166] The governing equations of electromagnetic waves within the rectangular grid region are processed to obtain a set of ordinary differential equations;

[0167] Based on the theory of ordinary differential equations, the Gaussian integral formula is constructed using two-point interpolation, and the iterative solution formula for electromagnetic field quantities is obtained.

[0168] Based on the von Neumann stability theory, the stability condition for the compact time-domain fine integration method based on artificial anisotropic parametric rectangular meshes can be derived as follows:

[0169]

[0170] Where Δt is the time step, and l = 2N N is a pre-selected positive integer, c0 is the speed of light in a vacuum, and ε x ε y and ε z The relative permittivity in the x, y, and z directions are β, respectively. z Let be the propagation constant in the z-direction. The simulation time step can be determined based on the spatial step size and the selected artificial anisotropy parameters using stability conditions.

[0171] The iterative solution process follows the solution process of the time-domain fine integration method, that is, the time partial differential operator and the space partial differential operator are processed separately. The space partial differential operator of equations (3)-(8) is discretized by second-order precision central difference, while the time partial differential operator is not processed. Thus, a set of ordinary differential equations is obtained and uniformly written in matrix form as shown in equation (26).

[0172]

[0173] Where X = (E x E y E z H x H y H z ) T M is a one-dimensional column vector containing all electromagnetic field quantities in a spatial discrete grid, M is a coefficient matrix determined by the spatial step size and medium parameters and does not change with time, and f(t) is a one-dimensional column vector introduced by the excitation source.

[0174] Based on the theory of ordinary differential equations and using the Gaussian integral formula constructed through two-point interpolation, the iterative solution formula is obtained as follows:

[0175]

[0176] Among them, X n+1 Let X be the electromagnetic field vector at time n+1, T be the exponential matrix, and X be the electromagnetic field vector. n Let f(t) be the electromagnetic field vector at time n, where n is the iteration step, Δt is the time step, M is the coefficient matrix, and f() is a one-dimensional column vector introduced by the excitation source.

[0177] When applying the compact scheme time-domain fine integration method for electromagnetic waves to solve problems with elongated structures, this application utilizes a rectangular spatial grid, which effectively reduces the number of grid subdivisions, decreases computer memory requirements, and significantly improves computational efficiency. Simultaneously, with a rectangular spatial grid, the method proposed in this application can effectively reduce the numerical dispersion error of traditional compact scheme time-domain fine integration methods, thereby improving computational accuracy. Furthermore, the related techniques of this application have a certain degree of versatility and can be extended to the construction of other numerical algorithms.

[0178] like Figure 2 As shown, the solution process of this compact time-domain fine integration method for electromagnetic waves based on artificial anisotropic parameters includes: for electromagnetic field problems with a long, straight, invariant structure in the propagation direction, a suitable rectangular grid is used to spatially mesh the computational domain according to the characteristics of the structure to be solved; an anisotropic parameter medium, namely the relative permittivity tensor and the relative permeability tensor, is introduced to establish the governing equations within the computational domain; the numerical stability condition and the numerical dispersion equation are derived, and parameters such as the aspect ratio of the rectangular grid, the spatial grid resolution, and the normalized numerical phase velocity are defined to transform the numerical dispersion equation for subsequent analysis; at α = 0° and α = 90°, the normalized numerical phase velocity is set to 1, and a method for establishing the relationship between ε and ε is established. x and ε y The system of equations was solved using the Newton-Raphson iterative method to obtain the parameter ε. x and ε y The initial selection value; the maximum normalized phase velocity A obtained from the initial selection of parameters. max The optimal normalized numerical phase velocity A is obtained. opt At α = 0° and α = 90°, let the normalized numerical phase velocity equal to A. opt Establish about ε x and ε y The system of equations was solved using the Newton-Raphson iterative method to obtain the parameter ε. x and ε y The optimal value is obtained; the solution is obtained by using an iterative solution formula based on the optimal value of the parameter.

[0179] Taking a rectangular grid with an aspect ratio of Z = 2 as an example, let the spatial resolution in the x-direction be R = 10, and the Courant constant be S = 1. Assume the angular frequency is ω = 2π × 10⁻⁶. 9 Given rad and a normalized wave propagation constant k = 0.2, solving the system of equations using the Newton-Raphson iterative method yields the initial parameter ε. x =0.9934, ε y =0.9691 and ε z =1. For example... Figure 3 As shown, the numerical phase velocity versus propagation direction curves (i.e., numerical dispersion curves) of the time-domain fine integration method using a compact scheme with a rectangular mesh and the time-domain fine integration method using an artificial anisotropic parameter rectangular mesh with initially selected parameters are presented. Compared with the compact scheme time-domain fine integration method with a rectangular mesh, the numerical dispersion curve of the time-domain fine integration method based on an artificial anisotropic parameter rectangular mesh is symmetrical, meaning that the propagation speed of the electromagnetic wave is the same in the x and y directions. Furthermore, under the rectangular mesh, the maximum relative error of the traditional compact scheme time-domain fine integration method is 1.69%, while the maximum relative error of the time-domain fine integration method based on an artificial anisotropic parameter rectangular mesh is reduced to 0.50%.

[0180] Furthermore, according to A max =0.50%, we can get A opt =0.9975, let A=A opt It can be found that under a rectangular grid with Z=2 and R=10, the optimal parameter is ε. x =0.9981, ε y =0.9736 and ε z =1. For example... Figure 4 As shown, numerical dispersion curves are presented for the time-domain fine integration method using a compact rectangular mesh scheme and the time-domain fine integration method using an artificial anisotropic parameter rectangular mesh with optimized parameters. The maximum relative error of the time-domain fine integration method using an artificial anisotropic parameter rectangular mesh is further reduced, ultimately reaching only 0.26%.

[0181] Furthermore, such as Figure 5 As shown, the relationship between the normalized numerical phase velocity and the Courant constant S, obtained using a time-domain fine integration method based on an artificial anisotropic parameter rectangular grid, is presented under different parameters when the wave propagation angle α = 45°. The numerical dispersion error of the proposed method is almost independent of the selection of the time step. Furthermore, under the optimal parameter ε... x =0.9981, ε y =0.9736 and ε z At a value of 1, the numerical dispersion error is minimized.

[0182] Taking a uniformly filled lossy rectangular waveguide as an example, its geometric dimensions are 0.156m × 0.078m. The perimeter is set as a perfect conductor, and the interior is uniformly filled with a lossy medium with a relative permittivity of 1 and a conductivity of 0.001 S / m. Let the normalized wave propagation constant k = 0.275, i.e., β... z =0.275β0, then the corresponding frequency is 1GHz, and the analytical solution of the quality factor is Q = ωε / σ = 55.633. Simulations were performed using the compact scheme time-domain fine integration method for electromagnetic waves under a square mesh (Method 1), the traditional compact scheme time-domain fine integration method under a rectangular mesh (Method 2), and the time-domain fine integration method based on an artificial anisotropic parameter rectangular mesh (Method 3). The simulation results are shown in Table 1. The spatial step size for the square mesh is Δx = Δy = 0.013m, and the spatial step size for the rectangular mesh is Δx = 0.026m and Δy = 0.013m, i.e., Z = 2. The artificial anisotropic parameter of the method proposed in this application is ε. x =0.9997, ε y =0.9826 and ε z =1.

[0183]

[0184] Table 1

[0185] As shown in Table 1, the time-domain fine integration method based on artificial anisotropic parameter rectangular meshes not only significantly reduces the computational error of traditional compact scheme time-domain fine integration methods under rectangular meshes, but also achieves or even surpasses the computational accuracy of traditional compact scheme time-domain fine integration methods under square meshes. Furthermore, due to the reduced number of meshes, the memory requirements and computer execution time of the time-domain fine integration method based on artificial anisotropic parameter rectangular meshes are much smaller than those of traditional compact scheme time-domain fine integration methods under square meshes. Therefore, the time-domain fine integration method based on artificial anisotropic parameter rectangular meshes can significantly improve computational efficiency while maintaining computational accuracy.

[0186] Figure 6 This is a schematic diagram of the structure of an electromagnetic wave compact time-domain fine integration device based on artificial anisotropic parameters, provided in Embodiment 2 of this application.

[0187] like Figure 6 As shown, the electromagnetic wave compact time-domain fine integration device based on artificial anisotropic parameters includes:

[0188] Mesh partitioning module 10 is used to obtain waveguides with long, straight, invariant structures and to partition the cross-section of the waveguides using rectangular meshes.

[0189] The governing equation construction module 20 is used to transform the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the governing equations of electromagnetic waves within a rectangular grid region.

[0190] The numerical dispersion equation construction module 30 is used to obtain the numerical dispersion equation through Fourier analysis based on the control equation, and to transform the numerical dispersion equation based on the shape information and parameter information of the rectangular grid to obtain the numerical dispersion equation of electromagnetic waves within the rectangular grid region.

[0191] The artificial anisotropic parameter initial selection module 40 is used to define the normalized numerical phase velocity value and, based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, to perform initial selection of the artificial anisotropic parameters and obtain the initial selection values ​​of the artificial anisotropic parameters.

[0192] The artificial anisotropy parameter optimization module 50 is used to calculate the optimal normalized numerical phase velocity value based on the initial selection value of the artificial anisotropy parameter, and to calculate the optimized value of the artificial anisotropy parameter based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of the electromagnetic wave in the rectangular grid area.

[0193] The iterative solution module 60 is used to obtain the iterative solution formula for electromagnetic field quantity based on the preferred values ​​of artificial anisotropy parameters and the control equation of electromagnetic waves within the rectangular grid region. The iterative solution is then performed based on the iterative solution formula to obtain the electromagnetic field quantity of electromagnetic waves within the rectangular grid region.

[0194] The electromagnetic wave compact time-domain fine integration device based on artificial anisotropic parameters according to embodiments of this application includes a mesh generation module for obtaining a waveguide with a long, straight, invariant structure and meshing the cross-section of the waveguide using a rectangular mesh; a control equation construction module for transforming the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the control equations for electromagnetic waves within the rectangular mesh region; a numerical dispersion equation construction module for obtaining the numerical dispersion equations through Fourier analysis based on the control equations and transforming the numerical dispersion equations according to the shape and parameter information of the rectangular mesh to obtain the numerical dispersion equations for electromagnetic waves within the rectangular mesh region; and an artificial anisotropic parameter initial selection module for defining normalized numerical parameters. The system calculates the phase velocity value and, based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, performs an initial selection of artificial anisotropic parameters to obtain the initial values ​​of the artificial anisotropic parameters. The artificial anisotropic parameter optimization module calculates the optimal normalized numerical phase velocity value based on the initial values ​​of the artificial anisotropic parameters, and, based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of electromagnetic waves within the rectangular grid region, calculates the optimal values ​​of the artificial anisotropic parameters. The iterative solution module derives the iterative solution formula for the electromagnetic field quantity based on the optimal values ​​of the artificial anisotropic parameters and the governing equation of electromagnetic waves within the rectangular grid region, and performs iterative solution based on the iterative solution formula to obtain the electromagnetic field quantity of electromagnetic waves within the rectangular grid region. Therefore, this method can solve the technical problems of existing methods that use square spatial grids to solve electromagnetic field problems with narrow and elongated structures, resulting in a large number of grid subdivisions, high memory requirements, and low computational efficiency. It also solves the numerical dispersion problem that exists when existing methods use rectangular grids to solve electromagnetic field problems with narrow and elongated structures. By introducing artificial anisotropy parameters to adjust the numerical dispersion error, the number of grid subdivisions can be significantly reduced, memory requirements can be reduced, and computational efficiency can be improved. In addition, it can effectively correct the anisotropic numerical dispersion error introduced by rectangular grids and ensure computational accuracy.

[0195] Furthermore, in this embodiment, the governing equation construction module is specifically used for:

[0196] The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region.

[0197] The governing equations for electromagnetic waves within the rectangular grid region are expressed as follows:

[0198]

[0199]

[0200] Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

[0201] To implement the above embodiments, this application also proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method described in the above embodiments.

[0202] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the electromagnetic wave compact time-domain fine integration method based on artificial anisotropic parameters as described in the above embodiments.

[0203] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0204] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0205] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0206] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0207] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0208] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0209] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0210] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A compact time-domain fine integration method for electromagnetic waves based on artificial anisotropic parameters, characterized in that, Includes the following steps: A waveguide with a long, straight, invariant structure is obtained, and the cross-section of the waveguide is meshed using a rectangular grid, wherein the electromagnetic waves within the rectangular grid region satisfy the curl equation of Maxwell's equations; By introducing artificial anisotropic parameters to transform the curl equation of Maxwell's equations, the governing equations of electromagnetic waves within a rectangular grid region are obtained. Numerical dispersion equations are obtained through Fourier analysis based on the governing equations. The numerical dispersion equations are then transformed based on the shape and parameter information of the rectangular grid to obtain the numerical dispersion equations of electromagnetic waves within the rectangular grid region. Define normalized numerical phase velocity values, and based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, perform preliminary selection of the artificial anisotropy parameters to obtain the preliminary values ​​of the artificial anisotropy parameters. Based on the initial selection of the artificial anisotropy parameters, the optimal normalized numerical phase velocity value is calculated, and based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of electromagnetic waves within the rectangular grid region, the preferred value of the artificial anisotropy parameters is calculated. Based on the preferred values ​​of the artificial anisotropy parameters and the governing equations of the electromagnetic waves within the rectangular grid region, an iterative solution formula for the electromagnetic field quantity is obtained. The electromagnetic field quantity of the electromagnetic waves within the rectangular grid region is obtained by iteratively solving the electromagnetic field quantity formula.

2. The method as described in claim 1, characterized in that, The method of transforming the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the governing equations of electromagnetic waves within a rectangular grid region includes: The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region. The governing equation for the electromagnetic waves within the rectangular grid region is expressed as: Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

3. The method as described in claim 1, characterized in that, The numerical dispersion equation is expressed as: Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, and ε x ε y and ε z are the relative permittivity in the x, y, and z directions, respectively. and These are the numerical wave propagation constants in the x and y directions, respectively; The numerical dispersion equation for electromagnetic waves within the rectangular grid region is expressed as: Where ω is the plane wave angular frequency, Δt is the time step, l is a pre-selected positive integer, c0 is the speed of light in vacuum, α is the wave propagation angle, A is the normalized numerical phase velocity, R is the spatial grid resolution, Z is the shape information of the rectangular grid, and β... z Let ε be the wave propagation constant in the z-direction. x ε y and ε z denoted as , and respectively as the relative permittivity in the x, y, and z directions.

4. The method as described in claim 1, characterized in that, The definition of normalized numerical phase velocity values, and the preliminary selection of artificial anisotropy parameters based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, yielding preliminary values ​​for the artificial anisotropy parameters, including: Define the normalized numerical phase velocity value as 1; By assigning wave propagation angles of 0 degrees and 90 degrees respectively, the numerical dispersion equations of electromagnetic waves within the rectangular grid region are obtained. Based on the normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the initial values ​​of the artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method. The numerical dispersion equations for electromagnetic waves within the rectangular grid region are expressed as follows: Where c0 is the speed of light in vacuum, Δt is the time step, l is a pre-selected positive integer, Z is the shape information of the rectangular grid, A is the normalized numerical phase velocity, R is the spatial grid resolution, and β z Let ε be the wave propagation constant in the z-direction. x ε y denoted as and , respectively, as the relative permittivity in the x and y directions.

5. The method as described in claim 1, characterized in that, The process of calculating the optimal normalized numerical phase velocity value based on the initial selected value of the artificial anisotropy parameter, and calculating the preferred value of the artificial anisotropy parameter based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of the electromagnetic wave within the rectangular grid region, includes: The initial values ​​of the artificial anisotropy parameters are substituted into the numerical dispersion equation of electromagnetic waves within the rectangular grid region, and the maximum normalized numerical phase velocity value is obtained by solving the equation. The optimal normalized numerical phase velocity value is calculated using the formula for calculating the optimal normalized numerical phase velocity based on the maximum normalized numerical phase velocity value. Based on the optimal normalized numerical phase velocity value and the numerical dispersion equations of electromagnetic waves within the rectangular grid region, the preferred values ​​of the artificial anisotropy parameters are obtained by solving the Newton-Raphson iterative method. The optimal normalized numerical phase velocity calculation formula is expressed as follows: Among them, A opt Represented as the optimal normalized numerical phase velocity value, A max It is represented as the maximum normalized numerical phase velocity value.

6. The method as described in claim 1, characterized in that, The step of obtaining the iterative solution formula for the electromagnetic field quantity based on the preferred values ​​of the artificial anisotropy parameters and the governing equations of the electromagnetic waves within the rectangular grid region includes: The governing equations of electromagnetic waves within the rectangular grid region are processed to obtain a set of ordinary differential equations; Based on the theory of ordinary differential equations, the Gaussian integral formula is constructed using two-point interpolation, and the iterative solution formula for electromagnetic field quantities is obtained.

7. A compact time-domain fine integration device for electromagnetic waves based on artificial anisotropic parameters, characterized in that, include: The meshing module is used to obtain waveguides with long, straight, invariant structures and to mesh the cross-section of the waveguides using rectangular meshes. The governing equation construction module is used to transform the curl equation of Maxwell's equations by introducing artificial anisotropic parameters to obtain the governing equations of electromagnetic waves within a rectangular grid region. The numerical dispersion equation construction module is used to obtain the numerical dispersion equation through Fourier analysis based on the control equation, and to transform the numerical dispersion equation according to the shape information and parameter information of the rectangular grid to obtain the numerical dispersion equation of electromagnetic waves in the rectangular grid region. The artificial anisotropy parameter initial selection module is used to define the normalized numerical phase velocity value and, based on the numerical dispersion equation of electromagnetic waves within the rectangular grid region, to perform initial selection of the artificial anisotropy parameters and obtain the initial selection values ​​of the artificial anisotropy parameters. The artificial anisotropy parameter optimization module is used to calculate the optimal normalized numerical phase velocity value based on the initial selection value of the artificial anisotropy parameter, and to calculate the optimized value of the artificial anisotropy parameter based on the optimal normalized numerical phase velocity value and the numerical dispersion equation of the electromagnetic wave in the rectangular grid area. The iterative solution module is used to obtain the iterative solution formula for electromagnetic field quantity based on the preferred values ​​of the artificial anisotropy parameters and the control equation of electromagnetic waves in the rectangular grid region, and to perform iterative solution based on the iterative solution formula to obtain the electromagnetic field quantity of electromagnetic waves in the rectangular grid region.

8. The apparatus as claimed in claim 7, characterized in that, The governing equation construction module is specifically used for: The electric and magnetic field components of the electromagnetic wave within the rectangular grid region are differentiated, and the curl equation of Maxwell's equations is transformed by introducing artificial anisotropic parameters based on the differentiated formulas to obtain the governing equations of the electromagnetic wave within the rectangular grid region. The governing equation for the electromagnetic waves within the rectangular grid region is expressed as: Among them, E x E y and E z H represents the electric field intensity components in the x, y, and z directions, respectively. x H y and H z ε represents the magnetic field strength components in the x, y, and z directions, respectively. x ε y and ε z ε0 represents the relative permittivity in the x, y, and z directions, respectively; ε0 is the permittivity of free space; μ0 is the permeability of free space; and β0 is the relative permittivity in the x, y, and z directions, respectively. z Let be the wave propagation constant in the z-direction.

9. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the method as described in any one of claims 1-6.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

Images