Time domain electromagnetic field calculation method

Abstract

The invention provides a time domain electromagnetic field calculation method, and belongs to the technical field of electromagnetic field calculation. The method comprises the following steps: constructing a two-dimensional Maxwell equation set according to electromagnetic field information in an application scene; the two-dimensional Maxwell equation set is converted into a Maxwell equation in a matrix form of a Laguerre domain; a high-order tiny error term is added to one side of the Maxwell equation in the matrix form, and a transformed Maxwell equation is obtained; solving the transformed Maxwell equation by using a step-by-step solving method to obtain an electric field component and a magnetic field component of a Laguerre domain; and obtaining the electric field component and the magnetic field component of the time domain based on the electric field component and the magnetic field component of the Laguerre domain. According to the method, the time domain electromagnetic field calculation efficiency can be greatly improved, and calculation memory consumption is reduced.

Description

Technical Field

[0001] The invention relates to a time domain electromagnetic field calculation method, belonging to the technical field of electromagnetic field calculation. Background Art

[0002] In the fields of radar target scattering cross section (RCS) calculation, broadband antenna and communication system analysis, broadband microwave circuit and subsystem analysis and design, etc., it is necessary to calculate the time domain electromagnetic field, and the Finite-Difference Time-Domain (FDTD) algorithm is an intuitive and commonly used method for calculating the time domain electromagnetic field. The traditional FDTD algorithm uses the method of alternating grid calculation of electric and magnetic field components to cleverly describe the propagation of Maxwell's equations in space. However, the traditional FDTD algorithm must meet the requirements of the Courant-Friedrich-Lewy (CFL) stability condition. When the spatial step size is very small, the time step size must also be correspondingly small, which greatly increases the calculation time of numerical simulation. It is especially not suitable for calculations with fine grids and is difficult to meet the calculation requirements of most occasions.

[0003] In recent years, with the development of communication technology, people have made many improvements based on the FDTD algorithm. For example, the FDTD algorithm based on the alternating-direction implicit method (ADI) breaks through the limitations of the CFL stability condition and is suitable for the numerical simulation of fine structures, but its numerical dispersion error has a greater impact; the FDTD algorithm based on the weighted Laguerre basis (WLP-FDTD) uses the Laguerre basis to expand the electromagnetic field components into the Laguerre domain, and uses the Galerkin method to decouple the influence of time variables and space variables. The Laguerre basis FDTD algorithm is not restricted by the CFL stability condition, is unconditionally stable, and has a small numerical dispersion error. However, the algorithm needs to solve a large set of linear equations, which requires a large amount of computer memory and affects the computational efficiency.

[0004] At present, most of the time-domain electromagnetic field calculation methods on the market have problems with errors or computational complexity, which brings many difficulties to practical applications and restricts the development of various technical fields that require time-domain electromagnetic field calculations. Summary of the invention

[0005] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a new time-domain electromagnetic field calculation method, and provide a two-dimensional WLP-FDTD algorithm based on a differential operator. The time-domain electromagnetic field calculation is performed using the two-dimensional WLP-FDTD based on the differential operator, which is not restricted by the CFL stability condition, has a small numerical dispersion error, and has high calculation efficiency, which can meet the needs of practical applications.

[0006] In order to achieve the above purpose / solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0007] In a first aspect, the present invention provides a time domain electromagnetic field calculation method, comprising the following steps:

[0008] Construct a two-dimensional Maxwell equation system based on the electromagnetic field information in the application scenario;

[0009] Transforming the two-dimensional Maxwell equations into a Maxwell equation in matrix form in a Laguerre domain;

[0010] Adding a high-order small error term on one side of the Maxwell equation in matrix form to obtain a transformed Maxwell equation;

[0011] Solving the transformed Maxwell equations using a step-by-step solution method to obtain the electric field component and the magnetic field component in the Laguerre domain;

[0012] The electric field component and the magnetic field component in the time domain are obtained based on the electric field component and the magnetic field component in the Laguerre domain.

[0013] Furthermore, in a lossless, homogeneous, isotropic medium, the two-dimensional time-domain Maxwell equations are:

[0014] ;

[0015] in, is the dielectric constant, is the magnetic permeability, , are the components of the electric field in the electromagnetic field along the x and y directions, is the component of the magnetic field along the z direction in the electromagnetic field, , are the components of the current source along the x and y directions, x, y, z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

[0016] Furthermore, the step of transforming the two-dimensional Maxwell equations into a Maxwell equation in a matrix form in a Laguerre domain comprises:

[0017] The two-dimensional Maxwell equations are expanded into the Laguerre domain using the Laguerre orthogonal basis, and three Maxwell equations in the Laguerre domain are obtained;

[0018] The three Maxwell equations in the Laguerre domain are transformed into a matrix equation form by using a column vector construction method, thereby obtaining the Maxwell equations in the matrix form of the Laguerre domain.

[0019] Furthermore, the two-dimensional Maxwell equations are expanded into the Laguerre domain using the Laguerre orthogonal basis to obtain three Maxwell equations in the Laguerre domain, including:

[0020] The electric field components and magnetic field components in the two-dimensional Maxwell equations are expanded using the Laguerre basis function to obtain the expanded Maxwell equations:

[0021] ;

[0022] ;

[0023] ;

[0024] in, represents the time domain electric field component in the x direction at time t and in r space, represents the time domain electric field component in the y direction at time t and in space r, represents the time domain magnetic field component in the z direction at time t and in r space, for Laguerre basis functions of order, , for Laguerre polynomial of order, s is the time factor, r is the space variable, e is the natural constant, , are the time domain electric field components , The p-order Laguerre coefficient, is the time domain magnetic field component The p-order Laguerre coefficient of

[0025] Laguerre basis functions Satisfy the following formula:

[0026] ;

[0027] ;

[0028] in, represents the q-order Laguerre basis function, is the Dirac function, represents any electric or magnetic field component at time t and space r, for The p-order Laguerre coefficient, for The k-order Laguerre coefficient of

[0029] Substitute the expanded Maxwell equations into the two-dimensional Maxwell equations and multiply both sides of the Maxwell equations by the Laguerre basis function ,exist After integrating and sorting out, we get the three Maxwell equations in the Laguerre domain, which are expressed as follows:

[0030] ;

[0031] ;

[0032] ;

[0033] in,

[0034] ;

[0035] ;

[0036] in, , are the time domain electric field components , The q-order Laguerre coefficient, is the time domain magnetic field component The q-order Laguerre coefficient, , are the time domain electric field components , The k-th order Laguerre coefficient, is the time domain magnetic field component The k-th order Laguerre coefficient, represents the time domain current source component in the x direction in the r space at time t, represents the time domain current source component in the y direction at time t and in r space, , They are the time domain current source components , The q-order Laguerre coefficient, To calculate the length of time.

[0037] Furthermore, the three Maxwell equations in the Laguerre domain are transformed into a matrix equation by using the column vector construction method to obtain the Maxwell equations in the matrix form of the Laguerre domain, including:

[0038] Use the column vector construction method to construct the following variables:

[0039] , ;

[0040] , ;

[0041] , ;

[0042] , ;

[0043] ;

[0044] Among them, a and b are process coefficients, Reason The vector of unknown electric field components of order, the superscript T represents the transpose operation, Reason The vector of unknown electric field components of order, , is a custom matrix consisting of partial differential symbols, , Reason The vectors composed of known electric and magnetic field components below the order, Reason The vector composed of the order field source components;

[0045] The three Maxwell equations in the Laguerre domain are written in matrix form according to the constructed variables:

[0046] ;

[0047] ;

[0048] The formula Substitute into the formula , we can get the Maxwell equation in the matrix form of Laguerre domain, which is expressed as follows:

[0049] ;

[0050] Where I is the 6th-order identity matrix.

[0051] Furthermore, the high-order small error term is ,in, , .

[0052] Furthermore, the high-order small error term is added to one side of the Maxwell equation in matrix form to obtain the transformed Maxwell equation, including:

[0053] make , substituting into the Maxwell equation in matrix form in Laguerre domain, we get:

[0054] ;

[0055] Adding high-order small error terms to the left side of the Maxwell equations in matrix form in the Laguerre domain , we get the transformed Maxwell equations:

[0056] ;

[0057] Decomposing the transformed Maxwell equation into two equations, we get:

[0058] ;

[0059] ;

[0060] in, is a non-physical intermediate variable, , is the Laguerre domain electric field component , The intermediate variable.

[0061] Furthermore, the transformed Maxwell equations are solved by using a step-by-step solution method to obtain the electric field component and the magnetic field component in the Laguerre domain, including:

[0062] Substituting the variables constructed by the column vector method into the transformed Maxwell equations and expanding the equations yields:

[0063] (a);

[0064] (b);

[0065] (c);

[0066] Wherein, the subscripts i and j represent the x and y coordinate values ​​of the field point, respectively;

[0067] According to formula (a), solve the intermediate variable of the electric field in the Laguerre domain , ;

[0068] The intermediate variable , Substituting the value of into formula (b) and (c), we can obtain the electric field component of the Laguerre domain and ;

[0069] The electric field component of the Laguerre domain and Substituting into Maxwell's equation, we get the magnetic field component in the Laguerre domain .

[0070] Furthermore, the electric field component and the magnetic field component in the Laguerre domain are transformed into the electric field component and the magnetic field component in the time domain by using the inverse process of the Laguerre orthogonal basis expansion.

[0071] In a second aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the time-domain electromagnetic field calculation method provided in the first aspect.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] The present invention proposes a time-domain electromagnetic field calculation method, improves the traditional time-domain electromagnetic field calculation algorithm, and proposes a two-dimensional WLP-FDTD algorithm based on a differential operator. The time-domain electromagnetic field calculation is performed using the two-dimensional WLP-FDTD based on a differential operator, which is not restricted by the CFL stability condition, that is, unconditionally stable. The method of the present invention is based on the Laguerre basis function, and eliminates the time variable in the Maxwell equation by transformation, so that the calculation time is not affected by the selection of the time step, which greatly improves the calculation efficiency and shortens the calculation time; the calculation efficiency is very high. The method of the present invention decouples the solution process of the electric and magnetic fields, and compared with the traditional time-domain electromagnetic field calculation algorithm, it greatly reduces the matrix dimension, reduces the amount of calculation, and improves the calculation efficiency. At the same time, because the present invention achieves the effect of decoupling and dimensionality reduction, it greatly reduces the demand for computer memory. Therefore, the calculation method of the present invention occupies very little memory resources and can better adapt to the actual application needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 FIG. 1 is a schematic diagram of the steps of a time domain electromagnetic field calculation method provided by an embodiment of the present invention;

[0075] Figure 2FIG. 2 is a schematic diagram of a two-dimensional parallel plate waveguide structure in an embodiment of the present invention;

[0076] Figure 3 The electric field components of the observation point obtained by different methods in the embodiment of the present invention are shown in FIG. Schematic diagram of the waveform. DETAILED DESCRIPTION

[0077] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0078] Example 1

[0079] This embodiment introduces a time domain electromagnetic field calculation method based on a two-dimensional WLP-FDTD algorithm of a differential operator. Figure 1 As shown, the specific steps include:

[0080] Step 1: Construct a two-dimensional Maxwell equation group according to the electromagnetic field information in the application scenario, and transform the two-dimensional Maxwell equation group into a Maxwell equation in matrix form in a Laguerre domain.

[0081] Step 101: Expand the two-dimensional Maxwell equations into the Laguerre domain using the Laguerre orthogonal basis to obtain three Maxwell equations in the Laguerre domain.

[0082] In a lossless, homogeneous, isotropic medium, the two-dimensional time-domain Maxwell equations are:

[0083] (1)

[0084] in, is the dielectric constant, is the magnetic permeability, , are the components of the electric field in the electromagnetic field along the x and y directions, is the component of the magnetic field along the z direction in the electromagnetic field, , are the components of the current source along the x and y directions, x, y, z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

[0085] By using the Laguerre basis function to expand the electric field component and the magnetic field component in formula (1), we can obtain:

[0086] (2)

[0087] (3)

[0088] (4)

[0089] in, represents the time domain electric field component in the x direction at time t and in r space, represents the time domain electric field component in the y direction at time t and in space r, represents the time domain magnetic field component in the z direction at time t and in r space, for Laguerre basis functions of order, , for Laguerre polynomial of order, s is the time factor, r is the space variable, e is the natural constant, , are the time domain electric field components , The p-order Laguerre coefficient, is the time domain magnetic field component The p-order Laguerre coefficient of .

[0090] , , It is only related to the spatial position and has nothing to do with time. The definitions of other Laguerre coefficients are similar.

[0091] The Laguerre basis function has the following properties:

[0092] (5)

[0093] (6)

[0094] in, represents the q-order Laguerre basis function, is the Dirac function, represents any electric or magnetic field component at time t and space r, that is, , for The p-order Laguerre coefficient, for The k-th order Laguerre coefficient of .

[0095] Combining the above formulas, substitute formula (2) to formula (6) into formula (1) and multiply both sides of the equation by the basis function , then Integrating and sorting out the three Maxwell equations in the Laguerre domain:

[0096] (7)

[0097] (8)

[0098] (9)

[0099] in,

[0100] (10)

[0101] (11)

[0102] in, , are the time domain electric field components , The q-order Laguerre coefficient, is the time domain magnetic field component The q-order Laguerre coefficient, , are the time domain electric field components , The k-th order Laguerre coefficient, is the time domain magnetic field component The k-th order Laguerre coefficient, represents the time domain current source component in the x direction in the r space at time t, represents the time domain current source component in the y direction at time t and in r space, , They are the time domain current source components , The q-order Laguerre coefficient, To calculate the length of time.

[0103] It can be seen that in formulas (7) to (9), the time variable t on the left side of the equation has been eliminated, leaving only the q-order Laguerre coefficient that needs to be solved; and the left side of the equation is all unknown, and the right side is all known.

[0104] Step 102: Use the column vector construction method to transform the three Maxwell equations in the Laguerre domain into a matrix equation form to obtain the Maxwell equations in the matrix form of the Laguerre domain.

[0105] Construct the following variables:

[0106] , (12)

[0107] , (13)

[0108] , (14)

[0109] , (15)

[0110] (16)

[0111] Among them, a and b are process coefficients, Reason The vector of unknown electric field components of order, the superscript T represents the transpose operation, Reason The vector of unknown electric field components of order, , is a custom matrix consisting of partial differential symbols, , Reason The vectors composed of known electric and magnetic field components below the order, Reason The vector consisting of the components of the field source of order .

[0112] Then formula (7) to formula (9) can be written in the following matrix form:

[0113] (17)

[0114] (18)

[0115] Substituting formula (18) into formula (17), we obtain the Maxwell equation in matrix form:

[0116] (19)

[0117] Where I is the 6th-order identity matrix.

[0118] Step 2: Add a high-order small error term to one side of the Maxwell equation in matrix form, so that the coefficient matrix on one side of the Maxwell equation is decomposed into the product of two square matrices to obtain the transformed Maxwell equation.

[0119] In order to decouple the solution process of the electric field component and the magnetic field component, the present invention actively adds an error term that causes an error on the left side of the Maxwell equation in matrix form, so that the coefficient matrix on the left side of formula (19) can be decomposed into the form of the product of two square matrices.

[0120] According to formula (14), we can know that:

[0121] (20)

[0122] make , and construct the operator matrices M and N respectively:

[0123] , (twenty one)

[0124] Then formula (19) can be written as:

[0125] (twenty two)

[0126] Add a high-order small error term to the left side of formula (22): ,have to:

[0127] (twenty three)

[0128] Formula (23) can be decomposed into two equations for calculation:

[0129] (twenty four)

[0130] (25)

[0131] in, is a non-physical intermediate variable, , is the Laguerre domain electric field component , The intermediate variable.

[0132] Step 3: Solve the transformed Maxwell equations using a step-by-step solution method to obtain the electric field component and magnetic field component in the Laguerre domain.

[0133] The present invention decomposes the transformed Maxwell equations into three steps for solving. The first step is to solve the intermediate variables of the electric field in the Laguerre domain based on the transformed Maxwell equations. The second step is to solve the electric field components in the Laguerre domain based on the intermediate variables. The third step is to solve the magnetic field components in the Laguerre domain based on the electric field components.

[0134] Step 301: Solve the intermediate variables of the electric field in the Laguerre domain based on the transformed Maxwell equations , .

[0135] By expanding formulas (24) to (25) using formulas (12) to (16), we can obtain a set of basic expressions for solving the electromagnetic field components in two-dimensional space:

[0136] (26)

[0137] (27)

[0138] (28)

[0139] By expanding the differential operators in formulas (26) to (28), we can obtain a set of differential equations for the two-dimensional efficient WLP-FDTD algorithm:

[0140] (29)

[0141] (30)

[0142] (31)

[0143] The subscripts i and j represent the x and y coordinate values ​​of the field point, respectively.

[0144] The left sides of formulas (29) and (30) form a tridiagonal system, which can be solved efficiently by the pursuit method. Using formula (29) to find , The value of .

[0145] Step 302: The intermediate variable , Substituting into formulas (30) and (31), we can obtain the electric field components in the Laguerre domain: and The value of .

[0146] Step 303: The electric field component of the Laguerre domain and Substituting into formulas (7) to (9), we can obtain the magnetic field component in the Laguerre domain: .

[0147] The calculation order of the field expansion coefficient is: first solve implicitly , and then solve implicitly , and finally solve explicitly After finding the Laguerre basis expansion coefficient of the q-order electric field component, the q-order Laguerre basis expansion coefficient of the magnetic field component can be solved by using the explicit equation (18). Finally, the signal is restored to the time domain using formulas (2) to (4), and the electromagnetic field waveform at any point in the calculation domain at any time can be obtained.

[0148] Step 4: Obtain the electric field component and magnetic field component in the time domain based on the electric field component and magnetic field component in the Laguerre domain. Specifically, the electric field component and magnetic field component in the Laguerre domain are transformed into the electric field component and magnetic field component in the time domain by using the inverse process of the Laguerre orthogonal basis expansion.

[0149] The embodiment of the present invention takes the numerical simulation of a two-dimensional parallel plate waveguide as an example to verify the effect of the method of the present invention. The structure of the two-dimensional parallel plate waveguide is as follows: Figure 2 As shown, the overall size is 0.12m×0.5m, the interior is filled with air, the two parallel plates are regarded as perfect conductors (PEC), the excitation source is Gaussian pulse, and the calculation time is ns, Figure 2 Point p in is the observation point, and ABC is the absorbing boundary condition. The embodiments of the present invention respectively use the traditional FDTD algorithm, the traditional Laguerre basis algorithm (WLP-FDTD) and the method of the present invention to perform numerical simulation and calculate the time domain electromagnetic field component of the two-dimensional parallel plate waveguide.

[0150] Figure 3 are the electric field components of the observation points calculated using different methods It can be seen from the waveform that the waveform of the method of the present invention is in good agreement with that of the other three algorithms, indicating that the electromagnetic field calculation accuracy of the method of the present invention is maintained at a high level.

[0151] Table 1 shows the calculation time and memory usage of different methods. It can be seen from Table 1 that the method of the present invention is very effective in saving memory, which is only 3.5% of the traditional WLP-FDTD. In addition, the calculation efficiency of the method of the present invention is also greatly improved, and the calculation time is only 39.9% of the traditional WLP-FDTD.

[0152] Table 1

[0153]

[0154] Example 2

[0155] Based on the same inventive concept as Example 1, this embodiment introduces a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the time domain electromagnetic field calculation method introduced in Example 1 can be implemented.

[0156] In summary, the ADI algorithm of the present invention and the idea of ​​using the Laguerre basis expansion improve the traditional time-domain electromagnetic field calculation algorithm, and propose a two-dimensional WLP-FDTD algorithm based on differential operators. The Maxwell equations in the Laguerre domain are written in matrix form. By actively adding high-order small error terms, the calculation of the electric and magnetic field components is decoupled. The unknown field quantities in the constructed linear equations are all on a straight line, which geometrically reduces the dimension of the linear equations, greatly improves the calculation efficiency, and reduces memory consumption. Finally, by the method of alternating direction iteration, the size of the error term is made to approach zero, and the exact solution of the electromagnetic field component is obtained.

[0157] The present invention uses a two-dimensional WLP-FDTD based on a differential operator to perform time-domain electromagnetic field calculations, which is not restricted by the CFL stability condition, that is, it is unconditionally stable. The method of the present invention is based on the Laguerre basis function, and the time variable in the Maxwell equation is eliminated by transformation, so the calculation time is not affected by the selection of the time step, which greatly improves the calculation efficiency and shortens the calculation time; the calculation efficiency is very high. The method of the present invention decouples the solution process of the electric and magnetic fields, and compared with the traditional time-domain electromagnetic field calculation algorithm, it greatly reduces the matrix dimension, reduces the amount of calculation, and improves the calculation efficiency. At the same time, because the present invention achieves the effect of decoupling and dimensionality reduction, it greatly reduces the demand for computer memory. Therefore, the method of the present invention occupies very little memory resources for calculation, and can better adapt to the needs of actual applications.

[0158] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0159] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0160] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0161] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0162] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. A time domain electromagnetic field calculation method, characterized in that: The steps include: Construct a two-dimensional Maxwell equation system based on the electromagnetic field information in the application scenario; Transforming the two-dimensional Maxwell equations into a Maxwell equation in matrix form in a Laguerre domain; Adding a high-order small error term on one side of the Maxwell equation in matrix form to obtain a transformed Maxwell equation; Solving the transformed Maxwell equations using a step-by-step solution method to obtain the electric field component and the magnetic field component in the Laguerre domain; The electric field component and the magnetic field component in the time domain are obtained based on the electric field component and the magnetic field component in the Laguerre domain.

2. The time domain electromagnetic field calculation method according to claim 1, characterized in that: In a lossless, homogeneous, isotropic medium, the two-dimensional time-domain Maxwell equations are: ； in, is the dielectric constant, is the magnetic permeability, , are the components of the electric field in the electromagnetic field along the x and y directions, is the component of the magnetic field along the z direction in the electromagnetic field, , are the components of the current source along the x and y directions, x, y, z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

3. The time domain electromagnetic field calculation method according to claim 2, characterized in that: The step of transforming the two-dimensional Maxwell equations into a Maxwell equation in a matrix form in a Laguerre domain comprises: The two-dimensional Maxwell equations are expanded into the Laguerre domain using the Laguerre orthogonal basis, and three Maxwell equations in the Laguerre domain are obtained; The three Maxwell equations in the Laguerre domain are transformed into a matrix equation form by using a column vector construction method, thereby obtaining the Maxwell equations in the matrix form of the Laguerre domain.

4. The time domain electromagnetic field calculation method according to claim 3, characterized in that: The two-dimensional Maxwell equations are expanded into the Laguerre domain using the Laguerre orthogonal basis to obtain three Maxwell equations in the Laguerre domain, including: The electric field components and magnetic field components in the two-dimensional Maxwell equations are expanded using the Laguerre basis function to obtain the expanded Maxwell equations: ； ； ； in, represents the time domain electric field component in the x direction at time t and in r space, represents the time domain electric field component in the y direction at time t and in space r, represents the time domain magnetic field component in the z direction at time t and in r space, for Laguerre basis functions of order, , for Laguerre polynomial of order, s is the time factor, r is the space variable, e is the natural constant, , are the time domain electric field components , The p-order Laguerre coefficient, is the time domain magnetic field component The p-order Laguerre coefficient of Laguerre basis functions Satisfy the following formula: ； ； in, represents the q-order Laguerre basis function, is the Dirac function, represents any electric or magnetic field component at time t and space r, for The p-order Laguerre coefficient, for The k-order Laguerre coefficient of Substitute the expanded Maxwell equations into the two-dimensional Maxwell equations and multiply both sides of the Maxwell equations by the Laguerre basis function ,exist After integrating and sorting out, we get the three Maxwell equations in the Laguerre domain, which are expressed as follows: ； ； ； in, ； ； in, , are the time domain electric field components , The q-order Laguerre coefficient, is the time domain magnetic field component The q-order Laguerre coefficient, , are the time domain electric field components , The k-th order Laguerre coefficient, is the time domain magnetic field component The k-th order Laguerre coefficient, represents the time domain current source component in the x direction in the r space at time t, represents the time domain current source component in the y direction at time t and in r space, , They are the time domain current source components , The q-order Laguerre coefficient, To calculate the length of time.

5. The time domain electromagnetic field calculation method according to claim 4, characterized in that: The method of constructing a column vector transforms the three Maxwell equations in the Laguerre domain into a matrix equation to obtain the Maxwell equations in the matrix form of the Laguerre domain, including: Use the column vector construction method to construct the following variables: ， ； ， ； ， ； ， ； ； Among them, a and b are process coefficients, Reason The vector of unknown electric field components of order, the superscript T represents the transpose operation, Reason The vector of unknown electric field components of order, , is a custom matrix consisting of partial differential symbols, , Reason The vectors composed of known electric and magnetic field components below the order, Reason The vector composed of the order field source components; The three Maxwell equations in the Laguerre domain are written in matrix form according to the constructed variables: ； ； The formula Substitute into the formula , we can get the Maxwell equation in the matrix form of Laguerre domain, which is expressed as follows: ； Where I is the 6th-order identity matrix.

6. The time domain electromagnetic field calculation method according to claim 5, characterized in that: The high-order small error term is ,in, , .

7. The time domain electromagnetic field calculation method according to claim 6, characterized in that: The high-order small error term is added to one side of the Maxwell equation in the matrix form to obtain the transformed Maxwell equation, including: make , substituting into the Maxwell equation in matrix form in Laguerre domain, we get: ； Adding high-order small error terms to the left side of the Maxwell equations in matrix form in the Laguerre domain , we get the transformed Maxwell equations: ； Decomposing the transformed Maxwell equation into two equations, we get: ； ； in, is a non-physical intermediate variable, , is the Laguerre domain electric field component , The intermediate variable.

8. The time domain electromagnetic field calculation method according to claim 7, characterized in that: The transformed Maxwell equations are solved by using a step-by-step solution method to obtain the electric field component and the magnetic field component in the Laguerre domain, including: Substituting the variables constructed by the column vector method into the transformed Maxwell equations and expanding the equations yields: (a)； (b)； (c)； Wherein, the subscripts i and j represent the x and y coordinate values ​​of the field point, respectively; According to formula (a), solve the intermediate variable of the electric field in the Laguerre domain , ; The intermediate variable , Substituting the value of into formula (b) and (c), we can obtain the electric field component of the Laguerre domain and ; The electric field component of the Laguerre domain and Substituting into Maxwell's equation, we get the magnetic field component in the Laguerre domain .

9. The time domain electromagnetic field calculation method according to claim 1, characterized in that: The electric field component and the magnetic field component in the Laguerre domain are transformed into the electric field component and the magnetic field component in the time domain by using the inverse process of the Laguerre orthogonal basis expansion.

10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the time-domain electromagnetic field calculation method described in any one of claims 1-9 are implemented.

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