Electromagnetic field simulation method based on sublattice and single-step ADI-FDTD

Abstract

The application discloses an electromagnetic field simulation method based on a sub-grid and a single-step ADI-FDTD, and comprises the following steps: based on a single-step ADI-FDTD, a sub-grid and FDTD, an electromagnetic field simulation model is constructed by setting an absorbing boundary condition, a periodic boundary condition, a total field boundary condition and a scattered field boundary condition, wherein the electromagnetic field simulation model is used to simulate the electromagnetic field by selecting a detection point and a detection surface, obtaining a time-domain waveform diagram of an electric field of a reflection field and a transmission field of a simulation region, and obtaining frequency domain information of the simulation region; compared with a traditional FDTD algorithm, the method provided by the application can save 39.28% of memory in a simulation process, and can save 98.01% of calculation time.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of the finite-difference time-domain method of electromagnetic waves, in particular to an electromagnetic field simulation method based on a sub-grid and a single-step ADI-FDTD. BACKGROUND

[0002] A traditional finite-difference time-domain method (FDTD) is widely applied due to its advantages of easy programming, suitability for processing non-uniform media and dispersive media and the like. However, for simulation of a model with a micro complex structure or a high dielectric constant, a fine grid needs to be used for subdivision, which consumes huge computing resources. Meanwhile, due to the limitation of the CFL stability condition, the time step of the FDTD algorithm is very small, which leads to a relatively long simulation time.

[0003] In order to solve the problem of excessive computing resources caused by fine grid subdivision, a sub-grid technology is applied to the FDTD algorithm. The technology can be used for fine subdivision in a region with a micro complex structure or a high dielectric constant, and coarse grid subdivision in other regions. The method can save a large amount of computing resources, and then due to the limitation of the fine grid CFL condition, the time step is still small. In order to solve this problem, researchers have proposed a single-step alternating direction implicit (ADI) technology. The technology breaks through the limitation of the CFL stability condition and can be applied to the sub-grid technology, expands the time step of the fine grid, and makes the time step of the whole simulation region only subject to the limitation of the fine grid CFL condition. In order to combine the advantages of the two technologies, the sub-grid technology and the single-step ADI-FDTD technology are applied to the traditional FDTD algorithm, which can effectively reduce the computing resources and the computing time. Therefore, the combination of the FDTD and the sub-grid technology and the single-step ADI-FDTD technology is a key problem to be solved by researchers in the field. SUMMARY

[0004] In order to solve the above problems, the purpose of the application is to provide an electromagnetic field simulation method based on a sub-grid and a single-step ADI-FDTD, which is used for improving the simulation efficiency of a traditional FDTD algorithm for fine micro structures and high refractive index media and reducing computing resources.

[0005] In order to achieve the above technical purpose, the application provides an electromagnetic field simulation method based on a sub-grid and a single-step ADI-FDTD, which comprises the following steps:

[0006] Based on the single-step ADI-FDTD, the sub-grid and the FDTD, an electromagnetic field simulation model is constructed by setting an absorbing boundary condition, a periodic boundary condition, a total field boundary condition and a scattered field boundary condition, wherein the electromagnetic field simulation model is used for selecting a detection point and a detection surface, acquiring a time-domain waveform diagram of an electric field of a reflection field and a transmission field of a simulation region and frequency domain information of the simulation region, and simulating an electromagnetic field.

[0007] Preferably, in the process of constructing the electromagnetic field simulation model, based on single-step ADI-FDTD, a first coefficient matrix corresponding to the full electric conductor boundary form and a second coefficient matrix corresponding to the periodic boundary condition are obtained;

[0008] Based on the microstructure and high dielectric constant of the simulation region, according to the first coefficient matrix and the second coefficient matrix, the absorption boundary condition and the periodic boundary condition are generated respectively.

[0009] Preferably, in the process of constructing the electromagnetic field simulation model, by setting the total field boundary condition and the scattered field boundary condition, the plane wave source is obtained.

[0010] According to the plane wave source, the detection point and the detection surface are selected.

[0011] Preferably, in the process of constructing the electromagnetic field simulation model, the simulation process of the electromagnetic field simulation model includes the following steps:

[0012] Based on the simulation region, the sub-grid is set;

[0013] The first electric field component and the first magnetic field component of the coarse grid and the fine grid are initialized;

[0014] The first electric field component of the coarse grid is obtained by FDTD;

[0015] After obtaining the electric field component of the interface by single-step ADI-FDTD, it is transmitted to the fine grid by linear interpolation method, and the second electric field component and the second magnetic field component of the fine grid are obtained by using single-step ADI-FDTD;

[0016] The magnetic field component of the interface is obtained by weighting the second magnetic field component, and the second magnetic field component of the coarse network is obtained by using FDTD.

[0017] Preferably, in the process of constructing the electromagnetic field simulation model, based on Maxwell's equations, a two-step ADI-FDTD form is generated by alternating direction implicit format;

[0018] Based on the two-step ADI-FDTD form, a single-step ADI-FDTD is generated by algebraic operation.

[0019] Preferably, in the process of generating the two-step ADI-FDTD form, the two-step ADI-FDTD form includes a first time step and a second time step;

[0020] The first time step is represented as:

[0021]

[0022] The second time step is represented as:

[0023]

[0024] wherein E represents an electric field, H represents a magnetic field, epsilon and mu are permittivity and permeability respectively,

[0025]

[0026] Preferably, in the process of generating the single-step ADI-FDTD, the single-step ADI-FDTD is represented as:

[0027]

[0028] Preferably, in the process of generating the absorbing boundary condition and the periodic boundary condition, the first coefficient matrix is represented as:

[0029]

[0030] The second coefficient matrix is represented as:

[0031]

[0032] wherein,

[0033] Preferably, in the process of obtaining the frequency domain information of the simulation region, the time domain results of the detection surface are obtained, and the frequency domain information is generated through Fourier transform.

[0034] Preferably, in the process of simulating the electromagnetic field, the electromagnetic field simulation method is used in the form of a computer program, stored in a storage medium, and applied to a device with a simulation function to simulate the electromagnetic field.

[0035] The present application discloses the following technical effects:

[0036] Compared with the traditional FDTD algorithm, the method provided by the present application can save 39.28% of the memory in the simulation process, and can save 98.01% of the calculation time. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0038] Figure 1 is the FDTD algorithm flowchart of the hybrid sublattice technology and the ADI-FDTD technology described in the present application;

[0039] Figure 2 is a schematic diagram of the coarse-fine grid interface and interpolation according to the present application (two-dimensional schematic diagram);

[0040] Figure 3 is a schematic diagram of the coarse-fine grid interface and weighted H z is a schematic diagram (three-dimensional schematic diagram);

[0041] Figure 4 is a schematic diagram of the simulation region and frequency selective surface structure according to the present application;

[0042] Figure 5 is a time-domain waveform diagram of the E z component of the reflection field region according to the present application;

[0043] Figure 6 is a time-domain waveform diagram of the E z component of the transmission field region according to the present application;

[0044] Figure 7 is a transmission coefficient and reflection coefficient of the frequency selective surface according to the present application. DETAILED DESCRIPTION

[0045] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0046] As shown in Figures 1-7 , the present application provides an electromagnetic field simulation method based on sub-grid and single-step ADI-FDTD, comprising the following steps:

[0047] Based on single-step ADI-FDTD, sub-grid and FDTD, an electromagnetic field simulation model is constructed by setting an absorbing boundary condition, a periodic boundary condition, a total field boundary condition and a scattered field boundary condition, wherein the electromagnetic field simulation model is used to simulate the electromagnetic field by selecting a detection point and a detection surface to obtain a time-domain waveform diagram of the electric field of the reflection field and the transmission field of the simulation region, and frequency domain information of the simulation region.

[0048] Preferably, in the process of constructing the electromagnetic field simulation model, based on single-step ADI-FDTD, a first coefficient matrix corresponding to a complete electric conductor boundary form and a second coefficient matrix corresponding to a periodic boundary condition are obtained;

[0049] Based on the microstructure and high dielectric constant of the simulation region, according to the first coefficient matrix and the second coefficient matrix, an absorbing boundary condition and a periodic boundary condition are respectively generated.

[0050] Preferably, in the process of constructing the electromagnetic field simulation model, a plane wave source is obtained by setting a total field boundary condition and a scattered field boundary condition.

[0051] According to the plane wave source, a detection point and a detection surface are selected.

[0052] Preferably, in the process of constructing the electromagnetic field simulation model, the simulation process of the electromagnetic field simulation model includes the following steps:

[0053] Based on the simulation region, a sub-grid is set;

[0054] The first electric field component and the first magnetic field component of the coarse grid and the fine grid are initialized;

[0055] The first electric field component of the coarse grid is obtained by FDTD;

[0056] After obtaining the electric field component of the interface by single-step ADI-FDTD, it is transmitted to the fine grid by linear interpolation method, and the second electric field component and the second magnetic field component of the fine grid are obtained by using single-step ADI-FDTD;

[0057] The magnetic field component of the interface is obtained by weighting the second magnetic field component, and the second magnetic field component of the coarse network is obtained by using FDTD.

[0058] Preferably, in the process of constructing the electromagnetic field simulation model, based on Maxwell's equations, a two-step ADI-FDTD form is generated by alternating direction implicit format;

[0059] Based on the two-step ADI-FDTD form, a single-step ADI-FDTD is generated by algebraic operation.

[0060] Preferably, in the process of generating the two-step ADI-FDTD form, the two-step ADI-FDTD form includes a first time step and a second time step;

[0061] The first time step is represented as:

[0062]

[0063] The second time step is represented as:

[0064]

[0065] wherein E represents an electric field, H represents a magnetic field, and ε and μ are permittivity and permeability, respectively,

[0066]

[0067] Preferably, in the process of generating the single-step ADI-FDTD, the single-step ADI-FDTD is represented as:

[0068]

[0069] Preferably, in the process of generating the absorbing boundary condition and the periodic boundary condition, the first coefficient matrix is represented as:

[0070]

[0071] The second coefficient matrix is represented as:

[0072]

[0073] wherein,

[0074] Preferably, in the process of obtaining the frequency domain information of the simulation region, the time domain results of the detection surface are obtained, and the frequency domain information is generated through Fourier transform.

[0075] Preferably, in the process of simulating the electromagnetic field, the electromagnetic field simulation method is used in the form of a computer program, stored in a storage medium, and applied to a device with a simulation function to simulate the electromagnetic field.

[0076] Embodiment 1: The present application provides a high-efficiency FDTD method based on sub-grid technology and single-step ADI technology. The method aims to reduce the resource consumption of the traditional FDTD algorithm and reduce the simulation time of the traditional FDTD algorithm. Starting from the alternating direction implicit format, first, the iteration formula of the single-step ADI-FDTD is given, second, considering the combination with the sub-grid, the coefficient matrix corresponding to the PEC boundary and the PBC boundary is given, then the interpolation method of coarse and fine grids is provided, finally, according to the characteristics of the sub-grid, the iteration formula of the electric field on the coarse-fine interface is provided, and finally, the accuracy and efficiency of the provided algorithm are verified by a frequency selective surface example. By recording the time domain waveforms of the electric field in the total field region and the scattering field region and the S parameters of the frequency selective surface, the accuracy of the proposed algorithm is proved, and by giving the memory occupation and time consumption of the traditional FDTD algorithm and the proposed algorithm, the efficiency of the proposed algorithm is proved.

[0077] Figure 1 is the flow chart of the FDTD algorithm combining the proposed hybrid sub-grid technology and ADI-FDTD technology, which specifically includes steps S01-S08:

[0078] S01 initialization of E in coarse grid t , H in fine grid t+1 / 2 ; t , h t+1 / 2 ;

[0079] S02 calculation of E in coarse grid using traditional FDTD t+1 ;

[0080] S03 calculation of E on interface between coarse and fine grids using modified FDTD t+1 ;

[0081] S04 transfer of E on interface between coarse and fine grids by linear interpolation

[0082] S05 calculation of e, h in fine grid using ADI-FDTD t+1 , h t+3 / 2 ;

[0083] S06 obtain H on interface between coarse and fine grids by h t+3 / 2 ; t+3 / 2 ;

[0084] S07 calculation of H in coarse grid using traditional FDTD t+3 / 2 ;

[0085] S08 judge whether to end loop iteration.

[0086] wherein E and H represent electric field and magnetic field in coarse grid, e and h represent electric field and magnetic field in fine grid, superscript represents time step.

[0087] In the embodiment, firstly, Maxwell equations are given as follows:

[0088]

[0089]

[0090] ε and μ are dielectric constant and magnetic permeability respectively, matrix A and matrix B are as follows:

[0091] and

[0092] wherein x, y and z represent three directions of space.

[0093] By alternating direction implicit format, the above Maxwell equations (1) can be written into two-step ADI-FDTD form, first sub-time step is:

[0094]

[0095]

[0096] The second sub-time step is:

[0097]

[0098]

[0099] By algebraic operation, the two-step ADI-FDTD can be converted into a single-step ADI-FDTD form:

[0100]

[0101]

[0102] The discrete forms of the electric field E x and the magnetic field H x can be obtained from the single-step ADI-FDTD form:

[0103]

[0104]

[0105] The electric field and magnetic field components in the y direction and the z direction can also be obtained in the same way.

[0106] The coefficient matrix on the left side of formula (5) is a tri-diagonal matrix, and has the following form:

[0107]

[0108] Wherein,

[0109] For this embodiment, since the ADI-FDTD technique needs to be combined with the sub-grid technique, and the periodic arrangement of the frequency selective surface is considered, the Λ matrix in the PEC boundary form and the periodic boundary form need to be used, which are respectively

[0110] and

[0111] The sub-grid technique used in the present application will be described in detail below according to Figure 2 and Figure 3

[0112] ​The traditional FDTD algorithm generally uses a uniform Yee grid to subdivide the target, which results in the need to use a fine grid to subdivide the target when the size of the target is too small, and eventually leads to too large memory occupation and too long simulation time of the entire simulation program. The sub-grid used in the present example has two advantages, one is that the iteration of the electric field and the magnetic field in the entire coarse grid region is not needed, and the other is that the values of the fine grid do not need to be inserted into the coarse grid. The interpolation method used in the present example is as shown in Figure 2 The specific implementation process is as follows:

[0113] When the electric field positions of the coarse and fine grids coincide:

[0114] e x2 = E x2 , e x11 = E x5 (7)

[0115] When the electric field positions of the coarse and fine grids do not coincide:

[0116]

[0117]

[0118]

[0119] For the calculation of the electric field on the interface, the traditional FDTD formula can be used, but the spatial step needs to be modified. Taking E x as an example

[0120]

[0121] Wherein is the ratio of the coarse and fine grids, C k is the coefficient of the magnetic field in each fine grid in the weight matrix. Corresponding to Figure 3 four cases, the coefficient matrix C has the following four forms:

[0122]

[0123]

[0124]

[0125]

[0126] In order to verify the correctness and efficiency of the algorithm, the present example takes a frequency selective surface as an example, and uses the traditional FDTD algorithm and the algorithm proposed in the present example to calculate the time-domain waveforms of the reflected and transmitted electric fields and the transmission and reflection coefficients of the frequency selective surface. The size of the frequency selective surface is as shown in Figure 4 The specific size is Lx = 0.15mm, L z = 0.12mm, L y = 0.3mm, h = 0.01mm, d = 0.1mm, w = 0.2mm, a = 0.02mm. The y direction uses 11 layers of CPML absorbing boundary to model infinite space, and the x direction and z direction use periodic boundary conditions. The plane wave with cosine modulation is introduced by the total field / scattered field boundary, and the specific expression of the source is as follows:

[0127]

[0128] Where f c = 1.25GHz, tau = 1.28ns, t0 = 4*tau.

[0129] For the sake of clear expression, CFLN = At / At CFL , At CFL is the time step of the traditional FDTD under the CFL condition. It can be seen from Figure 5 , Figure 6 and Figure 7 that the results obtained by the algorithm provided by the present application and the traditional FDTD algorithm are basically consistent. When CFLN = 1, the results of the algorithm provided by the present application and the traditional FDTD algorithm are almost completely consistent. With the increase of CFLN, the numerical error increases. Therefore, for the algorithm provided by the present application, the trade-off between efficiency and accuracy is needed.

[0130] In order to clearly illustrate the advantages of the algorithm provided by the present application in saving computing resources and computing time, Table 1 shows the comparison results of the memory and computing time required by the algorithm provided by the present application and the traditional FDTD.

[0131] Table 1

[0132]

[0133] It can be seen from Table 1 that, compared with the traditional FDTD, when CFLN = 5, the algorithm provided by the present application can save 39.28% of the memory, and can save 98.01% of the computing time.

[0134] The computer program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other processing device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other processing device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions specified in the flowchart block or blocks or in conjunction with the flowcharts and / or block diagram. Figure 1 one or more of the blocks or steps in the flowchart or block diagram. Figure 1 one or more of the blocks or steps in the flowchart or block diagram.

[0135] In the description of the present application, it is to be understood that the terms "first", "second", "third" and the like, merely identify features belonging to distinct categories, and do not imply or imply a relative importance or a specific number thereof. Thus, a feature identified as "first" or "second" can implicitly or explicitly include one or more of the features. In the description of the present application, the meaning of "a plurality" is two or more, unless otherwise expressly specified.

[0136] Obviously, various modifications and changes can be made to the present application by those skilled in the art without departing from the spirit and scope of the present application. Thus, it is intended that the present application also include such modifications and changes insofar as they come within the scope of the claims of the present application and their equivalents.

Claims

1. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD is characterized by: The following steps are involved: Based on single-step ADI-FDTD, subgrid, and FDTD, an electromagnetic field simulation model is constructed by setting absorption boundary conditions, periodic boundary conditions, total field boundary conditions, and scattered field boundary conditions. The electromagnetic field simulation model is used to simulate the electromagnetic field by selecting detection points and detection surfaces to obtain time domain waveforms of the electric field of the reflected field and the transmitted field in the simulation area, as well as frequency domain information of the simulation area; In the process of constructing the electromagnetic field simulation model, based on single-step ADI-FDTD, the first coefficient matrix corresponding to the perfect electric conductor boundary form and the second coefficient matrix corresponding to the periodic boundary condition are obtained; Based on the microstructure and high dielectric constant of the simulation area, the absorbing boundary condition and the periodic boundary condition are generated according to the first coefficient matrix and the second coefficient matrix respectively; In the process of constructing the electromagnetic field simulation model, a plane wave source is obtained by setting the total field boundary condition and the scattered field boundary condition; Selecting the detection point and the detection surface according to the plane wave source; The first coefficient matrix is ​​expressed as: The second coefficient matrix is ​​expressed as: in, 2. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 1, characterized in that: In the process of constructing the electromagnetic field simulation model, the simulation process of the electromagnetic field simulation model includes the following steps: Setting the subgrid based on the simulation area; Initialize the first electric field component and the first magnetic field component of the coarse grid and the fine grid; Obtaining a first electric field component of the coarse grid by FDTD; After obtaining the electric field component of the interface through the single-step ADI-FDTD method, the electric field component is transferred to the fine grid through a linear interpolation method, and the second electric field component and the second magnetic field component of the fine grid are obtained using the single-step ADI-FDTD method; The magnetic field component of the interface is obtained by weighting the second magnetic field component, and the second magnetic field component of the coarse grid is acquired using the FDTD method.

3. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 2, characterized in that: In the process of building the electromagnetic field simulation model, the two-step ADI-FDTD form is generated based on Maxwell's equations through the alternating direction implicit format; Based on the double-step ADI-FDTD form, the single-step ADI-FDTD is generated through algebraic operations.

4. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 3, characterized in that: In generating a two-step ADI-FDTD formalism, the two-step ADI-FDTD formalism includes a first time step and a second time step; The first time step is expressed as: The second time step is expressed as: Where E represents the electric field, H represents the magnetic field, ε and μ are the dielectric constant and magnetic permeability, respectively.

5. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 4, characterized in that: In the process of generating the single-step ADI-FDTD, the single-step ADI-FDTD is expressed as:

6. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 5, characterized in that: In the process of obtaining the frequency domain information of the simulation area, the time domain result of the detection surface is obtained, and the frequency domain information is generated through Fourier transform.

7. The electromagnetic field simulation method based on subgrid and single-step ADI-FDTD according to claim 6, characterized in that: In the process of simulating the electromagnetic field, the electromagnetic field simulation method is used to be stored in a storage medium in the form of a computer program, and is applied to a device with a simulation function to simulate the electromagnetic field.

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