MW-FDTD method based on bidirectional movement

Abstract

The invention discloses an MW-FDTD (Multi-Well Frequency Division Time Division) method based on bidirectional movement. The method comprises the following steps: calculating and detecting an energy ratio in a sliding window; determining the forward movement of a forward sliding window and the generation of a backward sliding window according to the energy detection boundary; when a medium with a strong reflection characteristic is processed, the improvement of the calculation cost of the traditional MW-FDTD is often not in direct proportion to the improvement of the precision, the method can generate a sliding window which moves backwards to continue to track reflected waves, the simulation precision can be remarkably improved, meanwhile, the high calculation efficiency is kept, and the method is suitable for large-scale popularization and application. And an accurate and efficient simulation method is provided for propagation of electromagnetic waves in a complex medium environment.

Description

Technical Field

[0001] The present invention relates to electromagnetic wave propagation simulation technology, in particular to an improved technology based on the MovingWindow–Finite Difference Time Domain (MW-FDTD) method, which is used to solve the problem of efficient simulation of electromagnetic wave propagation in complex media environments. The technology is particularly suitable for simulation scenarios with strong reflective media, such as wireless communication channel modeling in urban low-altitude economy and analysis of radio wave propagation characteristics in forest environments. Background Art

[0002] The Moving Window–Finite Difference Time Domain (MW-FDTD) method is based on FDTD and performs sliding calculations in the entire problem space by setting up a sliding window. This method only solves the Maxwell equations in the area containing the main pulse energy (i.e., the sliding window) at each time step, rather than the entire calculation domain. This processing method can still ensure the accuracy of the simulation results and reduce computing resources.

[0003] The MW-FDTD method is widely used to simulate wave propagation in irregular terrain due to its high efficiency. For example, this method shows good calculation results when it comes to long-distance propagation problems on rough sea surfaces, complex forest terrains, and complex urban environments. However, when faced with media that exhibit obvious specular reflection characteristics in the problem space, the effectiveness of the MW-FDTD method may be restricted by the size of the moving window. This limitation may ignore the calculation of reflected waves, thereby reducing the accuracy of the simulation results and narrowing the applicability of the method. In addition, to ensure the accuracy of the calculation, the traditional MW-FDTD needs to increase the size of the sliding window, which reduces the calculation efficiency. Often, this improvement in accuracy is not proportional to the increase in time consumption.

[0004] This patent aims to solve the problem that when traditional MW-FDTD simulates and calculates strong reflection scenes, it is easily neglected due to the limitation of sliding window size, resulting in decreased accuracy. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a MW-FDTD method based on bidirectional movement, which takes into account the high efficiency of the sliding window method and the high accuracy of the FDTD method.

[0006] To achieve the above object, the present invention provides the following method:

[0007] A MW-FDTD method based on bidirectional movement includes:

[0008] Set the size of the forward sliding window, the size of the backward sliding window, and the number of grids that the sliding window moves at a time;

[0009] According to the electromagnetic field iteration in the sliding window, the field energy proportion in the window is calculated in each time step;

[0010] Buffer grids are set at both sides of the sliding window's moving direction, and an energy detection boundary is set to determine whether the electromagnetic wave in the sliding window reaches the sliding window boundary, so as to determine the movement of the sliding window.

[0011] According to the energy proportion of the energy detection boundary, the determination mechanism of the forward sliding window moving forward and the generation of the backward sliding window is set. Specifically, the forward sliding window has a determination mechanism for moving forward and a determination mechanism for generating the backward sliding window, while the backward sliding window only has a determination mechanism for moving backward;

[0012] Backward sliding window generation, including:

[0013] The electromagnetic field components in the forward sliding window are copied to the backward sliding window to continue iterative calculation, and when a backward sliding window exists, the forward sliding window will not continue to trigger the generation mechanism of the backward sliding window.

[0014] A closing mechanism of the backward sliding window is set according to the total energy in the backward sliding window and the total energy during replication;

[0015] According to the energy proportion in the backward sliding window, the sliding window triggers backward movement according to the set sliding window movement mechanism until the backward sliding window is closed; BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of the MW-FDTD method based on bidirectional movement of the present invention;

[0017] Figure 2 It is the XZ section of the sliding window and the schematic diagram of its internal structure;

[0018] Figure 3 It is a principle diagram of the MW-FDTD method based on bidirectional movement of the present invention;

[0019] Figure 4 This is a schematic diagram of the simulation space of Example 1;

[0020] Figure 5 It is the energy proportion diagram in the forward sliding window at different time steps;

[0021] Figure 6 This is the energy ratio diagram in the forward sliding window when strong reflection occurs;

[0022] Figure 7 is the sampled electric field E of different FDTD methods in Example 1 s1 Comparison chart;

[0023] Figure 8 This is a schematic diagram of the simulation space of Example 2;

[0024] Fig. 9 is the sampled electric field E of different FDTD methods in Example 2 s1 Comparison chart;

[0025] Fig.10 is the sampled electric field E of different FDTD methods in Example 2 s2 Comparison chart;

[0026] Fig.11 is the sampled electric field E of different FDTD methods in Example 2 s3 Comparison chart; DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. The given embodiments are only part of the application scenarios of the present invention, rather than all the embodiments.

[0028] like Figure 1 FIG. 1 is a flow chart of the MW-FDTD method based on bidirectional movement of the present invention, which includes:

[0029] Step 101: Set relevant parameters of the solution scenario.

[0030] In this stage, it is necessary to define the problem to be solved, including the absorbing boundary conditions, the type of excitation signal source, the solution frequency, the spatial position of the target object and its medium parameters, so as to complete the state initialization stage of the MW-FDTD based on bidirectional movement.

[0031] Step 102: Set basic parameters of the sliding window.

[0032] Before simulation calculation, it is necessary to set the size of the forward sliding window in its moving direction. nx m , the size of the backward sliding window in its moving direction nx b , and the size in the other two directions is consistent with the entire simulation space. The number of grids that the sliding window moves each time M , and the number of buffer grids nx buffer The role of the buffer grid is to reserve a certain number of fault-tolerant grids, advance the energy detection boundary determination mechanism, and ensure the stable operation of the sliding window movement mechanism. The internal structure of the sliding window is as follows: Figure 2 As shown. It is worth noting that the forward sliding window has buffer grids on both sides, while the backward sliding window has a buffer grid only on the side of its moving direction. After setting the relevant sliding window parameters, the electromagnetic parameters of the corresponding position in the entire simulation space are converted to the sliding window, and the FDTD calculation is performed in the sliding window instead of the entire problem space, and the sliding window will be moved in the direction of wave propagation.

[0033] Step 103: Perform iterative calculation of the field value at each time step.

[0034] After setting the FDTD related parameters, the iterative calculation of the electromagnetic field components of the traditional FDTD is performed.

[0035] Step 104: Calculate the energy ratio in the sliding window at each time step.

[0036] In each time step iterative calculation, the energy proportion inside the sliding window is calculated according to the electric field and magnetic field components in the sliding window. Assuming that the propagation direction of the wave is the x direction, the energy proportion function P ( x ) is calculated as shown in formula (1). P ( x ) is a function of the energy proportion of the grid position in the sliding window, indicating the x The ratio of the energy of a grid position to the total energy of the sliding window.

[0037] (1)

[0038] Step 105: Control the forward movement of the forward sliding window and the generation of the backward sliding window according to the determination condition of the energy detection boundary.

[0039] In each time step, a judgment is made at the energy detection boundary. The judgment formulas for the forward movement of the forward sliding window and the backward movement of the backward sliding window are shown in (2), where: nx m represents the grid size of the forward sliding window in the moving direction, nx buffer Indicates the size of the buffer grid, a Indicates the decision threshold required for sliding window movement.

[0040] (2)

[0041] Buffer Grid nx buffer The value of will slightly affect the accuracy and efficiency of the calculation. nx bufferThe larger the value, the more accurate the result will be, because enough grids will be reserved and the electromagnetic energy leakage will be less, but it will affect the efficiency of the calculation. a The value of should be greater than zero, because before the wave front reaches the boundary, the energy ratio is almost negligible. In order to reduce the influence of clutter on the moving window judgment, it is recommended to a The value is set between 0% and 1%.

[0042] The generation decision formula of the backward sliding window is shown in (3), and the decision is performed in the forward sliding window.

[0043] (3)

[0044] When the backward sliding window is generated, the corresponding field component is copied from the forward sliding window to the backward sliding window to continue the backward iterative calculation. The size of the copied field component is equal to the size of the backward sliding window. At this time, the total energy of the copied field component is recorded as P copy , the calculation formula is shown in (4), where E copy Represents the replicated field component.

[0045] (4)

[0046] The decision formula for closing the backward sliding window is shown in (5), where E back represents the field component within the backward sliding window, coff Indicates the energy attenuation ratio, and the recommended value is between 0 and 1.

[0047] (5)

[0048] The principle diagram of the MW-FDTD method based on bidirectional movement of the present invention is as follows Figure 3 shown.

[0049] In order to make the advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation examples.

[0050] Embodiment 1:

[0051] This embodiment provides an application scenario of a single tree. The schematic diagram of the simulation model is as follows: Figure 4As shown. A simulation experimental space with a size of 20m×5m×8m was constructed to simulate the propagation characteristics of electromagnetic waves in an environment containing a single tree model. The maximum frequency of the Gaussian pulse signal used was set to 0.3GHz. The signal transmission point Tx is located at the coordinates (1m, 2m, 6.5m), while the electric field sampling point Es1 is located at (5m, 2m, 6.5m). The tree model is composed of cubes and cylinders. Based on the Monte Carlo idea, cubes are randomly generated to simulate the morphology of natural trees. The size of the cube is equivalent to a single Yee grid unit, that is, 0.66m×0.66m×0.66m, and its relative dielectric constant is set to 34.81-13.76j. The coordinates of the center of the bottom circle of the cylinder are (9m, 2m, 0m), the bottom radius is 0.15m, the height is 5m, and its relative dielectric constant is set to 18.90-7.49j. By constructing this tree model, simulation experiments can reflect the propagation of electromagnetic waves in environments with natural obstacles such as trees, providing a certain experimental basis for a deeper understanding of the propagation mechanism of electromagnetic waves in complex media.

[0052] The simulation experiments were carried out using traditional FDTD, traditional MW-FDTD and the bidirectional MW-FDTD method of the present invention. The simulation settings are as follows: the grid size of the entire problem space is 326×101×146, the grid size of the forward sliding window is 163×101×146, and the grid size of the backward sliding window is 106×101×146, where nx m =163, nx buffer =10, a =0.5%, coff =0.5, M =40, that is, the number of buffer grids of the sliding window is 10, the decision threshold of the sliding window movement is 0.5%, when the total energy in the backward sliding window decays to half of the total energy when the reflected signal is replicated, the backward sliding window is closed, and the number of grids that the sliding window moves each time is 40.

[0053] It can be observed that during the simulation process of the method of the present invention, the energy proportions at time steps 235 and 294 are as follows: Figure 5 As shown; and when the electromagnetic wave propagates to the location of the tree, its energy distribution diagram changes, as shown Figure 6 As shown. By calculating the energy proportion distribution in the sliding window, the movement of the sliding window can be controlled according to formulas (2) and (3).

[0054] The comparison of simulation results of three FDTD methods at sampling points is shown in the figure below. Figure 7As shown, it can be clearly observed that the advantages of the method of the present invention compared with the traditional MW-FDTD, the simulation results of the method of the present invention are very consistent with the results of the traditional FDTD, while the traditional MW-FDTD did not obtain ideal results at the sampling points, and the comparison of the computational cost and accuracy of the three FDTD algorithms is shown in Table 1.

[0055] Table 1 Comparison of calculation cost and accuracy of different FDTD methods in Example 1

[0056]

[0057] Embodiment 2:

[0058] This embodiment provides an application scenario of multiple trees. The schematic diagram of the simulation model is as follows: Figure 8 As shown. A problem space size of 36m×5m×8m is constructed, and a refined tree model is established. The coordinates of the transmitting point Tx are (1m, 2m, 6.5m), the coordinates of the sampling points Es1, Es2, and Es3 are (5m, 2m, 6.5m), (15m, 2m, 6.5m), and (25m, 2m, 6.5m), respectively. The maximum frequency of the Gaussian pulse signal is 0.3GHz. The tree model is composed of a combination of cubes and cylinders, where the size of the cube is the size of a single Yee grid, that is, 0.66m×0.66m×0.66m, and the relative dielectric constant is 34.81-j13.76; the coordinates of the center of the bottom circle of the cylinder are (11m, 2m, 0m), the radius of the cylinder is 0.15m, the height is 5m, and the relative dielectric constant is 18.90-j7.49. The interval between each tree is 10m.

[0059] The traditional FDTD, traditional MW-FDTD and the bidirectional MW-FDTD method of the present invention are used for simulation respectively. The grid size of the entire problem space is divided into 566×101×146. The grid size of the forward moving window of the traditional MW-FDTD and bidirectional MW-FDTD is set to 163×101×146, and the grid size of the backward sliding window is 106×101×146. nx m =163, nx buffer =10, a =0.5%, coff =0.5, M =40.

[0060] The comparison of simulation results of three FDTD methods at three sampling points is shown in the figure below. Figures 9 to 11As shown, it can also be observed that the method of the present invention has advantages over the traditional MW-FDTD. The simulation results of the method of the present invention clearly include the calculation of the reflected wave, and are highly consistent with the results of the traditional FDTD. The traditional MW-FDTD under the same setting does not effectively calculate the reflected wave, and the calculation results are less accurate. Specifically, the root mean square errors of the electric field curves obtained by the traditional FDTD method and the traditional MW-FDTD method are 9.96e-4, 3.30e-4, and 1.28e-4, respectively, while the root mean square errors of the sampled electric field curves obtained by the traditional FDTD method and the bidirectional MW-FDTD method have been significantly reduced to 2.45e-4, 8.45e-5, and 2.37e-5, respectively.

[0061] The comparison of the computational cost and accuracy of the three FDTD algorithms is shown in Table 2. According to the data in the table, it can be observed that the method of the present invention is more effective in dealing with strong reflection problems than the traditional MW-FDTD method.

[0062] Table 2 Comparison of calculation cost and accuracy of different FDTD methods in Example 2

[0063]

[0064] This article explains the working principle and implementation method of the present invention in detail through specific examples, aiming to help readers better understand the technical means and core concepts of the present invention. It should be emphasized that these examples are only used as auxiliary explanations and do not represent all application scenarios of the present invention. For professionals in this field, they can appropriately adjust and optimize the specific implementation methods and application scopes based on the core ideas of the present invention.

Claims

1. A MW-FDTD method based on bidirectional movement, the simulation method comprising: Calculate the energy proportion distribution within the sliding window; Set up the buffer grid and set the energy detection boundaries; According to the calculated energy proportion distribution, the energy detection boundary is used to control the forward movement of the forward sliding window and the generation of the backward sliding window; The closing of the backward sliding window is determined according to the total energy attenuation of the backward sliding window; The characteristic is that when the bidirectional moving MW-FDTD method simulates and calculates problems with strongly reflective media, when the forward sliding window size is not enough to satisfy the reflection wave calculation, an additional backward sliding window can be automatically generated to track and calculate the meaningful reflection wave. Under the same sliding window setting, the proposed method has higher accuracy and efficiency than the traditional MW-FDTD method.

2. The energy detection boundary according to claim 1 is used to control the forward movement of the forward sliding window and the generation of the backward sliding window, characterized in that: While the sliding window is moving, it is necessary to record the number of grids that the sliding window has moved N , which is used to calculate the conversion relationship between the local position of the electromagnetic parameters inside the sliding window and the overall problem space. In the direction of wave propagation, the position of the electromagnetic parameter position (1,2,3,...,nx) in the sliding window in the overall problem space can be expressed as N +(1,2,3,...,nx).

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