FDTD-RT method for simulating broadband electromagnetic environment of large-scale target

Abstract

The invention relates to an FDTD-RT method for simulating a broadband electromagnetic environment of a large-scale target, belongs to the technical field of computational electromagnetics, and solves the technical problems of low simulation solution precision and long time consumption of the broadband electromagnetic environment of the large-scale target. The FDTD-RT method comprises the following steps of: decomposing broadband into a radio field to form time harmonic superposition of different frequency components; according to a target size and an electromagnetic wave wavelength, dividing into low frequency and high frequency according to threshold frequency; solving a low-frequency time-domain incident wave, simulating by using an FDTD method, solving a low-frequency time-domain waveform, and obtaining a low-frequency component; simulating and solving the high-frequency time domain waveform by using an RT method to obtain a high-frequency component; and adding the low-frequency component and the high-frequency component to obtain a whole time domain waveform. The FDTD-RT method is used for broadband electromagnetic environment simulation of a large-scale target.

Description

Technical Field

[0001] The invention belongs to the technical field of computational electromagnetics, and in particular relates to a FDTD-RT method for simulating a broadband electromagnetic environment of a large-scale target. Background Art

[0002] The study of the interaction between broadband electromagnetic pulses and large-scale targets is of great significance in the fields of remote sensing, communication, and military. The numerical calculation of the target electromagnetic environment mainly includes low-frequency full-wave methods and high-frequency approximate methods. Low-frequency full-wave methods mainly include finite-difference time domain (FDTD), finite element method, moment method, etc. High-frequency approximate methods mainly include geometric optics, geometric diffraction theory, physical optics, physical diffraction theory, ray tracing method (RT), etc.

[0003] The low-frequency full-wave method has the advantages of high accuracy and good versatility, but as the scale of the calculation target increases, it faces bottlenecks such as large computing storage, large memory requirements, long calculation time, or even incomputation. If the large-scale target has an electrically large scale (on the order of one hundred wavelengths) for the high-frequency components in a wide band, it is difficult to calculate using the low-frequency full-wave algorithm. The high-frequency approximation method has the advantages of fast calculation speed and low memory requirements, but its scope of application is limited. It requires the target size to be much larger than the wavelength of the electromagnetic wave, and the solution accuracy of the low-frequency components in the wide band may not meet the requirements. There are limitations to using the low-frequency full-wave method or the high-frequency approximation method alone to solve large-scale complex targets. Take the IEC standard wide-band incident wave as an example. The frequency range of the IEC standard waveform is 0 to 300MHz. Assuming the simulation area is 500m×500m×100m, if a low-frequency full-wave method is used, such as FDTD, the spatial discrete interval is taken as λ m / 20,λ m = 1m is the wavelength corresponding to the highest frequency of 300MHz, so the number of grids required is 10000×10000×2000=2×10 11 , FDTD cannot calculate such a large number of grids; if the high-frequency method is used, the low-frequency component of IEC cannot meet the requirements of the high-frequency approximation method for the calculation target size.

[0004] A large number of scholars have improved traditional computational electromagnetics methods to improve computational efficiency and scale. Zhang Qilin, Luebbers, and others proposed a moving window FDTD method, which only processes field iterations within a specific window in each time step, and realizes large-scale full-domain calculations by continuously moving windows. This method is widely used in electromagnetic wave propagation problems, but cannot effectively calculate electromagnetic scattering problems. Z. Lai, S. Sun, and others proposed a regional decomposition method, which decomposes the original calculation area into several sub-areas, solves each sub-area separately and then integrates them, but needs to solve the coupling problem between sub-areas. Guo Lixin, Wang Ying, WCChew, and others proposed a hybrid method to solve the problem of electrically large size. The hybrid method achieves high efficiency or high precision by taking advantage of the strengths of different algorithms. At present, hybrid methods are generally mixed in the airspace, and different calculation methods are used in different spatial regions. They are suitable for calculating multi-scale targets, but difficult to use for calculating the broadband electromagnetic environment of large-scale targets. Summary of the invention

[0005] In order to overcome the shortcomings of low solution accuracy and long time consumption in the simulation of broadband electromagnetic environment of large-scale targets, the present invention proposes an FDTD-RT method for simulating broadband electromagnetic environment of large-scale targets.

[0006] The technical solution adopted by the present invention to solve the technical problem is:

[0007] An FDTD-RT method for simulating a wide-band electromagnetic environment of a large-scale target includes the following steps:

[0008] Step 1: Incident pulse frequency decomposition

[0009] The broadband incident electric field is decomposed into the time-harmonic superposition of different frequency components.

[0010] Step 2: Frequency range division

[0011] According to the target size and the wavelength of the electromagnetic wave, the frequency range is divided into low frequency and high frequency according to the threshold frequency of low frequency and high frequency.

[0012] Step 3: Solve for low-frequency components

[0013] Obtain the low-frequency time-domain incident wave, use the FDTD method to simulate, solve the low-frequency time-domain waveform, and obtain the low-frequency component.

[0014] Step 4: Solve for high frequency components

[0015] Use the RT method to simulate and solve the high-frequency time domain waveform to obtain the high-frequency component.

[0016] Step 5: Obtain the entire time domain waveform

[0017] Add the low-frequency component to the high-frequency component to obtain the entire time domain waveform.

[0018] In the above FDTD-RT method, the step 1, incident pulse frequency decomposition, further comprises:

[0019] The broadband incident electric field is E inc (t), the duration is [0, T p According to Fourier transform, the incident wave E inc (t) is decomposed into the superposition of harmonics of different frequency components, and the calculation formula is as follows:

[0020]

[0021] In formula (1), f k is the frequency of the time harmonic, f k = k / T p ; k is an integer, k min is the k value corresponding to the lowest frequency, k max is the k value corresponding to the highest frequency; a k f k The amplitude is the frequency, and t is the time.

[0022] In the above FDTD-RT method, the step 2, frequency range division, further comprises:

[0023] For an object of scale L, determine the threshold frequency X for dividing low frequency and high frequency.

[0024] When the incident wave frequency range is [f min , X], that is, the frequency is low, and the FDTD method is applicable.

[0025] When the incident wave frequency range is (X, f max ], that is, the frequency is high frequency, and the RT method is applicable.

[0026] Among them, f min is the lowest frequency of the broadband incident wave, f max is the highest frequency of the broadband incident wave.

[0027] In the above FDTD-RT method, the threshold frequency X is calculated as follows:

[0028]

[0029] In formula (2), c is the speed of light.

[0030] In the above FDTD-RT method, the step 3, solving the low-frequency component, further comprises:

[0031] Obtain low-frequency time-domain incident wave The calculation formula is as follows:

[0032]

[0033] Based on the low-frequency time domain incident wave Use FDTD method to perform time domain simulation and obtain low-frequency time domain waveform That is, the low-frequency component.

[0034] In the above FDTD-RT method, the step 4, solving the high frequency component, further comprises:

[0035] Use RT method to perform frequency domain simulation to obtain high-frequency time domain waveform That is the high frequency component, and its calculation formula is as follows:

[0036]

[0037] In the above FDTD-RT method, the step 5, obtaining the entire time domain waveform, further comprises:

[0038] The entire time domain waveform E s (t) is the sum of the low-frequency time domain waveform and the high-frequency time domain waveform, as shown below.

[0039]

[0040] The above-mentioned FDTD-RT method is a hybrid method of the finite difference time domain method FDTD and the ray tracing method RT.

[0041] The beneficial effects of the present invention are:

[0042] An FDTD-RT method for simulating the wide-band electromagnetic environment of large-scale targets is proposed. By frequency decomposing the wide-band incident wave, the FDTD method and the RT method are used to process electromagnetic waves in different frequency ranges, thereby effectively solving the computational bottleneck and accuracy problems of using only the low-frequency full-wave method or the high-frequency approximation method when processing large-scale complex targets.

[0043] An FDTD-RT method for simulating the electromagnetic environment of a large-scale target with a wide frequency band has been developed. By combining the advantages of FDTD and RT, the effective simulation of the electromagnetic environment of a large-scale target with a wide frequency band has been realized. Compared with the low-frequency full-wave method alone, the simulation scale has been effectively expanded. Through verification, it has been found that by combining FDTD with the TR method, the calculation scale can be improved by orders of magnitude, which reflects the creative value of the invention.

[0044] A FDTD-RT method is proposed to simulate the wide-band electromagnetic environment of large-scale targets. The hybrid method of FDTD and RT, FDTD-RT, can effectively improve the calculation scale. The wide-band incident wave is frequency-decomposed, [f min , X] frequency range using FDTD algorithm, (X, f max ] frequency range using the RT method, where f minis the lowest frequency of the broadband incident wave, f max is the highest frequency of the broadband incident wave. Taking the broadband incident wave of the IEC standard as an example, the frequency range of the IEC standard waveform is 0~300MHz. When the FDTD method is used alone, the spatial discrete interval is λ m =1m is the wavelength corresponding to the highest frequency of 300MHz. If the FDTD-RT method is used, the FDTD method is used in the frequency range of [0, 30MHz], and the RT method is used in the frequency range of (30, 300MHz). The spatial discretization interval of the FDTD method is λ m =10m is the wavelength corresponding to the highest frequency of 30MHz. In the FDTD-RT method, the FDTD spatial discrete interval is expanded 10 times compared with the FDTD method alone. In the electromagnetic simulation of the three-dimensional target in this example, the FDTD-RT method can expand the simulation scale by 1000 times compared with the FDTD method alone. The FDTD-RT method can effectively improve the simulation scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a schematic diagram of the FDTD-RT method flow chart of an embodiment of the present invention;

[0046] Figure 2 It is a time domain waveform diagram of IEC and its frequency domain decomposition diagram according to an embodiment of the present invention;

[0047] Figure 3 This is the time domain waveform of the electric field at z = 2.5m on the horizontal ground, which verifies the effectiveness of the FDTD-RT method;

[0048] Figure 4 It is a schematic diagram of the three-dimensional structure of the mountain, showing the specific form of the simulation object;

[0049] Figure 5 It is the time domain waveform of the electric field in the x direction at point A in the mountain terrain, showing the propagation characteristics of electromagnetic pulses at different locations;

[0050] Figure 6 It is the time domain waveform of the electric field in the x direction at point B in the mountain terrain, showing the propagation characteristics of the electromagnetic pulse at different locations. DETAILED DESCRIPTION

[0051] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Embodiment 1

[0053] The present invention proposes a FDTD-RT hybrid method to calculate the broadband electromagnetic environment of large-scale targets. The implementation scheme of the FDTD-RT method is as follows: Figure 1As shown, the method specifically comprises the following steps:

[0054] Step 1: Frequency decomposition of incident pulse: decompose the broadband incident electric field into time-harmonic superposition of different frequency components. The broadband incident electric field is E inc (t), the duration is [0, T p ]. According to Fourier transform, the incident wave E inc (t) is decomposed into harmonic superposition of different frequency components

[0055]

[0056] where f k = k / T p is the frequency of the time harmonic, a k When the harmonic frequency component is f k The amplitude, E inc The lowest frequency of (t) is k = k min The lowest frequency of the corresponding harmonic E inc The highest frequency of (t) is k = k max The highest frequency of the corresponding harmonic

[0057] Step 2: Frequency range division: Divide the applicable frequency range of FDTD and RT methods according to the target size and electromagnetic wave wavelength. For a target with a scale of L, determine the frequency X and divide the frequency range into [f min ,X], the incident wave is subjected to the FDTD method, and the frequency range is (X,f max ] uses the RT method. Because the RT method requires the target size to be greater than 10λ, where λ is the wavelength of the time harmonic, X can be set to:

[0058]

[0059] Where c is the speed of light.

[0060] The incident wave in the time domain can be written as:

[0061]

[0062] Where E l (t) is [f min ,X] frequency range of the incident wave, using FDTD calculation, E h (t) is (X,f max ] frequency range, using the ray tracing method to calculate. According to formula (1), E l (t) and E h (t) can be further written as

[0063]

[0064] Step 3: Low frequency component solution: Use FDTD method to simulate low frequency components. min ,X] frequency range is simulated using FDTD. Since FDTD is a time domain simulation, formula (4) is used to calculate [f min ,X] time domain incident wave in the frequency range Then the FDTD method is used to solve the low-frequency solution

[0065] Step 4: Solve high-frequency components: Use the RT method to simulate high-frequency components. Since the RT method is a frequency domain solution method, for (X, f max ] for each time-harmonic component within the range,

[0066]

[0067] The corresponding harmonic components are solved by RT method

[0068]

[0069] The entire time domain waveform of the high-frequency component is

[0070]

[0071] Step 5: Merge high and low frequency results: Add the high and low frequency results directly to get the final electromagnetic environment simulation result E s (t)

[0072]

[0073] In order to verify the correctness and effectiveness of the present invention, the broadband electromagnetic environment of the mountain is simulated. Without loss of generality, the broadband incident pulse used is the IEC standard double exponential incident pulse.

[0074] E inc (t) = E 0 k(e -αt -e -βt ) (10)

[0075] Among them, E 0 =5×10 4 V / m, k = 1.3, α = 4 × 10 7 s -1 , β=6×10 8 s -1The incident wave direction is the negative z direction, and the electric field polarization direction is the x direction. The frequency range of the IEC waveform is 0 to 300MHz. When using the FDTD-RT method, the IEC is first frequency-decomposed, and the FDTD method is used in the range of [0, 30MHz], and the RT method is used in the frequency range of (30, 300MHz]. Figure 2 The time domain waveform of IEC and the time domain waveform of IEC in the frequency range of [0, 30MHz] and (30, 300MHz] are shown. In this example, if the FDTD method is used alone, the spatial discretization interval is λ m =1m is the wavelength corresponding to the highest frequency of 300MHz. When the FDTD-RT method is used, the FDTD method is used in the frequency range of [0, 30MHz], and the RT method is used in the frequency range of (30, 300MHz). The spatial discrete interval of the FDTD method is λ m =10m is the wavelength corresponding to the highest frequency of 30MHz. In the FDTD-RT method, the FDTD spatial discrete interval is expanded 10 times compared with the FDTD method alone. In the electromagnetic simulation of the three-dimensional target in this example, the FDTD-RT method can expand the simulation scale by 1000 times compared with the FDTD method alone. The FDTD-RT method can effectively improve the simulation scale.

[0076] The reliability of the method is verified by taking the horizontal lossy ground as an example. The horizontal ground has the z = 0 plane as the interface, the free space above and the ground below. The ground parameters are ∈ r =10, σ=0.001S / m. The IEC field environment in the frequency range of [0, 30MHz] is simulated by the FDTD method, and the IEC field environment in the frequency range of (30, 300MHz] is simulated by the RT method. The electromagnetic pulse environment on the horizontal ground can be obtained by adding and merging the results. Figure 3 The results of the comparison between the electric field time domain waveform simulated by the FDTD-RT method at z = 5m and the theoretical analytical solution. Figure 3 It can be seen that the FDTD-RT method is in good agreement with the analytical method, which verifies the effectiveness of the method. Figure 3 The electromagnetic pulse waveforms of the IEC frequency components of FDTD simulation [0, 30MHz] and RT simulation (30, 300MHz] are also shown.

[0077] Taking the mountain as an example, the electromagnetic pulse environment of the irregular terrain is simulated. Figure 4 As shown in Figure 1. The mountain is a pyramid structure superimposed on a random rough surface with an area of ​​250m×250m. The base area of ​​the pyramid is 100m×100m and the height is 28.86m, that is, the side elevation angle of the pyramid is 30°. The electromagnetic parameters of the mountain are ∈ r =10,σ=0.001S / m. Figure 5 and6 The time domain electromagnetic pulse waveforms in the x direction at the top of the mountain A (0, 0, 30m) and B (0, 0, 35m) are given, and the electric fields in the y and z directions can be ignored. The incident field and the reflected field at the top of the mountain have opposite polarization directions. At position A, the incident field encounters a reflected field with an opposite polarization direction but a smaller amplitude than the incident field before it reaches its peak, which reduces the total field. At position B, after experiencing the peak of the incident field, the reflected field with the opposite polarization direction is encountered, and the peak value of the incident field is retained. The incident field waveform at position B is affected by the reflected field later than that at position A. Position B retains the incident waveform more completely, and the pulse width is wider than that at position A. The simulation results are in line with physical laws.

Claims

1. An FDTD-RT method for simulating the broadband electromagnetic environment of a large-scale target, characterized in that: The following steps are involved: Step 1, incident pulse frequency decomposition: Decompose the broadband incident electric field into the time-harmonic superposition of different frequency components; Step 2, frequency range division: According to the target size and the wavelength of the electromagnetic wave, the frequency range is divided into low frequency and high frequency according to the threshold frequency of low frequency and high frequency; Step 3, solve the low-frequency component: Obtain the low-frequency time-domain incident wave, use the FDTD method to simulate, solve the low-frequency time-domain waveform, and obtain the low-frequency component; Step 4, solve the high frequency components: Use RT method to simulate and solve the high-frequency time domain waveform to obtain the high-frequency component; Step 5, obtain the entire time domain waveform: Add the low-frequency component to the high-frequency component to obtain the entire time domain waveform.

2. The FDTD-RT method according to claim 1, characterized in that: The step 1, incident pulse frequency decomposition, further comprises: The broadband incident electric field is E inc (t), the duration is [0, T p ]; According to Fourier transform, the incident wave E inc (t) is decomposed into the superposition of harmonics of different frequency components, and the calculation formula is as follows: In formula (1), f k is the frequency of the time harmonic, f k =k / T p ; k is an integer, k min is the k value corresponding to the lowest frequency, k max is the k value corresponding to the highest frequency; a k f k The amplitude is the frequency, and t is the time.

3. The FDTD-RT method according to claim 1, characterized in that: The step 2, frequency range division, further comprises: For a target with a scale of L, determine the threshold frequency X for dividing low frequency and high frequency; When the incident wave frequency range is [f min , X], that is, the frequency is low, and the FDTD method is applicable; When the incident wave frequency range is (X, f max ], that is, the frequency is high frequency, and the RT method is applicable; Among them, f min is the lowest frequency of the broadband incident wave, f max is the highest frequency of the broadband incident wave.

4. The FDTD-RT method according to claim 3, characterized in that: The threshold frequency X is calculated as follows: In formula (2), c is the speed of light.

5. The FDTD-RT method according to claim 1, characterized in that: The step 3, solving the low-frequency component, further comprises: Obtain low-frequency time-domain incident wave The calculation formula is as follows: Based on the low-frequency time domain incident wave Use FDTD method to perform time domain simulation and obtain low-frequency time domain waveform That is, the low-frequency component.

6. The FDTD-RT method according to claim 1, characterized in that: The step 4, solving the high frequency component, further comprises: Use RT method to perform frequency domain simulation to obtain high-frequency time domain waveform That is the high frequency component, and its calculation formula is as follows:

7. The FDTD-RT method according to claim 1, characterized in that: The step 5, obtaining the entire time domain waveform, further comprises: The entire time domain waveform E s (t) is the sum of the low-frequency time domain waveform and the high-frequency time domain waveform, as shown below:

8. The FDTD-RT method according to claim 1, characterized in that: It is a hybrid method of the finite difference time domain method FDTD and the ray tracing method RT.

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