Incident wave loading method for simulating ground electromagnetic scattering based on FDTD

Abstract

The invention relates to an incident wave loading method for simulating ground electromagnetic scattering based on FDTD. The incident wave loading method comprises the steps of solving an attenuation factor at a certain depth of a PML, arranging the side face and the bottom face of a connection boundary CB on the PML, establishing a ground electromagnetic scattering model, connecting the boundary to load an incident wave, and solving an electric field value and a magnetic field value of the loaded incident wave. According to the method, the four side faces and the bottom face of the connecting boundary CB are completely arranged on the PML, incident waves penetrate through the CB to enter the PML in a non-reflection mode, the edge effect generated by truncation of the periphery of the ground is effectively reduced, and the precision of ground electromagnetic scattering calculation is improved. The truncated ground is limited in a CB boundary area, and calculation of a reflection field and a transmission field is avoided. The method does not depend on ground parameters, and electromagnetic scattering calculation of rough ground and layered ground can be achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational electromagnetics applications, and particularly relates to an incident wave loading method for simulating ground electromagnetic scattering based on FDTD. Background Art

[0002] Studying the interaction between electromagnetic waves and the ground has important scientific significance and application value in many fields such as target recognition, wireless communication, earth science, and remote sensing. The finite-difference time-domain (FDTD) method is a commonly used numerical calculation method for studying ground electromagnetic scattering. In the FDTD model for solving electromagnetic scattering, a connective boundary (CB) is usually set in the free space of the FDTD calculation region to load the incident wave. The CB divides the FDTD calculation region into the total field region (incident field and scattered field) and the scattered field region, and the incident wave is loaded at the CB by applying Huygens' principle. Since FDTD uses a finite calculation region to simulate the electromagnetic scattering process in an open domain, an absorbing boundary condition needs to be set on the truncation boundary of the calculation region. Currently, the perfectly matched layer (PML) absorbing boundary is widely used.

[0003] In the model of FDTD for calculating electromagnetic scattering, the traditional incident wave loading method is to load the incident wave at CB. CB is in free space, and the scatterer (target) is restricted within the CB boundary, requiring the scatterer to be of finite size and thus cannot be directly used for incident wave loading on an infinite ground. In solving the problem of electromagnetic scattering on the ground using the FDTD method, an effective incident wave loading method has always been regarded as the key point of research. Some scholars have studied by equivalent the ground to a horizontal ground, ignoring the undulating characteristics of the ground, and proposed the three-wave method or the one-dimensional modified Maxwell equation (1D MME) to load the incident wave. The three-wave method was first proposed by Wong. When solving the problem of electromagnetic scattering on the ground, this method loads the incident wave, reflected wave, and transmitted wave onto the CB boundary simultaneously. The disadvantage of this method is that it is necessary to analytically obtain the reflected wave and transmitted wave at the dielectric interface, which is difficult to generalize to the case of multi-layer ground and is not applicable to irregular ground. The 1DMME proposed by Capoglu, Smith, etc. can calculate the excitation field at the CB boundary in the case of single-layer or multi-layer ground. The shortcoming of this method is that the leapfrog format solution algorithm of 1DMME is unstable in the case of total reflection and is also not applicable to irregular ground. When dealing with irregular ground by FDTD, the loading of the incident wave is a very difficult problem. When solving actual irregular terrain, the ground is usually truncated, which will artificially generate edges and ridges that do not actually exist. At the edges and ridges, there will be reflected waves and diffracted waves that do not actually exist, that is, the edge effect is generated, affecting the accuracy of the calculation results. So far, there is no simple, easy-to-use, sufficiently general or completely effective method to solve the edge effect.

[0004] The incident wave loading method for electromagnetic scattering on the ground proposed by the present invention can handle irregular terrain and multi-layer ground models, effectively solve the edge effect, and does not require the calculation of the reflection field and transmission field. Summary of the Invention

[0005] In order to overcome the deficiency that the incident wave cannot be effectively loaded when calculating electromagnetic scattering of irregular ground by FDTD, the present invention proposes an incident wave loading method for simulating electromagnetic scattering on the ground based on FDTD.

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

[0007] An incident wave loading method for simulating electromagnetic scattering on the ground based on FDTD, comprising the following steps:

[0008] Step 1, obtaining the perfectly matched layer attenuation factor

[0009] The perfectly matched layer PML attenuation factor η att (θ inc , φ inc, d) is related to the PML depth, where the PML depth refers to the shortest distance from a point inside the PML to the inner surface of the PML. η is calculated based on the actual measured value and the free space value at the corresponding position. att (θ inc , φ inc , d), and the calculation formula is as follows;

[0010]

[0011] In Equation (1), is the amplitude of the electric or magnetic field at the PML depth d, is the amplitude of the electric or magnetic field in the corresponding free space at the PML depth d.

[0012] Step 2, set the connection boundary

[0013] The four side faces and the bottom surface of the connection boundary CB are located inside the PML, and the bottom surface of the truncated ground is located inside the PML. According to the positional relationship of the completed perfectly matched layer PML, the truncated ground, and the connection boundary CB, an electromagnetic scattering model of the ground is established, and the position points of the ground electromagnetic scattering are determined in the XYZ rectangular coordinate system, and the space grid is divided.

[0014] Step 3, load the incident wave on the connection boundary and obtain the electric field value and magnetic field value of the loaded incident wave

[0015] In the ground electromagnetic scattering model, load the incident wave on the CB, and equivalent the incident electromagnetic field to the grid region. The electric field value and magnetic field value of the incident wave loaded on the CB are: the actual incident wave electric field value and magnetic field value multiplied by the loading correction coefficient A PML (θ inc , φ inc ).

[0016] In the above incident wave loading method, the completed perfectly matched layer PML is in the shape of a hollow cuboid, which is composed of four side faces, an upper surface, and a bottom surface with a certain thickness. The four side faces have equal thickness, and the upper surface and the bottom surface can have the same thickness as the side faces, and the upper surface and the bottom surface are parallel to the horizontal plane.

[0017] In the above incident wave loading method, the step 2 of setting the connection boundary further includes:

[0018] Truncate the ground and its upper and lower part of the space in the shape of a cuboid to form a truncated ground, and the bottom surface of the truncated ground is parallel to the horizontal plane. The truncated ground is located inside the PML and the internal space of the PML, and a part of the truncated ground is located in the four side faces and the bottom surface of the PML.

[0019] The connection boundary CB encloses the truncated ground, which is cuboid-shaped and consists of four side faces, an upper face, and a bottom face with zero thickness. The four side faces and the bottom face are at the same depth in the PML, and a part of the upper face intersects with the side face of the PML. The space above the ground and outside the PML is free space.

[0020] For the above incident wave loading method, when dividing the spatial grid, 20 grids are set along the thickness direction of the PML, and 17 grids are set for the PML inward along the thickness direction from the position where CB is located.

[0021] For the above incident wave loading method, the loading correction coefficient A PML (θ inc , φ inc ) is related to the position of the connection boundary CB and the incident wave situation at this CB position. The loading correction coefficient is calculated as follows:

[0022] When CB is in free space, the loading correction coefficient is 1, that is, the loaded incident wave electric field value and magnetic field value at CB are the actual incident electric field value and magnetic field value.

[0023] When CB is in the perfectly matched layer PML and the incident wave arrives at this place, the loading correction coefficient is equal to the attenuation factor η att (θ inc , φ inc , d1) at the perfectly matched layer CB, where d1 is the depth at CB.

[0024] When CB is in the perfectly matched layer PML and the incident wave originates from this place, the loading correction coefficient is equal to the reciprocal of the attenuation factor η att (θ inc , φ inc , d1).

[0025] For the above incident wave loading method, after loading the incident wave at the connection boundary in step 3 and obtaining the loaded incident wave electric field value and magnetic field value, the following steps may further be included:

[0026] Step 4, calculating the electric field value and magnetic field value at the perfectly matched layer CB:

[0027] According to the coordinate system set by the ground electromagnetic scattering model, set the internal region range of CB, and the range is: i0 ≤ i ≤ i1, j0 ≤ j ≤ j1, k0 ≤ k ≤ k1, where i, j, k represent the discrete points in the x, y, z directions, and the discrete intervals are Δx, Δy, Δz respectively. Calculate the electric field value and magnetic field value at the perfectly matched layer CB according to the FDTD iteration formula.

[0028] Step 5, time iteration of the ground electromagnetic scattering model:

[0029] Using FDTD, the time iteration of the ground electromagnetic scattering model is carried out by using the calculated electric field and magnetic field values at the convolutional perfectly matched layer CB, and the ground electromagnetic scattering parameters are obtained.

[0030] For the above incident wave loading method, step 4 calculates the electric field and magnetic field values at the convolutional perfectly matched layer CB, which further includes:

[0031] The perfectly matched layer is a convolutional perfectly matched layer, and the calculation formulas for the electric field and magnetic field values at the convolutional perfectly matched layer CB are as follows:

[0032] The tangential electric field on the i0 boundary is:

[0033]

[0034]

[0035] The tangential electric field on the i1 boundary is:

[0036]

[0037]

[0038] The tangential electric field on the j0 boundary is:

[0039]

[0040]

[0041] The tangential electric field on the j1 boundary is:

[0042]

[0043]

[0044] The tangential electric field on the k0 boundary is:

[0045]

[0046]

[0047] The tangential electric field on the k1 boundary is:

[0048]

[0049]

[0050] The tangential magnetic field on the i0 boundary is:

[0051]

[0052]

[0053] The tangential magnetic field on the i1 boundary is:

[0054]

[0055]

[0056] The tangential magnetic field on the j0 boundary is:

[0057]

[0058]

[0059] The tangential magnetic field on the j1 boundary is:

[0060]

[0061]

[0062] The tangential magnetic field on the k0 boundary is:

[0063]

[0064]

[0065] The tangential magnetic field on the k1 boundary is:

[0066]

[0067]

[0068] In the above formula, the label m is the discrete position where the electric field or magnetic field is located; C b , D b are coefficients related to the medium in the FDTD iteration, κ w , c w (w = x, y, z) are iteration coefficients related to CPML and the medium, is the incident electric field component that needs to be added at the CB of the CPML layer, is the incident magnetic field component that needs to be added at the CB of the CPML layer, and the subscript is the iteration formula for the conventional CPML region.

[0069] For the above incident wave loading method, when the incident wave is a pulse wave, the time iteration is for one pulse time; when the incident wave is a time - harmonic wave, the time iteration is to the steady state of the ground electromagnetic scattering model. After the time iteration is completed, the ground electromagnetic scattering parameters are obtained.

[0070] The beneficial effects of the present invention are:

[0071] In the present invention, the CB part is placed in the PML region (the side and bottom are completely within the PML region, and the upper part is within the PML region). The reflected or diffracted fields generated by truncating the ground around the perimeter need to pass through the PML region before entering the internal grid of the FDTD and are thus attenuated. The present invention can effectively reduce the edge effects generated by truncating the ground around the perimeter, improving the accuracy of electromagnetic scattering calculations on the ground surface. Since the truncated ground is restricted within the CB boundary, only the incident fields required at the CB boundary need to be calculated, avoiding the calculation of reflected and transmitted fields. The implementation of this method does not depend on the parameters of the ground and can solve various ground conditions such as rough ground and layered ground. Description of the Drawings

[0072] Figure 1 For the traditional CB setting scheme, the CB is placed in free space;

[0073] Figure 2 For the CB setting scheme of the present invention, part of the CB is placed in the PML region;

[0074] Figure 3 Shows the electric field amplitudes at different heights on a layered ground (five layers). In the figure, the solid line is the FIT calculation result, and the dashed line is the calculation result of this embodiment;

[0075] Figure 4 Shows the electric field amplitude on the y = 0 plane of a layered ground (five layers);

[0076] Figure 5 Shows the electric field amplitude on the y = 0 plane of an irregular ground.

[0077] In the figure: 1. Perfectly Matched Layer, 2. Truncated Ground, 3. Connection Boundary, 4. FIT Calculation Result, 5. Calculation Result of this Embodiment. Detailed Implementation Manner

[0078] Embodiment 1

[0079] An incident wave loading method for simulating ground electromagnetic scattering based on FDTD includes the following steps:

[0080] Step 1, calculate the PML attenuation factor η att (θ inc , φ inc , d). Specifically, add a boundary surface parallel to the PML near the PML of interest and load a plane incident wave with an incident angle of (θ inc , φ inc ). Record the amplitudes of the electric or magnetic fields at a depth of d at each point in the PML The amplitudes of the electric or magnetic fields in free space at the corresponding positions That is the amplitude of the plane incident wave, and then the attenuation factors at different positions in the PML can be obtained as:

[0081]

[0082] Step 2, set CB. Specifically, as shown in Figure 2 , place the CB part in the PML layer, that is, place the four side faces and the bottom face of the CB in the PML. The thickness of the PML can be set to 20 grids, and the depth of the CB penetrating into the PML layer can be set to 17 grids.

[0083] Step 3, calculate the incident electric field and magnetic field values to be loaded on the CB. If the CB is in free space, the incident electric field and magnetic field values loaded on the CB boundary are the actual incident electric field and magnetic field values. If the CB is in the PML layer, the incident electric field and magnetic field values on the CB boundary in the PML layer need to be multiplied by the loading correction factor A PML (θ inc , φ inc ), to ensure that the correct incident electromagnetic field is equivalent to the main grid area. For the electromagnetic wave incident on the CB boundary of the PML layer, A PML (θ inc , φ inc ) is the attenuation factor η att (θ inc , φ inc , d) obtained in Step 1. For the electromagnetic wave originating from the PML region, A PML (θ inc , φ inc ) is the reciprocal of the attenuation factor η att (θ inc , φ inc , d) obtained in Step 1.

[0084] Step 4, calculate the electric field and magnetic field values at the CB of the perfectly matched layer. Perform time iteration of the electric field and magnetic field according to the FDTD iterative formula. The FDTD iterative formula on the CB boundary in the PML region is different from the FDTD iterative formula on the CB boundary in the traditional free space region.

[0085] Assume that the internal region range of the CB is i0 ≤ i ≤ i1, j0 ≤ j ≤ j1, k0 ≤ k ≤ k1, where i, j, k represent the discrete points in the x, y, z directions, and the discrete intervals are Δx, Δy, Δz respectively. Taking the Convolutional Perfectly Matched Layer (CPML) as an example, the tangential electromagnetic field iterative formulas on the CB boundary in the CPML layer are as follows:

[0086] The tangential electric field on the i0 boundary is:

[0087]

[0088]

[0089] The tangential electric field on the i1 boundary is:

[0090]

[0091]

[0092] The tangential electric field on the j0 boundary is:

[0093]

[0094]

[0095] The tangential electric field on the j1 boundary is:

[0096]

[0097]

[0098] The tangential electric field on the k0 boundary is:

[0099]

[0100]

[0101] The tangential electric field on the k1 boundary is:

[0102]

[0103]

[0104] The tangential magnetic field on the i0 boundary is:

[0105]

[0106]

[0107] The tangential magnetic field on the i1 boundary is:

[0108]

[0109]

[0110] The tangential magnetic field on the j0 boundary is:

[0111]

[0112]

[0113] The tangential magnetic field on the j1 boundary is:

[0114]

[0115]

[0116] The tangential magnetic field on the k0 boundary is:

[0117]

[0118]

[0119] The tangential magnetic field on the k1 boundary is:

[0120]

[0121]

[0122] In the above formula, the label m is the discrete position where the electric field or magnetic field is located; C b , D b are coefficients related to the medium in the FDTD iteration, κ w , c w (w = x, y, z) are iteration coefficients related to CPML and the medium, is the incident electric field component that needs to be added at the CB of the CPML layer, is the incident magnetic field component that needs to be added at the CB of the CPML layer, and the subscript is the iteration formula for the conventional CPML region.

[0123] Step 5, time iteration of the ground electromagnetic scattering model. Using FDTD, with the calculated electric field and magnetic field values at the perfectly matched layer CB, perform time iteration on the ground electromagnetic scattering model. When the incident wave is a pulsed wave, the time iteration is for one pulse time; when the incident wave is a time-harmonic wave, the time iteration is until the ground electromagnetic scattering model reaches a steady state. After the time iteration is completed, the ground electromagnetic scattering parameters are obtained.

[0124] To verify the correctness and effectiveness of the present invention, simulate the ground electromagnetic environment. Without loss of generality, use a time-harmonic incident wave E(t) = sin(2πft) with a frequency f = 300 MHz and a wavelength λ = 1 m, the incident wave direction is the negative z direction, and the electric field polarization direction is the x direction. The spatial discretization interval of FDTD is Adopt the CPML absorbing boundary with a thickness of 20 grid layers.

[0125] Simulate the case of a five-layer horizontal ground. The ground takes z = 0 as the interface, with free space above and the ground below. The thickness of each surface layer is λ / 8, and the electrical parameters of each layer from top to bottom are (∈ r1 = 2, σ1 = 0); (∈r2 = 5, ); (∈ r3 = 10, σ3 = 0.1 S / m); (∈ r4 = 20, σ4 = 1 S / m); (∈ r5 = 30, ). Figure 3 This is for calculating the electric field amplitude at different heights of a five - layer ground by the present invention and the Finite Integration Technique (FIT). The calculation results of the method of the present invention are in good agreement with those of FIT, verifying the effectiveness of the method of the present invention. Figure 4 This is for calculating the electric field amplitude on the y = 0 plane of a five - layer ground by the present invention. For the case of a horizontal ground, the electric field amplitude is independent of the horizontal direction. Since the incident wave and the reflected wave from the ground have opposite propagation directions and the same frequency, the distribution of the electric field along different heights should be in the form of a standing wave. The calculation results of the method of the present invention conform to the physical laws, and no clutter caused by edge effects can be observed, indicating that this method well solves the edge effect.

[0126] For numerical calculation of the electromagnetic environment of irregular terrain, let the relative permittivity of the ground ∈ r = 10, and the conductivity σ = 0.001 S / m. Figure 5 This is for calculating the field environment of irregular terrain by this method. This method can solve the calculation of electromagnetic scattering parameters for the case of an irregular ground.

Claims

1. An incident wave loading method for simulating ground electromagnetic scattering based on FDTD, characterized in that It includes the following steps: Step 1, obtaining the attenuation factor of the perfectly matched layer: PML attenuation factor η for the perfect matching layer att (θ inc ,φ inc ,d) is related to the PML depth, which refers to the shortest distance from a point inside the PML to the inner surface of the PML; η is calculated based on the actual measured value and the free space value at the corresponding position att (θ inc ,φ inc ,d), and the calculation formula is as follows; In Equation (1), is the amplitude of the electric or magnetic field at the PML depth d, is the amplitude of the electric or magnetic field corresponding to free space at the PML depth d; Step 2, setting the connection boundary: The four side faces and the bottom face of the connection boundary CB are located in the PML, and the bottom face of the truncated ground is located in the PML; according to the positional relationship of the perfectly matched layer PML, the truncated ground, and the connection boundary CB, a ground electromagnetic scattering model is established, the position points of the ground electromagnetic scattering are determined in the XYZ rectangular coordinate system, and the space grid is divided; Step 3, loading the incident wave on the connection boundary and obtaining the electric field value and magnetic field value of the loaded incident wave: In the ground electromagnetic scattering model, when a CB loads an incident wave and the incident electromagnetic field is equivalent to the grid region, the electric field value and magnetic field value of the incident wave loaded by the CB are: the actual electric field value and magnetic field value of the incident wave multiplied by the loading correction coefficient A PML (θ inc , φ inc ).

2. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 1, characterized in that The perfectly matched layer PML is in the shape of a hollow cuboid, which is composed of four side faces, an upper face, and a bottom face with a certain thickness. The thicknesses of the four side faces are equal, and the thicknesses of the upper face and the bottom face can be equal to the thickness of the side faces, and the upper face and the bottom face are parallel to the horizontal plane.

3. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 1 or 2, characterized in that The step 2 of setting the connection boundary further includes: Taking the ground and the upper and lower part spaces as a cuboid truncation to form a truncated ground. The truncated ground is located in the PML and the internal space of the PML, and a part of the truncated ground is located in the four side faces and the bottom face of the PML; The connection boundary CB surrounds the truncated ground and is in the shape of a cuboid, which is composed of four side faces, an upper face, and a bottom face with zero thickness. The four side faces and the bottom face are located at the same depth in the PML, and a part of the upper face intersects with the side face of the PML. The space above the ground and outside the PML is free space.

4. The incident wave loading method for simulating ground electromagnetic scattering based on FDTD according to claim 1, characterized in that For the division of the space grid, 20 grids are set along the thickness direction of the PML, and 17 grids are set in the PML inward along the thickness direction from the position where CB is located.

5. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 1, characterized in that The loading correction coefficient A PML (θ inc , φ inc ) is related to the position of the connection boundary CB and the incident wave situation at this CB position. The calculation of the loading correction coefficient is as follows: When CB is in the free space, the loaded correction factor is 1, that is, the loaded incident wave electric field value and magnetic field value at CB are the actual incident electric field value and magnetic field value; If CB is in the perfectly matched layer PML, and when the incident wave arrives at this point, the loading correction factor is equal to the attenuation factor η at CB of the perfectly matched layer att (θ inc , φ inc , d1), where d1 is the depth at CB; If CB is in the perfectly matched layer PML and the incident wave originates from this location, the loading correction factor is equal to the attenuation factor η at the perfectly matched layer CB att (θ inc , φ inc , d1).

6. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 1 or 5, characterized in that After loading the incident wave on the connection boundary in step 3 and obtaining the electric field value and magnetic field value of the loaded incident wave, the following steps may further be included: Step 4, calculating the electric field value and magnetic field value at the perfectly matched layer CB: According to the coordinate system set by the ground electromagnetic scattering model, the internal region range of CB is set, and the range is: i0 ≤ i ≤ i1, j0 ≤ j ≤ j1, k0 ≤ k ≤ k1, where i, j, k represent the discrete points in the x, y, z directions, and the discrete intervals are Δx, Δy, Δz respectively; according to the FDTD iteration formula, the electric field value and magnetic field value at the perfectly matched layer CB are calculated; Step 5, time iteration of the ground electromagnetic scattering model: Adopting FDTD, using the calculated electric field value and magnetic field value at the perfectly matched layer CB, time iteration is carried out on the ground electromagnetic scattering model to obtain the ground electromagnetic scattering parameters.

7. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 6, characterized in that The step 4 of calculating the electric field value and magnetic field value at the perfectly matched layer CB further includes: The perfectly matched layer is a convolutional perfectly matched layer, and the calculation formulas for the electric field value and magnetic field value at the convolutional perfectly matched layer CB are as follows: The tangential electric field on the i0 boundary is: The tangential electric field on the i1 boundary is: The tangential electric field on the j0 boundary is: The tangential electric field on the j1 boundary is: The tangential electric field on the k0 boundary is: The tangential electric field on the k1 boundary is: The tangential magnetic field on the i0 boundary is: The tangential magnetic field on the i1 boundary is: The tangential magnetic field on the j0 boundary is: The tangential magnetic field on the j1 boundary is: The tangential magnetic field on the k0 boundary is: The tangential magnetic field on the k1 boundary is: In the above formula, the label m is the discrete position where the electric or magnetic field is located; C b , D b are coefficients related to the medium in the FDTD iteration, κ w , c w (w = x, y, z) are iteration coefficients related to the CPML and the medium, is the incident electric field component to be added at the CPML layer CB, is the incident magnetic field component to be added at the CPML layer CB, and the subscript is the iteration formula for the conventional CPML region.

8. The incident wave loading method based on FDTD simulation of ground electromagnetic scattering according to claim 6, characterized in that The time iteration of the ground electromagnetic scattering model in step 5 further includes: When the incident wave is a pulsed wave, the time iteration is one pulse time; when the incident wave is a time-harmonic wave, the time iteration reaches the steady state of the ground electromagnetic scattering model; after the time iteration is completed, the ground electromagnetic scattering parameters are obtained.

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