Three-dimensional FDTD complex path ASF prediction method based on multiple GPUs

Abstract

The invention belongs to the technical field of radio wave propagation, and particularly discloses a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. According to the method, the three-dimensional FDTD algorithm is realized through multiple GPUs, and the method is used for predicting the ASF on a complex path. The method comprises the following steps: firstly, preprocessing parameters, and copying the parameters to a device end, namely a GPU end; secondly, updating an electric field component in the whole calculation area; then updating the field source, and exchanging the electric field components # imgabs0 # and # imgabs1 # on the adjacent GPUs; updating the magnetic field component in the whole calculation area; and finally, circulating and judging an end condition, and outputting the ASF when the calculation is finished. The method solves the problem of poor ASF prediction precision caused by the fact that a two-dimensional time delay prediction method cannot consider the transverse effect, overcomes the defect that a traditional three-dimensional FDTD method is difficult to simulate large-area low-frequency ground wave propagation, and provides a theoretical basis and technical support for improving the service precision of a low-frequency radio navigation time service system.

Description

Technical Field

[0001] The invention belongs to the technical field of radio wave propagation, and in particular relates to a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. Background Art

[0002] Loran-C and its enhanced systems have been widely used in remote positioning, navigation, and timing (PNT) services. However, when Loran-C signals propagate over complex paths in rugged terrain, they cause additional signal delays, namely Additional Secondary Factors (ASF), which can lead to serious PNT errors. Therefore, accurately predicting ASF in complex paths is crucial to improving the accuracy of Loran-C system services.

[0003] The modeling of Loran-C additional secondary factors has long been limited to two-dimensional space. Although this traditional two-dimensional modeling method simplifies the calculation process, its inherent limitation is that it ignores the potential impact of factors such as terrain undulation, lateral refraction effect, and complex terrain scattering on ASF in actual three-dimensional space. This simplification may have a good approximation effect in flat terrain or propagation paths with insignificant terrain changes, but when dealing with propagation paths with drastic terrain changes, the two-dimensional model cannot accurately represent the multipath effect and waveguide effect caused by the terrain, resulting in a significant deviation between the ASF prediction value and the actual observation value.

[0004] In addition, due to the inherent fragility of the integral equation (IE) method at the algorithm level, its extension to three-dimensional space faces significant difficulties. The three-dimensional parabolic equation (3DPE) method usually uses the virtual point method to deal with three-dimensional terrain boundary conditions, but this method will introduce inherent errors when dealing with inclined interfaces, and this error is difficult to effectively reduce through conventional methods.

[0005] In contrast, the three-dimensional finite-difference time-domain (3D-FDTD) method shows unique advantages and can handle complex propagation path problems in a natural and accurate way. However, the 3D-FDTD method faces severe challenges in predicting ASF over long distances, which is mainly limited by its extremely high computational complexity. Especially in large-scale computational domains and long-term simulation scenarios, the demand for computing resources increases significantly, making it difficult to meet the efficiency requirements of actual engineering applications.

[0006] Therefore, it is necessary to propose a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. Summary of the invention

[0007] The purpose of the present invention is to propose a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. This method uses a three-dimensional method to model complex terrain, and can accurately predict ASF on long-distance complex and irregular terrain. At the same time, based on a multi-GPU parallel computing architecture, it can expand the calculation area and reduce the calculation time.

[0008] In order to achieve the above object, the present invention adopts the following technical scheme: The ASF prediction method of complex paths based on three-dimensional FDTD of multiple GPUs includes the following steps: Step 1. Set and initialize the 3D terrain modeling parameters on the CPU side; Step 2. After preprocessing the three-dimensional terrain modeling parameters, the data of the three-dimensional terrain modeling parameters stored on the CPU side is copied to the device side, i.e., the GPU side; Step 3. Update the electric field components within the computational area that each GPU is responsible for , and ; Step 4. After updating the field sources in the computing area that each GPU is responsible for, synchronize the data between the CPU and GPU. Step 5. Swap the GPUs on the adjacent GPUs and Components, and then synchronize data between the CPU and GPU; Step 6. Update the magnetic field components within the computational area that each GPU is responsible for , and , and then synchronize the data between the CPU and GPU; Step 7. Determine whether the current running time step is equal to the preset running time step; if so, go to step 8; otherwise, update the current running time step The value of , and go to step 3; Step 8. Extract the electric field components within the computational area that each GPU is responsible for The ASF is calculated at the positive zero crossing point of the third carrier cycle.

[0009] In addition, based on the above-mentioned multi-GPU-based 3D FDTD complex path ASF prediction method, the present invention also proposes a computer device, which includes a memory and one or more processors; The memory stores executable codes, and when the processor executes the executable codes, the executable codes are used to implement the steps of the above-mentioned three-dimensional FDTD complex path ASF prediction method based on multiple GPUs.

[0010] In addition, based on the above-mentioned three-dimensional FDTD complex path ASF prediction method based on multiple GPUs, the present invention also proposes a computer-readable storage medium on which a program is stored; when the program is executed by a processor, it is used to implement the steps of the above-mentioned three-dimensional FDTD complex path ASF prediction method based on multiple GPUs.

[0011] The present invention has the following advantages: As described above, the present invention describes a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. This method introduces the 3D-FDTD method into ASF prediction for the first time. It uses three-dimensional terrain modeling, which can accurately characterize the electromagnetic propagation characteristics of complex and irregular terrains, and significantly improves the accuracy of ASF prediction results, solving the problem of poor ASF prediction accuracy caused by the inability to consider lateral effects in traditional two-dimensional modeling methods. At the same time, the present invention is implemented based on a multi-GPU parallel computing architecture, and improves the data transmission between different GPU devices according to the complex path ASF prediction problem, overcoming the shortcomings of the traditional three-dimensional FDTD method that it is difficult to simulate large-area low-frequency ground wave propagation. On the premise of ensuring calculation accuracy, the scale of the calculable area is greatly expanded, providing an efficient solution for ASF prediction in large-scale complex terrain scenes, and is more suitable for engineering promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a flow chart of a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs in an embodiment of the present invention.

[0013] Figure 2 Schematic diagram of the principle of a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs in an embodiment of the present invention.

[0014] Figure 3 Schematic diagram of ASF prediction results of the method of the present invention and the traditional method on a flat and smooth ground path.

[0015] Figure 4 Schematic diagram of ASF prediction results of the method of the present invention and the traditional method when there are Gaussian mountains on the propagation path. DETAILED DESCRIPTION

[0016] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 The present invention provides a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. The method improves the problem of poor ASF prediction accuracy of traditional two-dimensional modeling methods in actual complex propagation paths. The overall process is as follows: first, input model parameters and initialize. Then, perform parameter preprocessing. Then, update the electric field components in the entire calculation area. Then, update the field source. Then, exchange the electric field components on adjacent GPUs. and Then update the magnetic field components in the entire calculation area. Finally, loop and judge the end condition, and output ASF when the calculation is finished. Based on the above invention concept, the three-dimensional FDTD complex path ASF prediction method based on multiple GPUs proposed by the present invention is described in detail below in conjunction with the accompanying drawings.

[0017] like Figure 1 As shown in FIG. 1 , the ASF prediction method for complex paths based on three-dimensional FDTD using multiple GPUs specifically includes the following steps: Step 1. Set the 3D terrain modeling parameters and initialize them on the CPU.

[0018] The three-dimensional terrain modeling parameters are model parameters, which include the electrical parameters of the simulation path, the grid parameters of the simulation area, the parameters of the field source, the parameters of the absorbing boundary perfectly matched layer (PML), and the parameters of the time setting and the decomposition setting of the simulation area.

[0019] The electrical parameters of the simulation path include the relative dielectric constant of free space With conductivity , relative dielectric constant of the formation area With conductivity , relative dielectric constant of seawater area With conductivity The electrical parameters of the simulation path are used to accurately characterize the complex medium distribution.

[0020] The simulation area is the setting of the grid parameters of the entire calculation area, including defining the entire calculation area as a three-dimensional rectangular coordinate system ,in , , The number of grids in the direction is set to , , , the meshing steps are set to , , .

[0021] Set the parameters of the field source, including the number of field sources , the location of the field source, the type of field source, the Gaussian pulse width , Gaussian pulse delay , signal frequency and amplitude A; where the location of the field source includes the location of the field source at Starting point on axis , , the source is Starting point on axis , , the source is Starting point on axis , ; The types of field sources include soft source and hard source. When the field source type is set to soft source, the excitation signal is the superposition of the field source signal and the electric field value of the previous step. When the field source type is set to hard source, the excitation signal is completely determined by the field source signal and has nothing to do with the field value. By setting the parameters of the field source, the actual Loran-C signal can be simulated.

[0022] Set the parameters of the absorbing boundary PML, including the number of absorbing boundary layers The reflection error caused by artificial truncation is eliminated by setting an appropriate number of absorbing boundary layers.

[0023] The time setting includes the current running time step , time step and preset run time step . By setting the appropriate time, the stability of the value can be ensured.

[0024] The decomposition setting of the simulation area includes setting the number of simulation area boundaries to , and set the computation area that each GPU is responsible for to ,The method of the present invention adopts a regional decomposition strategy to solve the ,limitation of the upper limit of the video memory of a single GPU and ,then realizes the ASF prediction of a large area.

[0025] Then initialize the relevant parameters to 0. The parameters initialized to 0 specifically include: Electric field components: , , ,in , , Respectively , , The electric field component in the direction.

[0026] Magnetic field components: , , ,in , , Respectively , , Directional magnetic field component.

[0027] Intermediate variables: , , , ,in = , , , , , .

[0028] Electric field component calculation coefficients: , .

[0029] Magnetic field component calculation coefficients: , .

[0030] Intermediate variable calculation coefficients: , , .

[0031] Current running time step .

[0032] Output value at the zero-crossing point of the third cycle .

[0033] Construct the initial state of the iterative calculation of the electromagnetic field and establish a complete parameterized calculation framework for high-precision numerical simulation of electromagnetic wave propagation characteristics in three-dimensional terrain.

[0034] Step 2. Parameter preprocessing and copying related parameters: After preprocessing the 3D terrain modeling parameters, the data of the 3D terrain modeling parameters stored on the CPU side is copied to the device side, i.e., the GPU side.

[0035] First preprocess PML related parameters , , , specifically including: (1) (2) (3) in, ,when When represents the coordinate position of the field source on the x-axis, When represents the coordinate position of the field source on the y-axis, When represents the coordinate position of the field source on the z-axis; Indicates the location of the field source in a three-dimensional rectangular coordinate system The coordinate position on .

[0036] is a constant, The general value range is ,in Indicates wavelength. is an integer, The general value range is . is a constant, The general value range is . is the absorbing boundary thickness. To adjust the key parameters of PML performance, The absorbing boundary has the best absorption effect.

[0037] Then preprocess the electromagnetic field components to calculate the coefficients , , , : (4) (5) (6) (7) in, , and It represents the relative dielectric constant and conductivity in non-free space, i.e. non-air layer. = , represents the magnetic permeability of free space, and . Relative magnetic permeability is expressed as .

[0038] Specifically, when the region is free space, i.e., an air layer, the relative permittivity and conductivity are respectively and When the area is a stratum, the relative permittivity and conductivity are respectively and When the area is seawater, the relative permittivity and conductivity are and .

[0039] Preprocessing intermediate variables to calculate coefficients , , : (8) (9) (10) in, = , , , , , .

[0040] Some parameters that do not change with time iteration are calculated in advance on the CPU side and then directly transmitted to the GPU side, which can reduce the amount of calculation on the GPU side and improve calculation efficiency.

[0041] After the preprocessing is completed, the electric field component, magnetic field component, intermediate variables, electromagnetic field component calculation coefficients, intermediate variable calculation coefficients, field source parameters, and the output data at the time of the third carrier cycle crossing zero are copied to the GPU. The parameters copied to the GPU specifically include: Electric field components: , , , magnetic field component: , , .

[0042] Intermediate variables: , , , .

[0043] Calculation coefficients for electromagnetic field components: , , , .

[0044] Intermediate variable calculation coefficients: , , .

[0045] Source parameters: Number of sources , the location of the source , , , , , , type of field source, Gaussian pulse width , Gaussian pulse delay , signal frequency and amplitude A.

[0046] Output value at the zero-crossing point of the third cycle .

[0047] The components that need to be updated and calculated in the 3D-FDTD method are set on the GPU side to support the calculation operations performed on the GPU side in subsequent steps.

[0048] Step 3. Update the electric field components within the computational area that each GPU is responsible for , and .

[0049] The electric field components within the computational area responsible for each GPU The specific calculation formula is: (11) in, , , The space label. It is a space label introduced to simplify the formula, indicating that the calculation parameters are in The value at is aligned with the current calculated field value. For example, , , Respectively expressed in and exist The value of . and is an intermediate variable, and the calculation formula is: (12) (13) in, express exist The value of express exist The value of .

[0050] and Respectively , The central difference of y and z is expressed as: (14) (15) in and for The grid size in the y and z directions at = , = The following differential equations are calculated in the same way as formula (14) and formula (15), and will not be repeated here. and It is to further simplify the intermediate variables used in the formula, specifically: (16) (17) in, express exist The value of express exist The value of ; express exist The value of express exist Then, the electric field components in the calculation area responsible for each GPU are calculated. and The calculation is performed. Since it is an FDTD algorithm in a three-dimensional rectangular coordinate system, the propagation of radio waves along the x, y, and z directions is symmetrical, and the update formula structure of different field components is the same, so it is directly given as and The update formula of .

[0051] (18) (19) in, , , , The calculation method is the same as formula (12) and (13).

[0052] The iterative formula of the electric field component of the 3D-FDTD method of PML is used to achieve accurate simulation of electromagnetic waves. Compared with the traditional two-dimensional method, the method proposed in the present invention can take into account the lateral propagation effect of electromagnetic waves, thereby improving the ASF prediction accuracy in complex three-dimensional areas.

[0053] Step 4. After updating the field sources in the computing area that each GPU is responsible for, synchronize the data between the CPU and GPU.

[0054] The added source is the Loran-C signal, and the field source consists of the electric field component Excitation, its current waveform It is expressed as: (20) in, represents the current waveform, .

[0055] when hour, On the contrary, hour, .

[0056] Update the field source within the computing area that each GPU is responsible for according to the parameters set in step 1.

[0057] Specifically, the signal frequency, Gaussian pulse width, and Gaussian pulse delay of the updated field source in this embodiment are: , =0, . And update the field source according to the number of field sources, the location of the field source and the type of the field source set in step 1. For example, the field source is located in GPU (1), and the number of field sources is set to . The source location is: , , , , , . The field source type is soft source.

[0058] ASF is an additional delay in the arrival time of the Loran-C signal, which is due to changes in electrical parameters and rugged terrain when propagating on the actual path compared to the all-seawater path. A small deviation in ASF can result in an error of up to several kilometers. By simulating the actual Loran-C signal, the subsequent precise calculation of ASF is supported, providing theoretical support for the realization of more accurate Loran-C navigation and timing services.

[0059] After completing the update of the field source in the calculation area responsible for each GPU, the data synchronization between the CPU and GPU is performed. Data synchronization is to ensure that the current calculation has been completed when the data is transmitted, so as to ensure data consistency. For example, in the Visual Studio platform, after the field source update is completed, the data synchronization operation is performed through the command "cudaDeviceSynchronize".

[0060] Step 5. Swap the GPUs on the adjacent GPUs and Components, and then synchronize data between the CPU and GPU.

[0061] In the multi-GPU parallel implementation of the 3D FDTD algorithm, since the computational domain is decomposed along the x direction, data exchange between GPUs is completed by transferring the field components on the y and z planes. Excitation, just exchange the electric field components calculated by each GPU and The boundary value of can achieve data synchronization and unification among multiple GPUs. The specific implementation steps are as follows: Step 5.1. Put the electric field component in GPU (q) memory and The data is transferred to the CPU memory. GPU(q) represents the GPUs; express In the The y-direction electric field component on the yz plane, express In the The z-direction electric field component on the yz plane.

[0062] Step 5.2. The CPU passes the data received in step 5.1 to GPU (q+1) to update the electric field component in the memory of GPU (q+1) and Data. GPU(q+1) indicates the q+1th GPU; express The y-direction electric field component on the first yz plane is, express The z-direction electric field component in the first yz plane.

[0063] Step 5.3. Put the electric field component in GPU(q+1) memory and The data is transferred to the CPU memory. express The y-direction electric field component on the second yz plane is, express The z-direction electric field component in the second yz-plane.

[0064] Step 5.4. The CPU passes the data received in step 5.3 to the GPU (q) to update the electric field component in the GPU (q) memory. and Among them, express In the The y-direction electric field component on the yz plane, express In the The z-direction electric field component on the yz plane.

[0065] Step 5.5. Synchronize data between the CPU and GPU.

[0066] To ensure the continuity of data in the entire computational area, the field update in GPU(q+1) requires the update of the first In order to ensure the integrity of the data in GPU(q), GPU(q) also needs to receive the electric field data on the second yz plane in GPU(q+1). Each time the data is updated, the GPU devices complete the data exchange to achieve continuous calculation of electromagnetic waves. This is different from the traditional multi-GPU FDTD method that requires simultaneous transmission of electric field components. , With magnetic field component and Compared with the above scheme, the data transmission amount of the method of the present invention is reduced by half, the algorithm is implemented with the minimum data transmission amount, and the calculation efficiency is improved.

[0067] Step 6. Update the magnetic field components within the computational area that each GPU is responsible for , and , and then synchronize the data between the CPU and GPU.

[0068] The magnetic field components within the computation area that each GPU is responsible for Perform the calculation: (twenty one) in, It is a space label introduced to simplify the formula, which indicates that the calculation parameters are in The value at is aligned with the current calculated field value. For example, , , Respectively expressed in and exist The value of . and is an intermediate variable, and the calculation formula is: (twenty two) (twenty three) Intermediate variables and for: (twenty four) (25) Then, the magnetic field components in the calculation area of ​​each GPU are and Similarly, since it is a FDTD algorithm in a three-dimensional rectangular coordinate system, the propagation of radio waves along the x, y, and z directions is symmetrical, and the update formula structure of different field components is the same, so it is directly given as and The update formula is: (26) (27) in, , , , The calculation method is the same as formula (22) and (23).

[0069] Combined with the iterative formula of PML's 3D-FDTD method in the magnetic field component, accurate simulation of electromagnetic waves can be achieved. Compared with the two-dimensional method, this method can take into account the lateral propagation effect of electromagnetic waves and improve the ASF prediction accuracy in complex three-dimensional areas.

[0070] Step 7. Determine whether the current running time step is equal to the preset running time step; if so, go to step 8; otherwise, update the current running time step The value of , and go to step 3.

[0071] Specifically, determine whether the current running time step n satisfies If not satisfied, continue to repeat steps 3 to 6 to update the current running time step until it reaches the preset value. If satisfied, the loop ends.

[0072] Step 8. Extract the electric field components within the computational area that each GPU is responsible for The ASF is calculated at the positive zero crossing point of the third carrier cycle.

[0073] Output attenuation factor phase , the calculation formula is as follows: (28) in, is the electric field component When the third carrier cycle of is positively crossing zero, The speed of light. Represents the great circle distance that the wave travels.

[0074] When the three-dimensional terrain modeling parameters are set to the actual complex propagation path, that is, the simulation area is set to the complex terrain containing free space and stratum area, the attenuation factor phase of the Loran-C signal on the actual complex propagation path is obtained by formula (28): When the three-dimensional terrain modeling is set to a pure seawater propagation path, that is, the simulation area is set to a seawater area, the attenuation factor phase of the Loran-C signal on the pure seawater propagation path is obtained by formula (28): .

[0075] Then calculate the ASF: (29) During the field value update process of the 3D-FDTD method, the electric and magnetic field updates of each grid point only depend on the field values ​​of the adjacent grids, without global data dependency, and naturally support data parallelism. The GPU architecture can simultaneously schedule thousands of threads to process field updates of different grids and maximize computational density, which makes the 3D-FDTD method very compatible with GPU programming. For large-scale three-dimensional electromagnetic simulation problems, it is necessary to store tens or even hundreds of GB of field data, making it difficult for a single GPU to complete the computational task. Therefore, the multi-GPU-based three-dimensional FDTD complex path ASF prediction method breaks through the single-card resource limitations through the domain decomposition strategy. Each GPU independently manages the local computational area data and performs field update calculations, thereby realizing complex path ASF predictions in large three-dimensional areas.

[0076] In addition, in order to verify the effectiveness of the method proposed in the present invention, the following specific experiments are also given: Experiment 1 shows the ASF prediction results on a flat and smooth ground path.

[0077] The calculation area size is: {-0.72km≦ ≦104.4km, -4.86km≦ ≦4.86km, -1.44km≦ ≦4.86km}, grid size = = =18m, time step for The relative dielectric constant of the formation is , conductivity , the relative dielectric constant of seawater , conductivity .

[0078] Figure 3The ASF results of the 3D-FDTD method, 2D-FDTD method and flat ground formula proposed in this invention on the flat and smooth ground propagation path with different electrical parameters. Figure 3 It can be seen that the three methods have almost no errors, which proves that the 3D-FDTD method is suitable for ASF prediction.

[0079] Experiment 2 shows the ASF prediction results on the Gaussian mountain propagation path.

[0080] In this example, the terrain is set as a Gaussian mountain range with a width of 5 km and a height of 1.5 km / 0.5 km. The center of the Gaussian mountain is 50 km away from the source. The calculation area is set the same as in Example 1. ASF is predicted by the inventive method proposed in the present invention.

[0081] Figure 4 The figure is a schematic diagram comparing the ASF results on the central tangent line of the mountain range calculated along the horizontal direction by the method of the present invention and the 2D-FDTD method, where H represents the height of the Gaussian mountain. Figure 4 It can be seen that when the mountain height is low, the calculation results of the 2D-FDTD and 3D-FDTD methods are in good agreement. However, for terrain with high mountain height, the calculation results of the two methods begin to differ significantly in the mountain area. This difference reaches a peak in the area behind the mountain, then gradually converges and stabilizes within the propagation range, but the ASF error is still above 200ns. It is worth noting that the influence of the lateral terrain on the ASF is not only reflected in the shadow area, but also significantly exists in the lateral mountain periphery area. These ASF differences are mainly due to the lateral diffraction effect that the three-dimensional FDTD method can accurately capture, which is a physical phenomenon that the 2D-FDTD method cannot represent.

[0082] The method of the present invention overcomes the shortcomings of the traditional two-dimensional modeling method in predicting ASF in complex propagation paths. Compared with the 2D-FDTD algorithm, the method of the present invention can accurately characterize the lateral diffraction effect of radio waves in areas with irregular and discontinuous terrain through three-dimensional terrain modeling, and obtain more accurate ASF prediction results. In addition, the method of the present invention also expands the calculation area and improves the calculation efficiency without losing accuracy through multi-GPU parallel technology.

[0083] Example 2 This embodiment 2 describes a computer device, which includes a memory and one or more processors.

[0084] An executable code is stored in the memory. When the processor executes the executable code, it is used to implement the steps of the three-dimensional FDTD complex path ASF prediction method based on multiple GPUs in the above-mentioned embodiment 1.

[0085] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0086] Example 3 This embodiment 3 describes a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the program is used for the steps of a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs.

[0087] The computer-readable storage medium may be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc., equipped on the device.

[0088] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A multi-GPU based 3D FDTD complex path ASF prediction method, characterized by: The steps include: Step 1. Set and initialize the 3D terrain modeling parameters on the CPU side; Step 2. After preprocessing the three-dimensional terrain modeling parameters, the data of the three-dimensional terrain modeling parameters stored on the CPU side is copied to the device side, i.e., the GPU side; Step 3. Update the electric field components within the computational area that each GPU is responsible for , and ; Step 4. After updating the field sources in the computing area that each GPU is responsible for, synchronize the data between the CPU and GPU. Step 5. Swap the GPUs on the adjacent GPUs and Components, and then synchronize data between the CPU and GPU; Step 6. Update the magnetic field components within the computational area that each GPU is responsible for , and , and then synchronize the data between the CPU and GPU; Step 7. Determine whether the current running time step is equal to the preset running time step; if so, go to step 8; otherwise, update the current running time step The value of , and go to step 3; Step 8. Extract the electric field components within the computational area that each GPU is responsible for The ASF is calculated at the positive zero crossing point of the third carrier cycle.

2. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 1, characterized in that: The step 1 is specifically as follows: Set the 3D terrain modeling parameters on the CPU, including: Set the electrical parameters of the simulation path, including the relative permittivity of free space With conductivity , relative dielectric constant of the formation area With conductivity , relative dielectric constant of seawater area With conductivity ; Set the mesh parameters of the simulation area, i.e. the entire calculation area, and define the simulation area as a three-dimensional rectangular coordinate system , where the number of grids is set to , , , the meshing steps are set to , , ; Set the parameters of the field source, including the number of field sources , the location of the field source, the type of field source, the Gaussian pulse width , Gaussian pulse delay , signal frequency and amplitude A; where the location of the field source includes the location of the field source at Starting point on axis , , the source is Starting point on axis , , the source is Starting point on axis , ; Types of field sources include soft sources and hard sources; Set the parameters of the absorbing boundary PML, including the number of absorbing boundary layers ; The time setting includes the current running time step , time step and preset run time step ; The decomposition setting of the simulation area includes setting the number of simulation area boundaries to , and set the computational area that each GPU is responsible for to ; The parameters initialized to 0 include: Electric field component , , ; Magnetic field component , , ; Intermediate variables , , , ,in = , , , , , ; Electromagnetic field component calculation coefficients , , , ; Intermediate variable calculation coefficient , , ; Current running time step ; Output value at the time when the third carrier cycle passes through zero .

3. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 2, characterized in that: The step 2 is specifically as follows: PML related parameters , , Preprocessing: (1) (2) (3) in, ,when When represents the coordinate position of the field source on the x-axis, When represents the coordinate position of the field source on the y-axis, When represents the coordinate position of the field source on the z-axis; Indicates the location of the field source in a three-dimensional rectangular coordinate system The coordinate position on ; , represents the wavelength; u is a parameter used to adjust the PML performance; is the absorbing boundary thickness; is an integer, is a constant; Calculation coefficients for electromagnetic field components , , , Preprocessing: (4) (5) (6) (7) in, , and represent the relative permittivity and conductivity in non-free space respectively; = , represents the magnetic permeability of free space; Relative magnetic permeability. When the simulation area is free space, the relative permittivity and conductivity are and ; When the simulation area is the stratum, the relative permittivity and conductivity are respectively and ; When the simulation area is seawater, the relative dielectric constant and conductivity are and ; Calculate coefficients for intermediate variables , , Preprocessing: (8) (9) (10) After the preprocessing is completed, the data of the electric field component, magnetic field component, intermediate variables, electromagnetic field component calculation coefficients, intermediate variable calculation coefficients, field source parameters and output quantity at the zero-crossing point of the third carrier cycle stored on the CPU side are copied to the GPU side.

4. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 3, characterized in that: The step 3 is specifically as follows: The electric field components within the computational area responsible for each GPU The specific calculation formula is: (11) in, , , is the space label; and Respectively expressed in and exist The value of is the space label; and is an intermediate variable, and the calculation formula is: (12) (13) in, express exist The value of express exist The value of ; and Respectively , The central difference of y and z is expressed as: (14) (15) in, and for The grid size in the y and z directions at = , = ; Intermediate variables and for: (16) (17) in, express exist The value of express exist The value of ; express exist The value of express exist The value of ; The electric field components within the computational area responsible for each GPU and Calculate and get and The update formula is: (18) (19)。 5. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 4, characterized in that: The step 4 is specifically as follows: The added field source is the Loran-C signal, which consists of the electric field component Excitation, current waveform of the field source It is expressed as: (20) in, ; when hour, ;when hour, ; After updating the field sources in the calculation area that each GPU is responsible for according to the parameters set in step 1, data synchronization between the CPU and GPU is performed.

6. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 5, characterized in that: The step 5 is specifically as follows: Step 5.

1. Put the electric field component in GPU (q) memory and The data is transferred to the CPU memory; Among them, GPU(q) represents the GPUs; express In the The y-direction electric field component on the yz plane, express In the The z-direction electric field component on the yz plane; Step 5.

2. The CPU passes the data received in step 5.1 to GPU (q+1) to update the electric field component in the memory of GPU (q+1) and data; Among them, GPU(q+1) represents the q+1th GPU; express The y-direction electric field component on the first yz plane is, express The z-direction electric field component on the first yz plane; Step 5.

3. Put the electric field component in GPU(q+1) memory and The data is transferred to the CPU memory; in, express The y-direction electric field component on the second yz plane is, express The z-direction electric field component on the second yz plane; Step 5.

4. The CPU passes the data received in step 5.3 to the GPU (q) to update the electric field component in the GPU (q) memory. and data; in, express In the The y-direction electric field component on the yz plane, express In the The z-direction electric field component on the yz plane; Step 5.

5. Synchronize data between the CPU and GPU.

7. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 6, characterized in that: The step 6 is specifically as follows: The magnetic field components within the computation area that each GPU is responsible for Perform the calculation: (21) in, and Respectively expressed in and exist The value of ; and is an intermediate variable, and the calculation formula is: (22) (23) Intermediate variables and for: (24) (25) The magnetic field components within the computation area that each GPU is responsible for and Calculate and get and The update formula is: (26) (27) After completing the magnetic field component , and After the update, the data on the CPU and GPU are synchronized.

8. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 7, characterized in that: The step 8 is specifically as follows: Output attenuation factor phase The calculation formula is: (28) in is the electric field component When the third carrier cycle crosses zero in the positive direction, is the speed of light, is the great circle distance of wave propagation; When the three-dimensional terrain modeling is set to the actual complex propagation path, that is, the simulation area is set to the complex terrain containing free space and stratum area, the attenuation factor phase of the Loran-C signal on the actual complex propagation path is obtained by formula (28): ; When the three-dimensional terrain modeling is set to a pure seawater propagation path, that is, the simulation area is set to a seawater area, the attenuation factor phase of the Loran-C signal on the pure seawater propagation path is obtained by formula (28): ; Then calculate the ASF and get: (29)。 9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the multi-GPU based three-dimensional FDTD complex path ASF prediction method are implemented as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the multi-GPU based three-dimensional FDTD complex path ASF prediction method as described in any one of claims 1 to 8 are implemented.

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