3D FDTD Complex Path ASF Prediction Method Based on Multi-GPU

Abstract

The present invention belongs to the technical field of radio wave propagation, and specifically discloses a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs. The method of the present invention implements the three-dimensional FDTD algorithm through multiple GPUs and is used to predict the ASF on complex paths. First, the parameters are preprocessed and copied to the device side, i.e., the GPU side; secondly, the electric field components in the entire calculation area are updated; then the field source is updated, and the electric field components on adjacent GPUs are exchanged; then the magnetic field components in the entire calculation area are updated; finally, a loop is performed and the end condition is judged, and the ASF is output when the calculation ends. The method of the present invention solves the problem that the two-dimensional time delay prediction method has poor ASF prediction accuracy due to the inability to consider the lateral effect, and overcomes the deficiency that the traditional three-dimensional FDTD method is difficult to simulate the low-frequency ground wave propagation in a large area, providing a theoretical basis and technical support for improving the service accuracy of the low-frequency radio navigation and timing system.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio wave propagation, and particularly 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 along complex paths in rugged terrain, it will cause additional signal delay, namely the Additional Secondary Factor (ASF), which will lead to serious PNT errors. Therefore, accurately predicting ASF in complex paths is crucial for improving the service accuracy of the Loran-C system.

[0003] The modeling of the Loran-C additional secondary factor has long been mainly 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 in the actual three-dimensional space on ASF. This simplification may have a good approximation effect under flat terrain or propagation paths with insignificant terrain changes. However, when dealing with propagation paths with drastic terrain changes, the two-dimensional model cannot accurately characterize the multipath effect and waveguide effect caused by the terrain, resulting in a significant deviation between the predicted value and the actual observed value of ASF.

[0004] In addition, due to the inherent vulnerability 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 handle the three-dimensional terrain boundary conditions, but this method will introduce inherent errors when dealing with inclined interfaces, and it is difficult to effectively reduce these errors 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 at long distances, which is mainly limited by its extremely high computational complexity. Especially in large-scale computational domains and long-time simulation scenarios, the computational resource requirements increase 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 object 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 terrains, can accurately predict ASF on long-distance complex and irregular terrains, and at the same time, based on a multi-GPU parallel computing architecture, can expand the calculation area and reduce the calculation time.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] The three-dimensional FDTD complex path ASF prediction method based on multiple GPUs includes the following steps:

[0010] Step 1. Set and initialize three-dimensional terrain modeling parameters on the CPU side;

[0011] Step 2. After preprocessing the three-dimensional terrain modeling parameters, copy the data of the three-dimensional terrain modeling parameters stored on the CPU side to the device side, i.e., the GPU side;

[0012] Step 3. Update the electric field components within the calculation area responsible for each GPU , and ;

[0013] Step 4. After updating the field sources within the calculation area responsible for each GPU, synchronize the data between the CPU side and the GPU side;

[0014] Step 5. Exchange the and components on adjacent GPUs, and then synchronize the data between the CPU side and the GPU side;

[0015] Step 6. Update the magnetic field components within the calculation area responsible for each GPU , and , and then synchronize the data between the CPU side and the GPU side;

[0016] 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 value of the current running time step to , and go to Step 3;

[0017] Step 8. Calculate ASF by extracting the moment when the positive zero-crossing of the third carrier period of the electric field component within the calculation area responsible for each GPU.

[0018] In addition, based on the above-mentioned 3D FDTD complex path ASF prediction method based on multiple GPUs, the present invention also proposes a computer device, which includes a memory and one or more processors;

[0019] The memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the above-mentioned 3D FDTD complex path ASF prediction method based on multiple GPUs.

[0020] In addition, based on the above-mentioned 3D 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 the processor, it is used to implement the steps of the above-mentioned 3D FDTD complex path ASF prediction method.

[0021] The present invention has the following advantages:

[0022] As described above, the present invention describes a 3D FDTD complex path ASF prediction method based on multiple GPUs. This method first introduces the 3D-FDTD method into ASF prediction. It uses 3D terrain modeling, 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 traditional 2D modeling method's inability to consider lateral effects. At the same time, the present invention is implemented based on a multi-GPU parallel computing architecture, and the data transmission between different GPU devices is improved according to the complex path ASF prediction problem, overcoming the deficiency that the traditional 3D FDTD method is difficult to simulate large-area low-frequency ground wave propagation. On the premise of ensuring calculation accuracy, it greatly expands the scale of the computable area, provides an efficient solution for ASF prediction in large-scale complex terrain scenarios, and is more suitable for engineering promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the 3D FDTD complex path ASF prediction method based on multiple GPUs in an embodiment of the present invention.

[0024] Figure 2 It is a schematic diagram of the principle of the 3D FDTD complex path ASF prediction method based on multiple GPUs in an embodiment of the present invention.

[0025] Figure 3 It is a schematic diagram of the ASF prediction results of the method of the present invention and the traditional method on a flat and smooth ground path.

[0026] Figure 4 It is a schematic diagram of the ASF prediction results of the method of the present invention and the traditional method when there is a Gaussian mountain range on the propagation path. Detailed implementation manners

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners:

[0028] Embodiment 1

[0029] The present invention provides a three-dimensional FDTD complex path ASF prediction method based on multiple GPUs, which 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. Subsequently, exchange the electric field components on adjacent GPUs and . Then update the magnetic field components in the entire calculation area. Finally, perform a loop and judge the end condition, and output ASF when the calculation ends. Based on the above inventive concept, the three-dimensional FDTD complex path ASF prediction method proposed by the present invention will be described in detail below with reference to the accompanying drawings.

[0030] As Figure 1 shown, the three-dimensional FDTD complex path ASF prediction method based on multiple GPUs specifically includes the following steps:

[0031] Step 1. Set three-dimensional terrain modeling parameters on the CPU side and initialize them.

[0032] The three-dimensional terrain modeling parameters are the 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 perfectly matched layer (PML) of the absorbing boundary, as well as the parameters of the time setting and the decomposition setting of the simulation area.

[0033] Among them, the electrical parameters of the simulation path include the relative permittivity of free space and conductivity , the relative permittivity of the formation area and conductivity , and the relative permittivity of the seawater area and conductivity . The electrical parameters of the simulation path are used to accurately characterize the complex medium distribution.

[0034] 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 , where , , The number of grids in the directions are respectively set to , , , the grid division step sizes are respectively set to , , .

[0035] Set the parameters of the field source, which include the number of field sources , the position of the field source, the type of the field source, the Gaussian pulse width , the Gaussian pulse delay , the signal frequency and the amplitude A; among them, the position of the field source includes the starting point of the field source on the axis , , the starting point of the field source on the axis , , the starting point of the field source on the axis , ; the type of the field source includes soft source and hard source. When the type of the field source is set to soft source, the excitation signal is the superposition of the field source signal and the previous-step electric field value. When the type of the field source 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 is simulated.

[0036] Set the parameters of the absorbing boundary PML, which include the number of absorbing boundary layers . By setting an appropriate number of absorbing boundary layers, the reflection error caused by artificial truncation is eliminated.

[0037] The time setting includes the current running time step , the time step and the preset running time step . By setting an appropriate time, the numerical stability is ensured.

[0038] The decomposition setting of the simulation area includes setting the number of simulation area boundaries to be , and setting the calculation area responsible for each GPU to be . The method of the present invention adopts a domain decomposition strategy to solve the problem of the upper limit of the single-GPU video memory, and further realizes the large-area ASF prediction.

[0039] Then initialize the relevant parameters to 0. The parameters initialized to 0 specifically include:

[0040] Electric field components: , , , where , , respectively represent , , The electric field component in the direction.

[0041] Magnetic field component: 、 、 , where 、 、 respectively represent 、 、 the magnetic field components in the directions.

[0042] Intermediate variables: 、 、 、 , where = , , , , , .

[0043] Electric field component calculation coefficients: 、 .

[0044] Magnetic field component calculation coefficients: 、 .

[0045] Intermediate variable calculation coefficients: 、 、 .

[0046] The current running time step .

[0047] The output quantity at the zero-crossing moment of the third period .

[0048] Construct the initial state of the electromagnetic field iterative calculation to establish a complete parametric calculation framework for the high-precision numerical simulation of the electromagnetic wave propagation characteristics in the three-dimensional terrain.

[0049] Step 2. Parameter preprocessing, copy relevant parameters: After preprocessing the three-dimensional terrain modeling parameters, copy the data of the three-dimensional terrain modeling parameters stored on the CPU side to the device side, i.e., the GPU side.

[0050] First, preprocess the PML-related parameters 、 、 , specifically including:

[0051] (1)

[0052] (2)

[0053] (3)

[0054] Among them, when , it represents the coordinate position of the field source on the x-axis. When , it represents the coordinate position of the field source on the y-axis. When , it represents the coordinate position of the field source on the z-axis; represents the coordinate position of the location of the field source in the three-dimensional rectangular coordinate system .

[0055] is a constant. Generally, the value range is , where represents the wavelength. is an integer. Generally, the value interval is . is a constant. Generally, the value interval is . is the absorption boundary thickness. is a key parameter for adjusting the PML performance. The absorption effect of the absorption boundary is the best.

[0056] Next, preprocess the calculation coefficients of the electromagnetic field components , , , :

[0057] (4)

[0058] (5)

[0059] (6)

[0060] (7)

[0061] Among them, , and represent the relative permittivity and conductivity in the non-free space, i.e., the non-air layer. = , represents the magnetic permeability of free space, taking . represents the relative magnetic permeability, taking .

[0062] Specifically, when the region is free space, i.e., the air layer, the relative permittivity and conductivity are taken as and . When the region is the formation, the relative permittivity and conductivity are taken as and . When the region is seawater, the relative permittivity and conductivity are taken as and .

[0063] Preprocessing intermediate variable calculation coefficients , , :

[0064] (8)

[0065] (9)

[0066] (10)

[0067] Among them, = , , , , , .

[0068] Some parameters that do not change with time iteration are calculated in advance on the CPU side and then directly transferred to the GPU side, which can reduce the computational load on the GPU side and improve the computational efficiency.

[0069] After preprocessing, the data of the electric field components, magnetic field components, intermediate variables, electromagnetic field component calculation coefficients, intermediate variable calculation coefficients, field source parameters, and the output quantity at the zero-crossing moment of the third carrier period stored on the CPU side are copied to the GPU side. The parameters copied to the GPU side specifically include:

[0070] Electric field components: , , , magnetic field components: , , .

[0071] Intermediate variables: , , , .

[0072] Electromagnetic field component calculation coefficients: , , , .

[0073] Intermediate variable calculation coefficients: , , .

[0074] Source parameters: Number of sources , the location of the field source , , , , , , type of field source, Gaussian pulse width , Gaussian pulse delay , signal frequency and amplitude A.

[0075] Output value at the zero-crossing point of the third cycle .

[0076] 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.

[0077] Step 3. Update the electric field components within the computational area that each GPU is responsible for , and .

[0078] The electric field components within the computational area responsible for each GPU The specific calculation formula is:

[0079] (11)

[0080] 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:

[0081] (12)

[0082] (13)

[0083] wherein denotes the value at ; denotes the value at .

[0084] and respectively denote and the central differences of y and z, expressed as:

[0085] (14)

[0086] (15)

[0087] wherein and are the grid sizes in the y and z directions at = , = . The following difference formulas are calculated in the same way as formulas (14) and (15), and will not be elaborated further. and are intermediate variables used to further simplify the formula, specifically:

[0088] (16)

[0089] (17)

[0090] wherein denotes the value at ; denotes the value at ; denotes the value at ; denotes the value at . Then, the electric field components and in the calculation area responsible for each GPU are calculated. Since it is the FDTD algorithm in a three-dimensional rectangular coordinate system and the radio wave propagation has symmetry in the x, y, and z directions, and the update formula structures of different field components are the same, the update formulas for and are directly given.

[0091] ​​​​​​​​​​ (18)

[0092] (19)

[0093] Among them, 、 、 、 have the same calculation method as formulas (12) and (13).

[0094] The iterative formula for the electric field component of the 3D-FDTD method in cooperation with PML is used to achieve accurate simulation of electromagnetic waves. Compared with the traditional 2D method, the method proposed by the present invention can consider the transverse propagation effect of electromagnetic waves, thereby improving the ASF prediction accuracy in complex three-dimensional regions.

[0095] Step 4. After updating the field sources in the calculation area responsible for each GPU, synchronize the data between the CPU side and the GPU side.

[0096] The added source is the Loran-C signal, and the field source is excited by the electric field component Its current waveform is expressed as:

[0097] (20)

[0098] Among them, represents the current waveform, .

[0099] When , . Conversely, when , .

[0100] Update the field sources in the calculation area responsible for each GPU according to the parameters set in the above step 1.

[0101] Specifically, in this embodiment, the signal frequency, Gaussian pulse width, and Gaussian pulse delay for updating the field source are: , = 0, . And update the field source according to the number, position, and type of the field source set in the above step 1. For example, the field source is located in GPU(1), and the number of field sources is set to . The field source positions are: 、 、 、 、 、 . The field source type is a soft source.

[0102] ASF is the additional delay in the arrival time of Loran-C signals due to the changes in electrical parameters and rugged terrain along the actual path compared to the all-seawater path. A small deviation in ASF can lead to errors of up to several kilometers. By simulating the actual Loran-C signals, it supports the accurate calculation of subsequent ASF, providing theoretical support for achieving more precise Loran-C navigation and timing services.

[0103] After completing the update of the field sources within the computational region responsible for each GPU, data synchronization is performed between the CPU side and the GPU side. Data synchronization is to ensure that when data transfer is executed, the current calculations have all been completed, thereby ensuring data consistency. For example, in the Visual Studio platform, after the field source update is completed, the data synchronization operation is carried out through the command "cudaDeviceSynchronize".

[0104] Step 5. Exchange the and components on adjacent GPUs, and then perform data synchronization between the CPU side and the GPU side.

[0105] In the multi-GPU parallel implementation of the three-dimensional FDTD algorithm, since the computational region is decomposed along the x direction, the data exchange between GPUs is completed by transferring the field components on the y and z planes. Considering that the field sources are excited by , only the boundary values of the electric field components and calculated by each GPU need to be exchanged to achieve data synchronization and unification between multiple GPUs. The specific implementation steps are as follows:

[0106] Step 5.1. Transfer the data of the electric field components and in the memory of GPU(q) to the CPU memory. Among them, GPU(q) represents the th GPU; represents the electric field component in the y direction on the th yz plane, and represents the electric field component in the z direction on the th yz plane.

[0107] Step 5.2. The CPU transfers the data received in Step 5.1 to GPU(q + 1) for updating the electric field components and in the memory of GPU(q + 1).​ The data. Among them, GPU(q + 1) represents the (q + 1)-th GPU; represents the y-direction electric field component on the first yz plane, represents the z-direction electric field component on the first yz plane.

[0108] Step 5.3. Transfer the electric field components in the GPU(q + 1) memory to the CPU memory. Among them, represents the y-direction electric field component on the second yz plane, represents the z-direction electric field component on the second yz plane.

[0109] Step 5.4. The CPU transfers the data received in Step 5.3 to GPU(q) for updating the electric field components in the GPU(q) memory and. Among them, represents the y-direction electric field component on the -th yz plane, represents the z-direction electric field component on the -th yz plane.

[0110] Step 5.5. Synchronize the data between the CPU side and the GPU side.

[0111] For the continuity of the data in the entire calculation region, the update of the field quantity in GPU(q + 1) requires the data support on the -th yz plane in the calculation region responsible by GPU(q). And 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 time is updated, the data exchange is completed between the GPU devices to realize the continuous calculation of electromagnetic waves. Different from the traditional multi-GPU implementation of the FDTD method that requires simultaneous transmission of the electric field components , and the magnetic field components and Compared with the [scheme], the data transmission volume of the method of the present invention is reduced by half, and the algorithm is implemented with the minimum data transmission volume, improving the calculation efficiency.

[0112] Step 6. Update the magnetic field components within the calculation region responsible for each GPU 、 and , and then synchronize the data between the CPU side and the GPU side.

[0113] For the magnetic field components within the calculation region responsible for each GPU perform the calculation:

[0114] (21)

[0115] Among them, is the spatial label introduced to simplify the arithmetic formula, which represents the value of the calculation parameter at , aligned with the current calculated field value. For example, at this time , 、 respectively represent the values at and at . and are intermediate variables, and the calculation formula is:

[0116] (22)

[0117] (23)

[0118] The intermediate variable and are:

[0119] (24)

[0120] (25)

[0121] Then, perform the calculation on the magnetic field components and within the calculation region responsible for each GPU. Similarly, since it is the FDTD algorithm in a three-dimensional rectangular coordinate system, the propagation of radio waves in the x, y, and z directions has symmetry, and the update formula structures of different field components are the same. Therefore, directly give the update formulas for and :

[0122] (26)

[0123] (27)

[0124] Among them, , , , are calculated in the same way as formulas (22) and (23).

[0125] The iterative formula for the magnetic field component of the 3D-FDTD method combined with PML realizes the accurate simulation of electromagnetic waves. Compared with the two-dimensional method, this method can consider the transverse propagation effect of electromagnetic waves and improve the ASF prediction accuracy in complex three-dimensional regions.

[0126] 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 to , and go to Step 3.

[0127] Specifically, determine whether the current running time step n satisfies . If not, continue to repeat the above steps 3 to 6 to update the value of the current running time step until it reaches the preset value. If satisfied, end the loop.

[0128] Step 8. Calculate ASF by extracting the moment of the positive zero-crossing of the third carrier period of the electric field component within the calculation area responsible for each GPU.

[0129] Output the attenuation factor phase , and the calculation formula is as follows:

[0130] (28)

[0131] Among them, is the moment of the positive zero-crossing of the third carrier period of the electric field component , is the speed of light. represents the great circle distance of wave propagation.

[0132] When the three-dimensional terrain modeling parameters are set to the actual complex propagation path, that is, the simulation area is set to a complex terrain including free space and formation area, the attenuation factor phase of the Loran-C signal on the actual complex propagation path is obtained through formula (28). When the three-dimensional terrain modeling is set to the pure seawater propagation path, that is, the simulation area is set to the seawater area, the attenuation factor phase of the Loran-C signal on the pure seawater propagation path is obtained through formula (28).

[0133] Then calculate ASF:

[0134] (29)

[0135] During the field value update process of the 3D-FDTD method, the update of the electric and magnetic fields at each grid point only depends on the field values of neighboring grids, without global data dependence, and naturally supports data parallelism. The GPU architecture can schedule thousands of threads simultaneously to process the field updates of different grids and maximize the computing density, which makes the 3D-FDTD method very suitable for GPU programming. For large-scale three-dimensional electromagnetic simulation problems, it is necessary to store field data of dozens or even hundreds of GB, resulting in a single GPU being difficult to complete the computing task. Therefore, the three-dimensional FDTD complex path ASF prediction method based on multiple GPUs breaks through the single-card resource limit through the domain decomposition strategy. Each GPU independently manages the data in the local computing area and executes the field update calculation, thereby realizing the prediction of complex path ASF in a large three-dimensional area.

[0136] In addition, in order to verify the effectiveness of the method proposed in the present invention, the following specific experiments are also given:

[0137] Experiment 1 is the ASF prediction result on a flat and smooth ground path.

[0138] The size of the calculation area is: {-0.72 km ≤ ≤ 104.4 km, -4.86 km ≤ ≤ 4.86 km, -1.44 km ≤ ≤ 4.86 km}, the grid division size = = = 18 m, the time step is . The relative dielectric constant of the formation is , the conductivity , the relative dielectric constant of seawater , the conductivity .

[0139] Figure 3 This is the ASF result of the 3D-FDTD method proposed in the present invention, the 2D-FDTD method, and the flat ground formula on the propagation path of a flat and smooth ground with different electrical parameters. From Figure 3 it can be seen that there is almost no error in the three methods, proving that the 3D-FDTD method is applicable to ASF prediction.

[0140] Experiment 2 is the ASF prediction result on the propagation path of a Gaussian mountain range.

[0141] 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, and the ASF is predicted by the method proposed in the present invention.

[0142] Figure 4 It is a schematic diagram comparing the ASF results on the central tangent line of the mountain calculated by the method of the present invention and the 2D-FDTD method in the horizontal direction, where H represents the height of the Gaussian mountain. From Figure 4 It can be seen that when the mountain height is relatively low, the calculation results of the 2D-FDTD and 3D-FDTD methods are in good agreement. However, for terrains with relatively high mountain heights, significant differences begin to appear in the calculation results of the two methods in the mountain area. This difference reaches a peak in the area behind the mountain, and then gradually converges and stabilizes within the propagation range, but the ASF error is still above 200 ns. It should be noted that the influence of the lateral terrain on ASF is not only reflected in the shadow area, but also significantly exists in the peripheral area outside the lateral mountain. These ASF differences mainly stem from the lateral diffraction effect that can be accurately captured by the three-dimensional FDTD method, which is a physical phenomenon that cannot be characterized by the 2D-FDTD method.

[0143] The method of the present invention overcomes the deficiencies of traditional two-dimensional modeling methods in predicting ASF for 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 terrains 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 through multi-GPU parallel technology without loss of accuracy.

[0144] Embodiment 2

[0145] This Embodiment 2 describes a computer device, which includes a memory and one or more processors.

[0146] Executable code is stored in the memory, and 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 multi-GPU in the above-mentioned Embodiment 1.

[0147] The computer device in this embodiment is any device or apparatus with data processing capabilities, which will not be elaborated here.

[0148] Embodiment 3

[0149] This Embodiment 3 describes a computer-readable storage medium, on which a program is stored. When the program is executed by the processor, it is used for the steps of the three-dimensional FDTD complex path ASF prediction method based on multi-GPU.

[0150] 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 may be 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.

[0151] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to listing the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any person skilled in the art under the teaching of this specification fall within the substantial scope of this specification and should be protected by the present invention.

Claims

1. A three-dimensional FDTD complex path ASF prediction method based on multiple GPUs, 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 component E in the computational area that each GPU is responsible for x 、E y and E z ; 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 E on adjacent GPUs y and E z Components, and then synchronize data between the CPU and GPU; Step 6. Update the magnetic field component H within the computational area that each GPU is responsible for x , H y and H z , 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 value of the current running time step n to n+1, and go to step 3; Step 8. Extract the electric field component E in the computational area that each GPU is responsible for z Calculate ASF at the positive zero crossing point of the third carrier cycle; 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 ε r and conductivity σ r , relative dielectric constant ε of the formation area g and conductivity σ g 、Relative dielectric constant ε of seawater area s and conductivity σ s ; 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 (x, y, z), where the number of meshes is set to N x 、N y 、N z , the meshing step size is set to d x ,d y ,d z ; Set the parameters of the field source, including the number of field sources N s , the location of the field source, the type of field source, the Gaussian pulse width G ω , Gaussian pulse delay G d , signal frequency f and amplitude A; where the position of the field source includes the starting point S of the field source on the x-axis xs , S xe , the starting point S of the field source on the y axis ys , S ye , the starting point S of the field source on the z-axis zs , S ze ; 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 N p ; The time settings include the current running time step n, time step d t and preset running time step N t ; The decomposition setting of the simulation area includes setting the number of simulation area boundaries to N and setting the computation area that each GPU is responsible for to (N x / N,N y ,N z ); The parameters initialized to 0 include: Electric field component E x 、E y 、E z ; Magnetic field component H x , H y , H z ; Intermediate variables Γ χη ,Ψ χη , where χη=xy, xz, yx, yz, zx, zy; Electromagnetic field component calculation coefficient CA e CB e , CA h CB h ; Intermediate variable calculation coefficient C χη0 , C χη1 , C χη2 ; Current running time step n; Output value T at the time of the third carrier cycle crossing zero ω ; Output attenuation factor phase T ω The calculation formula is: Where T is the electric field component E z At the moment when the third carrier cycle crosses zero in the positive direction, C is the speed of light, and D 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:

2. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 1, characterized in that: The step 2 is specifically as follows: For PML related parameters σ η , κ η , α η Preprocessing: Where η = x l ,y l ,z l , when η=x l When η = y l When η=z l η0 represents the coordinate position of the field source on the z-axis; η1 represents the coordinate position of the field source on the three-dimensional rectangular coordinate system (x, y, z); λ represents the wavelength; u is a parameter used to adjust the PML performance; d is the absorption edge thickness; κ max is an integer, α max is a constant; Calculation coefficients CA for electromagnetic field components e CB e , CA h CB h Preprocessing: THAT h =1 (6) Where γ = x, y, z, ε γ With σ γ Respectively represent the relative permittivity and conductivity in non-free space; Δt = d t , μ0 represents the magnetic permeability of free space; μ r Relative magnetic permeability. When the simulation area is free space, the relative permittivity and conductivity are ε r and σ r ; When the simulation area is a stratum, the relative permittivity and conductivity are ε g and σ g ; When the simulation area is seawater, the relative dielectric constant and conductivity are ε s and σ s ; Calculate the coefficient C for the intermediate variable χη0 , C χη1 , C χη2 Preprocessing: 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.

3. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 2, characterized in that: The step 3 is specifically as follows: The electric field component E in the computational area responsible for each GPU x The specific calculation formula is: Among them, i, j, k are space labels; CA e (m) and CB e (m) respectively represent the CA e and CB e The value at m, where m is the space index; and is an intermediate variable, and the calculation formula is: Among them, C yz1 (m) means C yz1 The value at m, C zy1 (m) means C zy1 The value at m; and Respectively represent H z , H y The central difference of y and z is expressed as: Among them, Δy and Δz are the grid sizes in the y and z directions at (i+1 / 2,j,k), Δy=d y , Δz=d z ; Intermediate variable Ψ yz With zy for: Among them, C zy0 (m) means C zy0 The value at m, C yz0 (m) means C yz0 The value at m; C zy2 (m) means C zy2 The value at m, C yz2 (m) means C yz2 The value at m; The electric field component E in the computational area responsible for each GPU y and E z Calculate and get E y and E z The update formula is:

4. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 3, 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 E z Excitation, current waveform of the field source i s (t) is expressed as: in, When t≤0, h(t)=0; when t>0, h(t)=1; 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.

5. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 4, 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; Wherein, GPU(q) represents the qth GPU; Indicates E y In the The y-direction electric field component on the yz plane, Indicates E z 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 E in the memory of GPU (q+1) y (1,N y ×N z ) and E z (1,N y ×N z ) data; Wherein, GPU(q+1) represents the q+1th GPU; E y (1,N y ×N z ) means E y The y-direction electric field component on the first yz plane, E z (1,N y ×N z ) means E z The z-direction electric field component on the first yz plane; Step 5.

3. Put the electric field component E in GPU(q+1) memory y (2,N y ×N z ) and E z (2,N y ×N z ) data is transferred to the CPU memory; Among them, E y (2,N y ×N z ) means E y The y-direction electric field component on the second yz plane, E z (2,N y ×N z ) means E z 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 GPU(q) for updating the electric field component in the GPU(q) memory. and data; in, Indicates E y In the The y-direction electric field component on the yz plane, Indicates E z In the The z-direction electric field component on the yz plane; Step 5.

5. Synchronize data between the CPU and GPU.

6. The multi-GPU based 3D FDTD complex path ASF prediction method according to claim 5, characterized in that: The step 6 is specifically as follows: The magnetic field component H in the computation area responsible for each GPU x Perform the calculation: Among them, CA h (m) and CB h (m) respectively represent the CA h and CB h The value at m; and is an intermediate variable, and the calculation formula is: Intermediate variable Γ yz With Γ zy for: The magnetic field component H in the computation area responsible for each GPU y and H z Calculate and get H y and H z The update formula is: After completing the magnetic field component H x , H y and H z After the update, the data on the CPU and GPU are synchronized.

7. 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 6.

8. 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 6 are implemented.

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