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CN-122021206-A - Underwater very low frequency electromagnetic wave propagation characteristic prediction method

CN122021206ACN 122021206 ACN122021206 ACN 122021206ACN-122021206-A

Abstract

The invention belongs to the technical field of electric wave propagation and discloses an underwater very low frequency electromagnetic wave propagation characteristic prediction method, which adopts a 3D-HIE-FDTD method to carry out numerical modeling on a very low frequency electromagnetic wave propagation process with a source positioned under water, can relatively accurately predict the electromagnetic wave propagation characteristic in an underwater complex environment, and simultaneously adopts a PCR solver to carry out parallel solving on a tri-diagonal linear equation set generated in an implicit updating process, thereby effectively improving solving efficiency and shortening calculating time, and further meeting the actual requirements of high-precision rapid prediction of the propagation characteristic under the conditions of underwater navigation and communication. The method not only solves the problems that the traditional 3D-FDTD method is limited by CFL stability and has overlarge calculation cost in the underwater electromagnetic wave propagation, but also overcomes the defects that the 3D-HIE-FDTD method adopts a serial Thomas solver, has low parallelism and is difficult to accelerate and expand efficiently on the GPU.

Inventors

  • WANG DANDAN
  • KONG WENJUN
  • PU YURONG
  • WANG HONGLEI
  • HAN CHAO
  • OU MING

Assignees

  • 济南大学

Dates

Publication Date
20260512
Application Date
20260415

Claims (10)

  1. 1. The method for predicting the propagation characteristics of the underwater very low frequency electromagnetic wave is characterized by comprising the following steps of: Step 1, inputting and initializing a model file, wherein the content of the input model file comprises grid parameters, excitation source parameters, electric parameters of an electric wave propagation path, electric parameters of a free space, absorption boundary CFS-PML parameters and time setting of a calculation region; step 2, updating the whole calculation area Component of electric field in direction Component of magnetic field An auxiliary component; step 3, constructing implicit expression Component of directional electric field And Component of directional electric field A formed tri-diagonal linear equation set; Step 4, carrying out parallel acceleration solving on the tri-diagonal linear equation set constructed in the step 3 by adopting a PCR solver to obtain an electric field component updated in the current time step 、 Is a numerical value of (2); Step 5, adding an excitation source to Electric field component in direction Applying; Step 6, updating the whole calculation area And Component of magnetic field in direction 、 An auxiliary component; Step 7, updating the current running time step The value of (2) is ; Judging whether the current running time step is equal to the preset running time step, if so, turning to step 8, otherwise, turning to step 2; Step 8, extracting the calculation region Component of electric field in direction And output the peak field strength of the (c).
  2. 2. The method for predicting propagation characteristics of an electromagnetic wave under water according to claim 1, wherein, The step 1 specifically comprises the following steps: In a three-dimensional rectangular coordinate system In defining the size of the calculation region as Wherein Is a transverse coordinate The number of grids in the direction, Is a longitudinal coordinate The number of grids in the direction, Is the height coordinate The number of grids in the direction; 、 、 The mesh subdivision step sizes of the directions are respectively set as 、 、 ; The excitation source parameters comprise an excitation source position, an excitation source loading mode, a signal frequency and a signal amplitude; Wherein the position of the excitation source is defined by 、 、 The method comprises the steps of determining initial coordinates and final coordinates in three directions, wherein an excitation source loading mode comprises a hard source loading mode and a soft source loading mode, wherein in a source model, an excitation signal adopts sine waves, the excitation source is equivalent to a horizontal electric dipole, and the current I and the dipole length dl of the excitation source are preset; the electrical parameter of the wave propagation path, i.e. the electrical parameter of the sea level, comprises the relative permittivity of the sea water And conductivity of ; The electrical parameter of free space includes the dielectric constant of air And air permeability ; The absorption boundary CFS-PML parameter includes the number of absorption boundary layer layers Conductivity distribution parameter Coefficient of elongation Attenuation coefficient Wherein: (1) (2) (3) Wherein, the Representing the order of parameter distribution; , Indicating the operating wavelength; The direction of the coordinates is indicated as a variable, Coordinate values representing the start position of the absorbent layer; Represents the absorption boundary thickness; Is an integer of the number of the times, Is a constant; the time setting includes a current run-time step Time step And a preset run time step ; Parameters initialized to 0 include: 、 、 Component of electric field in direction 、 、 ; 、 、 Component of magnetic field in direction 、 、 ; Electric field auxiliary component And magnetic field auxiliary component Wherein ; Electric field component calculation coefficient 、 Calculating coefficients of magnetic field components 、 The calculation expression is as follows: (4) (5) (6) (7) Wherein, the = ; Representing the relative permeability; Parameters of auxiliary variables under CFS-PML framework 、 、 Wherein ; Current run time step 。
  3. 3. The method for predicting propagation characteristics of an electromagnetic wave under water according to claim 2, wherein, The step 2 specifically comprises the following steps: Updating in an entire computing area Component of electric field in direction Component of magnetic field Electric field auxiliary component And Auxiliary component of magnetic field And The specific calculation formula is as follows: (8) (9) (10) (11) (12) (13) Wherein, the 、 、 Is an index of a three-dimensional discrete space, Representation of At a time step Space of space The value of the position is taken out, The time difference is indicated as such, 、 、 The difference in space is represented by a difference in space, Comprising electric field components 、 、 Component of magnetic field 、 、 Electric field auxiliary component Auxiliary component of magnetic field ; Representation of In the x direction The values at the positions of the grids, Representation of In the y direction The values at the positions of the grids, Representation of In the z direction The values at the grids; parameters including auxiliary variables under CFS-PML framework 、 、 。
  4. 4. The method for predicting propagation characteristics of an electromagnetic wave under water according to claim 3, wherein, The step 3 specifically comprises the following steps: Constructional implicit expression Component of directional electric field The set of tri-diagonal linear equations formed is: (14) Constructional implicit expression Component of directional electric field The set of tri-diagonal linear equations formed is: (15) Constructional implicit expression And Direction related auxiliary component 、 、 、 The tri-diagonal linear equation set of (2) is: (16) (17) (18) (19)。
  5. 5. the method for predicting propagation characteristics of an electromagnetic wave under water according to claim 4, wherein, The step 4 specifically comprises the following steps: Step 4.1, establishing coefficient representation of a tri-diagonal linear equation set; Scale of acquisition of Is a tri-diagonal linear system of equations First, the The following equations are written: (20) Wherein, the , ; Is the number of equations; Index number for equation; For the vector of unknowns to be solved, 、 、 Respectively represent the first First, second First, second An unknown quantity; For the lower diagonal coefficient, correspond to Coefficient of (2) ; Is the main diagonal coefficient corresponding to Coefficient of (2) ; For the upper diagonal coefficient, correspond to Coefficient of (2) ; For the right-hand known item, written in vector form ; And Absent, the boundary is treated in the following equivalent way: The time equation is: equivalent to ; The time equation is: equivalent to ; Step 4.2, initializing PCR iteration level and span parameters; Setting the number of layers of protocol ; Defining a stride for each layer , And will be at The equation set of the layers is written as Wherein, the method comprises the steps of, 、 、 、 Respectively represent the first Layer specification postth The lower diagonal coefficient, the main diagonal coefficient, the upper diagonal coefficient, and the right-hand known term of the individual equations; The initial layer satisfies , , , ; In the first place After the layer protocol is finished, the original system is divided into Each subsystem is not coupled with each other, and the unknown quantity of each subsystem is Is integrally arranged at Finishing in the layer protocol; Step 4.3, parallel reduction and generation of a half-size subsystem; Will be the first Layer specification postth The equation is linearly combined with the adjacent equations on the left side and the right side to obtain the first equation New coefficients of layer: (21) (22) (23) (24) (25) Wherein, the 、 、 、 Respectively represent the first Layer specification postth The lower diagonal coefficient, the main diagonal coefficient, the upper diagonal coefficient, and the right-hand known term of the individual equations; 、 、 、 Respectively represent the first Layer protocol time and th Lower diagonal coefficients, main diagonal coefficients, upper diagonal coefficients, and right-hand known terms for adjacent equations to the left of the individual equations; 、 、 、 Respectively represent the first Layer protocol time and th Lower diagonal coefficients, main diagonal coefficients, upper diagonal coefficients, and right-hand known terms for adjacent equations to the right of the individual equations; 、 Represent the first The layer protocol is used for eliminating the element elimination coefficient influenced by left and right adjacent unknowns; At the completion of the first After layer updating, two independent tri-diagonal sub-equation sets are obtained; Then, using each sub-equation set as a processing object, continuously adopting a parallel circulation protocol process shown in formulas (21) to (25) to update and calculate a coefficient of the next layer, and repeatedly executing the parallel circulation protocol on the sub-equation sets until each subsystem is defined as a2 multiplied by 2 tri-diagonal subsystem containing only two unknown quantities; Step 4.4, solving all 2X 2 tri-diagonal subsystems in parallel; only two unknown quantities remain 、 When, a2×2 linear equation system is solved in parallel: (26) Wherein, the And Respectively represent the first Layer specification postth Sum of equations Principal diagonal coefficients of the individual equations; Represent the first Layer specification postth Upper diagonal coefficients of the individual equations; Represent the first Layer specification postth Lower diagonal coefficients of the individual equations; And Respectively represent the first Layer specification postth Sum of equations The right-hand known term of the equation; all 2X 2 three diagonal subsystems are synchronously and parallelly solved to obtain a final solution vector, namely Is a component of (a); Step 4.5. Backfilling and combining the unknowns obtained by all 2X 2 tri-diagonal subsystems according to the original index positions to complete the solution of the tri-diagonal equation set, thereby obtaining the electric field component updated in the current time step 、 Is a numerical value of (2).
  6. 6. The method for predicting propagation characteristics of an electromagnetic wave under water according to claim 5, wherein, The step 5 specifically comprises the following steps: the added field source, i.e. the excitation source, is a sinusoidal signal, composed of electric field components Current waveform of excitation, field source Expressed as: (27) Wherein, the ; When (when) In the time-course of which the first and second contact surfaces, When (1) In the time-course of which the first and second contact surfaces, 。
  7. 7. The method for predicting propagation characteristics of an electromagnetic wave under water according to claim 6, wherein, The step 6 specifically comprises the following steps: Updating in an entire computing area Component of magnetic field in direction 、 Component of magnetic field in direction Auxiliary component 、 、 、 The specific calculation formula is as follows: (28) (29) (30) (31) (32) (33)。
  8. 8. the method for predicting propagation characteristics of an electromagnetic wave under water according to claim 7, wherein, The step 8 specifically comprises the following steps: the radiation power is calculated to be the envelope peak value When (1) The calculation formula is as follows: (34) Wherein, the Representing the level of the extracted receiving point signal Component of directional electric field The peak value of the peak value is, Is a constant value; Extracting the calculated region by the formula (34) Component of electric field in direction And output the peak field strength of the (c).
  9. 9. A computer device comprising a memory and one or more processors, the memory having executable code stored therein, wherein the processor, when executing the executable code, performs the steps of the method of predicting propagation characteristics of underwater very low frequency electromagnetic waves as claimed in any one of claims 1 to 8.
  10. 10. A computer-readable storage medium having a program stored thereon, which when executed by a processor, implements the steps of the underwater very low frequency electromagnetic wave propagation characteristic prediction method as claimed in any one of claims 1 to 8.

Description

Underwater very low frequency electromagnetic wave propagation characteristic prediction method Technical Field The invention belongs to the technical field of electric wave propagation, and particularly relates to a prediction method of underwater very low frequency electromagnetic wave propagation characteristics. Background Very low frequency (Very Low Frequency, VLF) electromagnetic waves refer to radio waves having a frequency in the range of 3kHz to 30kHz, with a wavelength of about 10km to 100km. The VLF electromagnetic wave has the characteristics of long wavelength, relatively small propagation loss, good phase stability, certain penetration capacity to seawater and the like, so that the VLF electromagnetic wave has important application value in the fields of telecommunication, navigation, time service, underwater information transmission and the like. Particularly in marine environments, VLF electromagnetic waves can penetrate sea water to a certain depth, can provide communication and navigation signal support for submarines, unmanned underwater vehicles and other underwater equipment, and therefore has unique advantages in the fields of underwater navigation and underwater communication. Most of the existing systems adopt a land-based transmitting mode, and rely on a large ground transmitting station and a large-size transmitting antenna to realize long-distance radiation, but the problems of huge antenna volume, complex transmitting device, high construction and maintenance cost, poor deployment flexibility, insufficient concealment and the like generally exist. At present, aiming at the problem of propagation of VLF electromagnetic waves with a source under water, in particular to propagation modeling and rapid prediction for underwater navigation and communication application, a mature theoretical model and a numerical method which are compatible with precision and efficiency are not available. Because the problems have the characteristics of low-frequency long wave, strong attenuation, multi-boundary coupling, long-distance propagation and the like, the modeling and solving difficulty is obviously higher than that of the conventional electromagnetic field problem. The Finite-difference-DIFFERENCE TIME-Domain (FDTD) method is widely applied to electromagnetic propagation numerical analysis because the method can directly carry out time Domain discrete solution on Maxwell equations and better process complex medium and complex boundary problems. However, in VLF navigation and communication problems with sources located underwater, due to the greater attenuation of the seawater medium, fine discretization with smaller grid sizes is often required to ensure accuracy of the propagation process and field distribution calculations. Under the three-dimensional modeling condition, if the traditional explicit FDTD method is adopted, the total number of grids is increased sharply along with the reduction of the grid size, and meanwhile, the time step of the method also has to meet the strict Courant-Friedrichs-Lewy, namely CFL stability condition, so that the number of calculation steps is increased remarkably, further, the problems of long calculation time, high storage cost, low solving efficiency and the like are brought, and the practical requirement of quick prediction of the propagation characteristics of underwater navigation is difficult to meet. In order to solve the problems, a Hybrid Explicit time-Domain Finite difference (HIE-FDTD) method provides an effective way for electromagnetic wave propagation calculation under the condition of unidirectional fine grids, and the method can effectively relax time step limit of the traditional Explicit FDTD method while maintaining higher solving precision by introducing an Implicit solving mechanism in the updating of electric field components in the x and y directions, thereby reducing the calculation burden brought by fine grid subdivision. In particular, in the three-dimensional underwater VLF propagation problem, compared with the traditional FDTD method, the HIE-FDTD method is more suitable for processing complex scenes with large calculation area, fine grids and high stability requirements. However, the HIE-FDTD method generally needs to solve a tri-diagonal linear equation set in the implicit updating process, and the existing method mostly adopts a Thomas solver for calculation. The Thomas solver is simple to realize, but has strong serialization and insufficient parallel computing capability in the recursive computing process, and particularly in the large-scale three-dimensional problem and GPU parallel realization, the computing advantage of high-performance hardware is difficult to fully develop, so that the further improvement of the integral solving efficiency of the HIE-FDTD method is limited. Disclosure of Invention The invention aims to provide an underwater very low frequency electromagnetic wave propagation characteristic predictio