Search

CN-122021207-A - HIE-FDTD-based VLF electromagnetic wave propagation characteristic prediction method

CN122021207ACN 122021207 ACN122021207 ACN 122021207ACN-122021207-A

Abstract

The invention belongs to the technical field of wave propagation, and discloses a VLF electromagnetic wave propagation characteristic prediction method based on HIE-FDTD, according to the method, a two-dimensional HIE-FDTD method is adopted to carry out numerical modeling on the propagation process of very low frequency electromagnetic waves under the excitation condition of an underwater source, and simultaneously, a CR solver is adopted to carry out parallel solving on a tri-diagonal linear equation set formed in the implicit updating process. The method fully considers the influence of ionosphere change on the long-distance propagation characteristic of the VLF electromagnetic wave, solves the problems that the traditional FDTD method is limited by CFL stability and has overlarge calculation cost under the condition of modeling the underwater electromagnetic wave propagation fine grid, and overcomes the defects that the HIE-FDTD adopts a serial Thomas solver, has low parallelism and is difficult to accelerate and expand efficiently on a GPU, thereby realizing the high-precision rapid prediction of the underwater VLF electromagnetic wave propagation characteristic in the sea-air-ionosphere environment.

Inventors

  • WANG DANDAN
  • KONG WENJUN
  • WANG HONGLEI
  • CHEN YU
  • 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 VLF electromagnetic waves based on HIE-FDTD is characterized by comprising the following steps: 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 Electric displacement vector of direction Electric field component And auxiliary components thereof; step 3, constructing implicit expression Directional electric displacement vector A formed tri-diagonal linear equation set; step 4, adopting a CR solver to carry out parallel acceleration solving on the tri-diagonal linear equation set constructed in the step 3 to obtain an electric displacement vector updated in the current time step Is a numerical value of (2); Step 5, adding an excitation source to Electric displacement vector in direction Applying; Step 6, updating the whole calculation area Component of electric field in direction Component of magnetic field And auxiliary components thereof; 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 the propagation characteristics of VLF electromagnetic waves based on HIE-FDTD according to claim 1, wherein said step 1 specifically comprises: in a two-dimensional cylindrical coordinate system In defining the size of the calculation region as Wherein Is a transverse coordinate The number of grids in the direction, N z , is the number of grids in the z direction of the height coordinate, The mesh dissection step sizes in the direction and the z direction are respectively set as And ; 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 two 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 electric parameters of the wave propagation path include relative dielectric constant of seawater and ionosphere 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; Representing a power-of-the-power gradient function along the coordinate direction within the CFS-PML region, , The direction of the coordinates is indicated as a variable, Coordinate values representing the starting 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: Electric displacement vector of direction Electric displacement vector in z direction ; Component of electric field in direction Component of electric field in z-direction Component of magnetic field in z-direction ; Electric field auxiliary component Auxiliary component of magnetic field Wherein , Indicating the direction of rotation about the axis in the cylindrical coordinates, Representing a geometric correction term marker in a cylindrical coordinate system; electromagnetic field component calculation coefficient 、 、 、 、 The calculation expression is as follows: (4) (5) (6) (7) (8) Wherein, the ; = ; The collision frequency is indicated as such, Representing the plasma angular frequency; Parameters of auxiliary variables under CFS-PML framework 、 、 Wherein = ; Current run time step 。
  3. 3. The method for predicting the propagation characteristics of VLF electromagnetic waves based on HIE-FDTD according to claim 2, wherein said step 2 specifically comprises: For the whole calculation area Electric displacement vector of direction Electric field component And its auxiliary component The specific calculation formula is as follows: (9) (10) (11) Wherein, the 、 Is a discrete spatial index; Representation of At a time step Space of space The value of the position is taken out, The time difference is indicated as such, 、 Representing a spatial difference; Comprising electric displacement vectors And Electric field component And Component of magnetic field Auxiliary component of electric field Auxiliary component of magnetic field ; Representation of At the position of In the direction of The values at the positions of the grids, Representation of In the z direction The values at the positions of the grids, Parameters including auxiliary variables under CFS-PML framework 、 、 。
  4. 4. The method for predicting the propagation characteristics of a VLF electromagnetic wave based on HIE-FDTD as set forth in claim 3, wherein said step 3 specifically includes: Constructional implicit expression Directional electric displacement vector The set of tri-diagonal linear equations formed is: (12) Wherein, the Representing the relative permeability.
  5. 5. The method for predicting the propagation characteristics of VLF electromagnetic waves based on HIE-FDTD as set forth in claim 4, wherein said step 4 is specifically: 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: (13) 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 CR iteration level and span parameters; In the first place Introducing layer-dependent coupling spans in layer specifications, the th The coupling span of the layer protocol is , The coupling span is doubled layer by layer along with the progress of the protocol; step 4.3, a forward protocol stage; In the forward protocol stage, the even numbered equations in the current system are updated in parallel to the first The first equation is adjacent to it Equation (V) The equations are linearly combined, odd-numbered unknowns are eliminated, and a new tri-diagonal linear equation set only containing even-numbered unknowns is obtained; In the first place In the calculation of the layer specification coefficients, The new coefficients of the layer are written as: (14) (15) (16) (17) (18) Wherein, the 、 Respectively represent the current equation, namely the first Adjacent equation indexes of the coupling of the left side and the right side of each equation; 、 、 、 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 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 of left-hand coupled equations adjacent to each equation; 、 、 、 Respectively represent the first Layer protocol time and th Lower diagonal coefficients, main diagonal coefficients, upper diagonal coefficients, and right-end known terms of right-side coupling equations adjacent to each equation; 、 Respectively represent the first The layer protocol is used for eliminating the element elimination coefficient influenced by left and right adjacent unknowns; Updating coefficients according to the formulas (14) to (18) to obtain a new system after the specification; Repeatedly executing forward reduction to halve the scale of the equation set layer by layer until the original tri-diagonal linear equation set is reduced to a binary linear equation set containing only two unknowns; Step 4.4. Solving the 2×2 subsystem; when the forward protocol proceeds to the last layer, a binary linear equation set containing only two unknowns is obtained; Let the final layer be the first Layer, the system writes: (19) Wherein, the 、 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; 、 Representing the two unknowns that ultimately remain; 、 Respectively represent the first Layer specification postth Sum of equations The right-hand known term of the equation; step 4.5, layer-by-layer substitution, recovering all unknowns; Layer-by-layer back substitution is performed according to the hierarchical sequence opposite to the forward direction protocol until all unknowns are recovered, and a complete solution vector of the original tri-diagonal linear equation set is obtained; in reverse order of the hierarchy from Layer by layer substitution is started, for the first Layer to recover unknowns Solving the following equation: (20) Wherein, the 、 The representations respectively represent the first Known unknowns at adjacent positions to the left and right of the current unknown in the layer substitution process, the current unknown being Layer to recover unknowns ; Step 4.6. Backfilling and combining the unknowns obtained by all the subsystems according to the original index positions to complete the solution of the three-diagonal equation set, thereby obtaining the electric displacement vector updated in the current time step Is a numerical value of (2).
  6. 6. The method for predicting the propagation characteristics of a VLF electromagnetic wave based on HIE-FDTD as set forth in claim 5, wherein said step 5 is specifically: 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: (21) 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 the propagation characteristics of VLF electromagnetic waves based on HIE-FDTD as set forth in claim 6, wherein said step 6 is specifically: For the whole calculation area Component of electric field in direction Component of magnetic field And its auxiliary component 、 、 The specific calculation formula is as follows: (22) (23) (24) (25) (26)。
  8. 8. the method for predicting the propagation characteristics of VLF electromagnetic waves based on HIE-FDTD as set forth in claim 7, wherein said step 8 is specifically: the radiation power is calculated to be the envelope peak value When (1) The calculation formula is as follows: (27) Wherein, the Representing the extracted receiving point signal the peak value of the electric field in the horizontal direction, Is a constant value; Extracting the calculated region by the formula (27) 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 HIE-FDTD based VLF electromagnetic wave propagation characteristics prediction method of 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 HIE-FDTD-based VLF electromagnetic wave propagation property prediction method according to any one of claims 1 to 8.

Description

HIE-FDTD-based VLF electromagnetic wave propagation characteristic prediction method Technical Field The invention belongs to the technical field of electric wave propagation, and particularly relates to a VLF electromagnetic wave propagation characteristic prediction method based on HIE-FDTD. Background The very low frequency (Very Low Frequency, VLF) electromagnetic wave refers to radio wave with the frequency of 3kHz to 30kHz, has the characteristics of long wavelength, relatively small propagation loss, good phase stability, certain penetrability to seawater and the like, and has important application value in the fields of telecommunication, navigation, time service, underwater information transmission and the like. The existing VLF system adopts a land-based transmitting mode, and long-distance radiation is realized by a large ground station and a large-size antenna, but the problems of large equipment volume, high construction and maintenance cost, poor deployment flexibility, insufficient concealment and the like are generally existed. Aiming at the problem of VLF electromagnetic wave propagation of a source under water, particularly propagation modeling and quick prediction for underwater navigation and communication application, a mature model and method which have the advantages of both precision and efficiency still lack at present, the problem has the characteristics of low-frequency long wave, strong attenuation, multi-boundary coupling, long-distance propagation and the like, multimode interference and modal conversion are easy to generate in a seawater-air-ionosphere coupling environment, and propagation rule analysis and numerical solution are more complicated. The traditional Finite-time-Domain difference (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 well process complex medium and complex boundary problems. However, in the problem of propagation of underwater VLF electromagnetic waves in a complex ionosphere environment, in order to accurately describe the electromagnetic wave rapid attenuation process in seawater, the near-field distribution variation characteristics attached to the sea-air interface, and the influence of ionosphere parameter variation on propagation characteristics, fine grid dispersion is generally required for a calculation region. If the traditional explicit FDTD method is adopted, the total number of grids is increased sharply along with the decrease of the grid size, and meanwhile, the time step of the method also has to meet strict Courant-Friedrichs-Lewy, namely CFL stability conditions, so that the number of calculation steps is increased remarkably, further, the problems of long calculation time, large storage cost, low solving efficiency and the like are brought, and the practical requirement of rapid prediction of the propagation characteristics of underwater navigation is difficult to meet. To solve the above problems, a Hybrid Implicit time-Domain Finite difference (HIE-FDTD) method provides an effective approach for electromagnetic wave propagation calculation under unidirectional fine grid conditions by using the methodAn implicit solving mechanism is introduced in the updating of the direction electric field, so that the time step limit of the traditional explicit FDTD method can be effectively relaxed while higher solving precision is maintained, and the calculation load brought by fine grid subdivision is reduced. 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 a HIE-FDTD-based VLF electromagnetic wave propagation characteristic prediction method, which can accurately predict the propagation characteristic of an underwater VLF electromagnetic wave under the condition of coupling seawater, air and ionized layer multimedia, and simultaneously shortens the calculation time, thereby meeting the actual requirements of high-precision and rapid prediction of the propagation characteristic in underwater navigation and communication application. In order to achieve the above purpose, the invention adopts the following technical scheme: the method for predicting the propagation characteristics of the VLF electromagnetic waves based on HIE-FDTD comprises the following steps: Step 1, inputting and initializing a mod