CN-116187130-B - Quick simulation method, system and equipment for time domain finite element of ground penetrating radar

CN116187130BCN 116187130 BCN116187130 BCN 116187130BCN-116187130-B

Abstract

The invention discloses a method, a system and equipment for quickly simulating a time domain finite element of a ground penetrating radar. The method comprises the steps of setting geometric parameters and electrical parameters of a two-dimensional complex electric model, constructing a weak form of a two-dimensional electromagnetic wave equation, forming a time domain finite element equation, establishing a linear equation set after central difference time dispersion, judging whether the time step meets CFL stability conditions or not according to a given time step, if so, directly solving the linear equation set, if not, carrying out LU decomposition on coefficient matrixes of the linear equation set, perturbing unstable characteristic values in the coefficient matrixes until absolute values of all characteristic values of the decomposed coefficient matrixes are smaller than or equal to 1, generating a reconstruction coefficient matrix, and solving the reconstructed linear equation set to enable the time step to break through the CFL stability conditions. The invention can improve the simulation precision of the ground penetrating radar.

Inventors

WANG HONGHUA
WANG MINLING
WU QIMING

Assignees

桂林理工大学

Dates

Publication Date: 20260508
Application Date: 20230113

Claims (8)

1. The method for rapidly simulating the finite element in the time domain of the ground penetrating radar is characterized by comprising the following steps of: Setting geometrical parameters and electrical parameters of the complex ground model, wherein the geometrical parameters comprise the size of the complex ground model; Utilizing a Delaunay unstructured grid discrete complicated ground model, adopting fine grid subdivision in a target body area, and adopting sparse grid subdivision in an area with gentle electromagnetic field change, wherein the fine grid is a small space step length, and the sparse network is a large space step length; based on the geometric parameters and the electrical parameters, constructing a weak form of a two-dimensional electromagnetic wave equation according to a Galerkin method; On the basis of network subdivision, the weak form of the two-dimensional electromagnetic wave equation is spatially dispersed by utilizing a finite element method to construct a finite element equation, wherein the network subdivision comprises a fine network subdivision and a sparse network subdivision; Performing time dispersion on the finite element equation by using a central difference method to form a linear equation set after time dispersion; giving a time step and a time step number, judging whether the time step meets the CFL stability condition or not, and obtaining a first judgment result; if the first judgment result shows that the time step meets the CFL stability condition, directly solving the linear equation set after the time dispersion, and starting iteration from zero time under the time step until the time step length number is reached; If the first judgment result indicates that the time step does not meet the CFL stability condition, decomposing the coefficient matrix of the linear equation set after the time dispersion, and disturbing unstable characteristic values in the coefficient matrix after the decomposition by using a characteristic value disturbance method until absolute values of all characteristic values of the coefficient matrix after the decomposition are less than or equal to 1, reconstructing the coefficient matrix to generate the linear equation set after the coefficient matrix is reconstructed, wherein the disturbance of the unstable characteristic values in the coefficient matrix after the decomposition by using the characteristic value disturbance method specifically comprises the following steps: Using the formula Disturbing unstable characteristic values in the decomposed coefficient matrix, wherein, The characteristic value after the ith disturbance is the characteristic value; is the ith eigenvalue; As the coefficient of the disturbance(s), ; And solving a linear equation set after the coefficient matrix is reconstructed, and starting iteration from zero time under the time step until the time step number is reached.
2. The method of claim 1, wherein the weak form of the two-dimensional electromagnetic wave equation is: Wherein, the The calculation area of the complex ground model is calculated; is the conductivity of the medium; Is the magnetic permeability of the medium; E is an electric field; is a transmit wavelet function; is a laplace operator.
3. The method for rapid simulation of a ground penetrating radar time domain finite element according to claim 1, wherein the finite element equation is: Wherein, the A vector consisting of electric field values at three nodes of the triangle; is a quality matrix; Is a damping matrix; is a rigidity matrix; Is a source vector.
4. A method of fast simulation of a time domain finite element of a ground penetrating radar according to claim 3, wherein the system of linear equations after time dispersion is: Wherein, the Is the time step; The electric field intensity at the current moment; representing the next at the current instant t The electric field intensity of the moment; For the last time at the current time t The electric field intensity of the moment; for the source energy injected at the current instant t.
5. The method for quickly simulating the time domain finite element of the ground penetrating radar according to claim 4, wherein the step of determining whether the time step meets the CFL stability condition, to obtain a first determination result, specifically includes: When the formula is Determining that the time step meets the CFL stability condition, wherein l min is the minimum space step, and v max is the maximum speed of electromagnetic wave propagation in the medium; When the formula is And if not, determining that the time step does not meet the CFL stability condition.
6. A ground penetrating radar time domain finite element rapid simulation system, characterized in that the ground penetrating radar time domain finite element rapid simulation system performs the ground penetrating radar time domain finite element rapid simulation method of any one of claims 1 to 5, the ground penetrating radar time domain finite element rapid simulation system comprising: the system comprises a geometric parameter and electrical parameter setting module, a parameter setting module and a parameter setting module, wherein the geometric parameter and electrical parameter setting module is used for setting the geometric parameter and the electrical parameter of the complex earth model, the geometric parameter comprises the size of the complex earth model, and the electrical parameter comprises resistivity and relative dielectric constant; The discrete and mesh subdivision module is used for utilizing a Delaunay unstructured mesh discrete complicated ground model, adopting fine mesh subdivision in a target body area and adopting sparse mesh subdivision in an area with gentle electromagnetic field change, wherein the fine mesh is a small space step length, and the sparse network is a large space step length; the weak form construction module is used for constructing a weak form of the two-dimensional electromagnetic wave equation according to the Galerkin method based on the geometric parameters and the electrical parameters; The finite element equation construction module is used for constructing a finite element equation by utilizing a weak form of the two-dimensional electromagnetic wave equation through a finite element method space discrete on the basis of network subdivision, wherein the network subdivision comprises a fine network subdivision and a sparse network subdivision; The time discrete module is used for performing time discrete on the finite element equation by using a central difference method to form a linear equation set after the time discrete; the first judging module is used for giving a time step and a time step length number and judging whether the time step meets the CFL stability condition or not to obtain a first judging result; The time-discrete linear equation set solving module is used for directly solving the time-discrete linear equation set if the first judging result shows that the time step meets the CFL stability condition, and iterating from zero time under the time step until the time step number is reached; the decomposition and disturbance module is used for decomposing the coefficient matrix of the linear equation set after the time dispersion if the first judgment result shows that the time step does not meet the CFL stability condition, and disturbing unstable characteristic values in the decomposed coefficient matrix by using a characteristic value disturbance method until absolute values of all characteristic values of the decomposed coefficient matrix are less than or equal to 1, reconstructing the coefficient matrix and generating the linear equation set after reconstructing the coefficient matrix; and the linear equation system solving module is used for solving the linear equation system after the coefficient matrix is reconstructed, and iterating from zero time under the time step until the time step length number is reached.
7. An electronic device comprising a memory for storing a computer program and a processor that runs the computer program to cause the electronic device to perform the ground penetrating radar time domain finite element fast simulation method of any one of claims 1-5.
8. A computer readable storage medium, characterized in that it stores a computer program which, when executed by a processor, implements the ground penetrating radar time domain finite element fast simulation method according to any one of claims 1-5.

Description

Quick simulation method, system and equipment for time domain finite element of ground penetrating radar Technical Field The invention relates to the field of forward modeling of ground penetrating radar, in particular to a method, a system and equipment for quickly modeling a finite element in the time domain of the ground penetrating radar. Background The forward simulation of the Ground penetrating radar (group PENETRATING RADAR, GPR) is an important means for researching the propagation rule of high-frequency electromagnetic waves in complex media, and the response characteristics of the Ground penetrating radar of a typical geological body can be accurately analyzed through the forward simulation, so that important references are provided for the interpretation of actual measured radar data. At present, the forward modeling method of the ground penetrating radar mainly comprises a time domain finite difference method, a time domain pseudo-spectrum method technology, a time domain finite element method and the like. In recent years, the time domain finite element method is widely applied in the field of forward modeling of the ground penetrating radar by using the method which has an unstructured grid discrete two-dimensional complex ground model and can ignore internal boundary conditions and program programming standardization. In order to ensure time iteration stability and eliminate numerical value dispersion phenomenon, when the time domain finite element method is used for forward modeling of the ground penetrating radar, the time step and the grid size need to meet the Ke Lang-Friedrichs-Lewy (Courant-Friedrichs-Lewy, CFL) stability condition, namely, the larger the grid size is, the longer the time step is, and the smaller the grid size is, the shorter the time step is. However, with the increasing complexity of ground penetrating radar research objects and the increasing interpretation precision, high-precision ground penetrating radar forward modeling technology of complex shallow and small targets has become an urgent need in practical engineering application. When the finite element forward modeling of the ground penetrating radar of a complex shallow small target body is carried out, a fine grid subdivision is generally adopted near the target body, and sparse grid subdivision is adopted in other calculation areas, but due to the limitation of CFL stability conditions, the fine grid requires the time step length in the simulation calculation, so that the calculation efficiency is reduced, the algorithm is limited, and the simulation precision of the ground penetrating radar is low. Disclosure of Invention The invention aims to provide a method, a system and equipment for quickly simulating a time domain finite element of a ground penetrating radar, which are used for solving the problems that in the process of dividing a fine grid, the calculation efficiency is reduced and the simulation precision of the ground penetrating radar is low due to the fact that the fine grid requires a time step of simulation calculation. In order to achieve the above object, the present invention provides the following solutions: a method for rapidly simulating a time domain finite element of a ground penetrating radar comprises the following steps: Setting geometrical parameters and electrical parameters of the complex ground model, wherein the geometrical parameters comprise the size of the complex ground model; Utilizing a Delaunay unstructured grid discrete complicated ground model, adopting fine grid subdivision in a target body area, and adopting sparse grid subdivision in an area with gentle electromagnetic field change, wherein the fine grid is a small space step length, and the sparse network is a large space step length; based on the geometric parameters and the electrical parameters, constructing a weak form of a two-dimensional electromagnetic wave equation according to a Galerkin method; On the basis of network subdivision, the weak form of the two-dimensional electromagnetic wave equation is spatially dispersed by utilizing a finite element method to construct a finite element equation, wherein the network subdivision comprises a fine network subdivision and a sparse network subdivision; Performing time dispersion on the finite element equation by using a central difference method to form a linear equation set after time dispersion; giving a time step and a time step number, judging whether the time step meets the CFL stability condition or not, and obtaining a first judgment result; if the first judgment result shows that the time step meets the CFL stability condition, directly solving the linear equation set after the time dispersion, and starting iteration from zero time under the time step until the time step length number is reached; If the first judgment result shows that the time step does not meet the CFL stability condition, decomposing the coefficient matrix of the linear equation set a