Numerical Simulation Method, System and Product for Electromagnetic Field Based on Multi-Fork Tree Mesh Division

Abstract

The present invention belongs to the technical field of grid meshing of numerical models in the geophysical field, and provides an electromagnetic field numerical simulation method, system and product based on multi - fork tree grid meshing. The technical solution is to mesh the calculation area of the geoelectric model; determine the electromagnetic field sampling positions in the grid according to the multi - fork tree grid layout after meshing the calculation area; when calculating the first - order partial derivative of the magnetic field at the interface where the adjacent grid sizes are not equal according to the sampling positions of the electromagnetic field in the calculation area, select the non - adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling positions, so that the magnetic field partial derivative at the boundary of different - sized grids has second - order calculation accuracy; assemble the calculation equations of all discrete electric and magnetic fields in the calculation area, and solve to obtain the discrete electric and magnetic fields at the sampling points. By this method, the calculation accuracy is improved without reducing the calculation efficiency, ensuring that the calculation results have second - order accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of grid meshing of numerical models in the geophysical field, and particularly relates to an electromagnetic field numerical simulation method, system and product based on multi - fork tree grid meshing. Background Technique

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] The transient electromagnetic method is an efficient geophysical exploration method. This method judges the spatial distribution of underground electrical parameters according to the different sensitivities of the electromagnetic field to the electrical property differences of different targets. The Maxwell equations are the basic equations describing the changes of the electromagnetic field. When considering exploring the electromagnetic physical change laws of different geoelectric models through numerical simulation methods, it is necessary to discretize the time and space partial differential operators in the Maxwell equations. The finite - difference time - domain (FDTD) method has advantages such as high computational efficiency and easy programming implementation, so it is widely used to solve transient electromagnetic problems.

[0004] The CN - FDTD (Crank - Nicolson FDTD) method is an unconditionally stable method. This method uses the central - difference method to discretize the partial differential operators in the time domain and the space domain; when the time discretization step size is a uniform step size and the spatial meshing grid is a uniform grid, the calculation result of this method has second - order computational accuracy. However, when simulating transient electromagnetic problems, it is necessary to use a finite model to simulate the physical phenomenon of electromagnetic wave propagation in an infinite space, and satisfy the Dirichlet boundary condition that the tangential component of the electric field at the model boundary is 0. Therefore, a large computational area needs to be set outside the core calculation area to consume the electromagnetic waves from the core calculation area. At this time, the uniform grid meshing method will increase the number of electric and magnetic fields to be solved, while the multi - fork tree grid meshing method can encrypt the grid in the key - concerned calculation area (including the core calculation area such as the emission source, observation point and anomaly body), and adopt a larger grid meshing model in other areas.

[0005] When using the multi - tree grid method to divide the calculation model, coarse grids and fine grids nested in the coarse grids will appear in the model. There will be hanging discrete electric fields at the interface between the coarse grids and the fine grids. When calculating the magnetic field partial derivative at the position of the electric field on the edge, four discrete magnetic fields at symmetric positions around the edge are required. However, according to the Yee grid definition rule, the discrete magnetic fields are only defined at the center of the grid faces. The faces of the four fine grids share the edge with hanging discrete electric fields with the face of a coarse - fine grid, and the distances from this edge to the four surrounding discrete magnetic fields are no longer equal. Therefore, using the central - difference method to calculate the magnetic field partial derivative at this edge will no longer have second - order calculation accuracy. That is, the traditional central - difference method only has first - order calculation accuracy for the curl operator in the discrete Maxwell's equations in the multi - tree grid model. When the ratio of grids of different sizes is large, the error caused by boundary reflection is likely to produce incorrect calculation results in the core calculation area. Summary of the Invention

[0006] To solve at least one of the technical problems existing in the above - mentioned background technology, the present invention provides an electromagnetic field numerical simulation method, system and product based on multi - tree grid division, which calculates the electromagnetic field at the interface by selecting appropriate discrete magnetic fields, so that the calculation result of the electromagnetic field at this position has second - order calculation accuracy. By this method, the calculation accuracy is improved without reducing the calculation efficiency, ensuring that the calculation result has second - order accuracy.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] The first aspect of the present invention provides an electromagnetic field numerical simulation method based on multi - tree grid division, including the following steps:

[0009] Divide the calculation area of the geoelectric model based on the multi - tree grid method, including: dividing the entire calculation area of the geoelectric model to obtain a basic electromagnetic field sampling network; for the calculation area near the anomaly body, encrypt the grid of the basic electromagnetic field sampling network;

[0010] Determine the electromagnetic field sampling positions in the grid according to the multi - tree grid layout after the calculation area is divided;

[0011] When calculating the first - order partial derivative of the magnetic field at the interface where the adjacent grid sizes are not equal according to the sampling positions of the electromagnetic field in the calculation area, select the non - adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling position, so that the magnetic field partial derivative at the boundary of different - sized grids has second - order calculation accuracy;

[0012] Assemble the calculation equations of all discrete electric and magnetic fields in the calculation area to obtain a fully - discrete electromagnetic field equation with second - order calculation accuracy, and solve this equation to obtain the electric and magnetic fields at the sampling points at any time.

[0013] Furthermore, the coarse grid discretization method is adopted to discretize the entire calculation region of the geoelectric model. Specifically, through the Yee grid scheme, the discrete electric field is sampled at the grid edges, and the discrete magnetic field is sampled at the center of the grid faces, and the adjacent electric and magnetic fields have the same distance.

[0014] Furthermore, for the calculation region near the anomaly, the grid of the basic electromagnetic field sampling network is encrypted, including:

[0015] For the calculation region near the anomaly, the basic electromagnetic field sampling network is further discretized according to the coarse grid discretization method to generate medium grids; when the variation law of the electromagnetic field at the boundary of the anomaly needs to be obtained, the medium grids crossed by the boundary of the anomaly are further encrypted according to the coarse grid discretization method to generate fine grids, and the grid sizes of the same level are equal.

[0016] Furthermore, the electromagnetic field sampling positions in the grid are as follows: based on the Yee cell, the spatial sampling positions of the electric and magnetic fields in the multi - fork tree grid are determined. The electric field is located at the center of the cell edges, while the magnetic field is located at the center of each cell face.

[0017] Furthermore, the calculation formula for the magnetic field partial derivative at the boundaries of grids with different sizes and second - order calculation accuracy is:

[0018] ,

[0019] When the second term on the right - hand side of the equation is zero, the equation has second - order calculation accuracy. Let the distances be δ L and δ R The grid numbers where the discrete magnetic fields are located are K 1 and K 2 , then δ L and δ R The expressions of are:

[0020] ,

[0021] , when δ L = δ R there is: ,

[0022] Among them, represents the position of the discrete magnetic field in one - dimensional space, represents y 0 the grid size of the space on the left side, represents along y0 Increment on the right side, indicating along y 0 Increment on the left side, indicating the first derivative of the magnetic field at indicating the second derivative of the magnetic field at indicating the magnetic field at indicating the magnetic field at indicating the magnetic field at and indicating and the grid number where the discrete magnetic field of indicating y 0 the grid size of the right - hand space.

[0023] Furthermore, the fully - discrete equation of the electromagnetic field with second - order computational accuracy is:

[0024] ,

[0025] , ,

[0026] ,

[0027] , ,

[0028] In the formula, , and are respectively the index numbers of the discrete electromagnetic field at the spatial position, is the x directional virtual electric field, is the y directional virtual electric field, is the z directional virtual electric field, is the n time x directional electric field, is the n time y directional electric field, is the n time z directional electric field, is the n time xMagnetic field in the is n at time y Magnetic field in the is n at time z Magnetic field in the is at time x Electric field in the is at time y Electric field in the is at time z Electric field in the 、 、 、 、 and are respectively the parameters of the complementary derivative method in the x 、 y 、 z directions. At the same time, each direction satisfies the formula , and the corresponding grid sizes are and , 、 and are respectively the sizes of the large grids on both sides of the interface of the non-uniform grid; , , , , μ and ε are respectively the permeability of vacuum and the permittivity of vacuum, σ is the conductivity, is the step time.

[0029] The second aspect of the present invention provides an electromagnetic field numerical simulation system based on multi-tree grid division, including:

[0030] A calculation area division module, which is used to divide the calculation area of the geoelectric model based on the multi-tree grid method, including: dividing the entire calculation area of the geoelectric model to obtain a basic electromagnetic field sampling network; for the calculation area near the anomaly body, encrypting the grid of the basic electromagnetic field sampling network;

[0031] A sampling method determination module, which is used to determine the electromagnetic field sampling positions in the grid according to the multi-tree grid layout after the calculation area is divided;

[0032] An electromagnetic field numerical simulation module, which is used to calculate the first-order partial derivative of the magnetic field at the interface where the adjacent grid sizes are not equal according to the sampling positions of the electromagnetic field in the calculation region, and select the non-adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling positions, so that the magnetic field partial derivative at the boundary of different-sized grids has second-order calculation accuracy;

[0033] Assemble the calculation equations of all discrete electric and magnetic fields in the calculation region, and combine the magnetic field partial derivatives at the boundaries of different-sized grids with second-order calculation accuracy to solve and obtain the electromagnetic field numerical simulation results.

[0034] Furthermore, in the calculation region meshing module, the entire calculation region of the geoelectric model is meshed by using the coarse grid meshing method. Specifically, through the Yee grid scheme, the discrete electric field is sampled at the grid edges, and the discrete magnetic field is sampled at the center of the grid faces, and the adjacent electric and magnetic fields have the same distance.

[0035] Furthermore, in the sampling method determination module, the sampling positions of the electromagnetic field in the grid are as follows: based on the Yee cell, determine the spatial sampling positions of the electric and magnetic fields in the multi-fork tree grid. The electric field is located at the center of the cell edges, and the magnetic field is located at the center of each face of the cell.

[0036] The third aspect of the present invention provides a program product.

[0037] A computer-readable storage medium, the program product is a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the steps in the electromagnetic field numerical simulation method based on multi-fork tree grid meshing as described above.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] The present invention proposes a calculation method that enables the electromagnetic field in the multi-fork tree grid model to have second-order calculation accuracy. When solving the "isolated" electromagnetic field at the interface between the coarse and fine grids, the complementary derivatives method (CDM) is introduced. By selecting appropriate discrete magnetic fields, the electromagnetic field at the interface is calculated, so that the calculation result of the electromagnetic field at this position has second-order calculation accuracy. Through this method, the calculation accuracy is improved without reducing the calculation efficiency, ensuring that the calculation result has second-order accuracy. The present invention provides a new numerical calculation method for electromagnetic field simulation with a more accurate and efficient electromagnetic field simulation method, especially when dealing with calculation problems with complex geometric features and different-sized regions.

[0040] The advantages of the additional aspects of the present invention will be partially given in the following description, partially will become obvious from the following description, or will be understood through the practice of the present invention. Description of the Drawings

[0041] The accompanying drawings forming a part of this invention are used to provide a further understanding of the invention. The schematic embodiments and descriptions thereof of the invention are used to explain the invention and do not unduly limit the invention.

[0042] Figure 1 is a flowchart of a numerical simulation method for electromagnetic fields based on multi - fork tree grid dissection provided by an embodiment of the invention;

[0043] Figure 2 is a schematic diagram of a multi - fork tree grid provided by an embodiment of the invention;

[0044] Figure 3 is a schematic diagram of electromagnetic field sampling of a multi - fork tree grid provided by an embodiment of the invention;

[0045] Figure 4 is a schematic diagram of the principle of the CDM method provided by an embodiment of the invention. Detailed implementation manners

[0046] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0047] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanations of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0048] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0049] In view of the prior art mentioned in the background art, in the traditional central difference method in the prior art, the curl operator in the Maxwell equation is discretized only with first - order calculation accuracy in the multi - fork tree grid model. When the ratio of grids of different sizes is relatively large, the error caused by boundary reflection is likely to produce incorrect calculation results in the core calculation area. The present invention proposes a calculation method that enables the electromagnetic field in the multi - fork tree grid model to have second - order calculation accuracy. When solving the "isolated" electromagnetic field at the interface between thick and thin grids, the CDM method is introduced. By selecting an appropriate discrete magnetic field and calculating the electromagnetic field at the interface, the calculation result of the electromagnetic field at this position has second - order calculation accuracy. By this method, the calculation accuracy is improved without reducing the calculation efficiency, ensuring that the calculation result has second - order accuracy.

[0050] Embodiment 1

[0051] As Figure 1 shown, this embodiment provides a numerical simulation method of electromagnetic field based on multi - fork tree grid subdivision, including the following steps:

[0052] Step 1: Subdivide the calculation region of the geoelectric model based on the multi - fork tree grid method;

[0053] First, perform a coarse grid subdivision on the entire calculation region to form the most basic electromagnetic field sampling network. For the calculation region that requires high - precision simulation, through grid encryption technology, further generate nested grids with smaller sizes. In the obtained model with multi - resolution grids, the ratio of the sizes of adjacent grids is n ( n is an integer).

[0054] The coarse grid subdivision means that through the Yee grid scheme, the discrete electric field is sampled at the grid edges, the discrete magnetic field is sampled at the center of the grid faces, and the adjacent electric and magnetic fields have the same distance.

[0055] The grid encryption technology means that by setting a threshold, a smaller - sized grid can be further established for the key - concerned region to discretize the calculation region. At the same time, each refinement subdivision still follows the coarse grid subdivision scheme, and the grid sizes at the same level are equal.

[0056] It should be noted that the set threshold needs to effectively control the degree of grid encryption. For example, for the smallest grid size obtained by subdividing the calculation region of the concerned region, when the smallest grid size meets the requirements during adaptive grid subdivision, the refinement subdivision stops.

[0057] Taking a two - dimensional model as an example:

[0058] As Figure 2 shown, first perform a coarse grid subdivision on the entire calculation region. The coarse grid is as shown in Level 1 shown. During the numerical simulation process, it is often necessary to focus on the variation law of the electromagnetic field near the abnormal body ( Figure 2 the Material part in). Therefore, it is necessary to encrypt the grids in this type of region, and then calculate a sufficient number of electromagnetic field sampling points. For example, continue to encrypt the grid in the upper - right corner of the model and generate a medium - sized grid. The size of the medium - sized grid is 1 / 4 of the size of the coarse grid. The medium - sized grid is as shown in Level 2 shown. When it is necessary to further focus on the variation law of the electromagnetic field at the boundary of the abnormal body, the medium - sized grids crossed by the boundary of the abnormal body can be further encrypted to generate fine grids. The size of the fine grids is 1 / 4 of the size of the medium - sized grids. The fine grids are as shown in Level 3 shown.

[0059] Step 2: Determine the sampling positions of the electromagnetic field in the grids according to the multi - fork tree grid layout after the subdivision of the calculation region;

[0060] Based on the Yee cell, the spatial sampling positions of the electric field and the magnetic field are determined. The electric field is located at the center of the edges of the cell, while the magnetic field is located at the center of each face of the cell. When calculating the curl operator of the discrete magnetic field in the Maxwell equations, it is necessary to obtain the discrete magnetic fields around the positions of the electric field corresponding to the magnetic field.

[0061] The Yee cell refers to a structured grid. In three-dimensional space, when the edge sizes in the three directions of the grid are different, it represents a non-uniform grid, and when the sizes are the same, it is a uniform grid. In this embodiment, a uniform grid is used to divide the calculation region.

[0062] As Figure 3 shown in the two-dimensional model: The spatial positions of the electric field and the magnetic field are determined by the Yee cell. The electric field is located at the center of the edges of the cell, while the magnetic field is located at the center of each face of the cell. The red circles represent the midpoints at the edges of the grid, where the discrete electric field is sampled. When calculating the curl operator of the discrete magnetic field at the position of the red circle (such as E z ), it is necessary to obtain the discrete magnetic fields around this point, that is, H x1 , H x2 , H y1 and H y2 ;

[0063] It should be noted that when introducing the calculation method of the algorithm below, since the index numbers of the electromagnetic fields need to be considered, only this symbol is used here to indicate their positional relationship for the sake of explaining the principle.

[0064] Step 3: According to the sampling positions of the electromagnetic fields in the calculation region, when calculating the first-order partial derivative of the magnetic field at the interface where the adjacent grid sizes are not equal, select the non-adjacent and existing discrete magnetic fields on both sides of the interface, so that the magnetic field partial derivative at the boundary of different-sized grids has second-order calculation accuracy;

[0065] Based on the calculation principle of the complementary derivatives method (CDM): Denote one side of the junction grid as the larger grid and the other side as the smaller grid. In order to make the calculation of the magnetic field partial derivative at the boundary of different-sized grids have second-order calculation accuracy, in this embodiment, instead of directly using the adjacent discrete magnetic fields, non-adjacent and existing discrete magnetic fields on both sides are selected. Then can be expressed as:

[0066] (1),

[0067] According to Equation (1), the equation has second-order computational accuracy when the second term on the right side of the equation is zero. Let the distance be and The grid numbers where the discrete magnetic fields are located are and , then and The expressions are:

[0068] (2),

[0069] (3),

[0070] When = there is:

[0071] (4),

[0072] Among them, represents the position of the discrete magnetic field in one-dimensional space, represents y 0 The grid size of the left space, represents the increment along y 0 The right side, represents the increment along y 0 The left side, represents The first derivative of the magnetic field at, represents The second derivative of the magnetic field at, represents The magnetic field at, represents The magnetic field at, represents The magnetic field at, and represent and The grid numbers where the discrete magnetic fields are located, represents y 0 The grid size of the right space.

[0073] It can be seen from this that as long as two existing discrete magnetic fields are selected on the right side of the interface y = y 0 and the grid numbers satisfy Equations (2) and (3), the calculation result of Equation (1) can be guaranteed to have second-order accuracy.

[0074] Specifically, let Figure 2 The larger grid size in is , the smaller grid size is . The formula for calculating the magnetic field partial derivative by the traditional central difference method is as follows:

[0075] (5),

[0076] where and are the first-order and second-order partial derivatives of the magnetic field respectively; H ( y 0 ) is at the same position as Figure 2 in E z ; represents the high-order error term with respect to the grid size, is the magnetic field at, is the magnetic field at, H ( y 0 ) represents the magnetic field at.

[0077] If = , then the second term on the right side of equation (5) is zero, and the calculation result has second-order calculation accuracy. However, observing Figure 2 it can be seen that ≠ , then the calculation result only has first-order calculation accuracy.

[0078] To make the calculation result have second-order accuracy, this embodiment introduces the complementary derivatives method (CDM), and the calculation principle of this method is as Figure 4 shown.

[0079] Set y = y 0 The left side of is the larger grid with a grid size of ; y = y 0 The right side of is the smaller grid with a grid size of . If it is required to solve y = y 0 the first-order partial derivative H' at, H y0 - / 2 and H y0 + / 2, but since the grid sizes on both sides are not equal, H y0 + / 2 may not exist. Therefore, we use the existing discrete magnetic fields at distances of δ L and δ R from both sides of this point. Then H' can be expressed as Equation (1). When the discrete magnetic field selected for calculation satisfies Equation (4), the calculation result of Equation (1) has second-order accuracy. The Equation (1) with second-order accuracy will be used to substitute into the calculation of the magnetic field partial derivatives in (8)-(10).

[0080] Step 4: Assemble the calculation equations of all discrete electric and magnetic fields within the calculation region to obtain the fully discrete equation of the electromagnetic field with second-order calculation accuracy, and solve this equation to obtain the electric and magnetic fields at the sampling points at any time.

[0081] In the quasi-static case, the Maxwell equations for an isotropic medium can be expressed as:

[0082] (6),

[0083] (7),

[0084] where E and H are the electric and magnetic fields; μ and ε are the vacuum permeability and the vacuum permittivity, respectively; J is the current density, and J s is the source current density; represents the curl operator.

[0085] When solving for the discrete magnetic field in Figure 2 and the discrete electric field with uniform grids on both sides of the edge, the central difference method and the backward Euler method are used to discretize the spatial domain and the time domain of this equation, respectively. The fully discrete equation of the BEDS-FDTD forward modeling algorithm can be obtained:

[0086] (8),

[0087] (9),

[0088] (10),

[0089] where , , , , σ is the conductivity, is the step time; n and n+1 represents the n and computing moment; represents the directional difference operator, is the directional difference operator, is the directional difference operator, The space rotation operator is expressed as x , y and z directions, such as then = z and = y ; is the directional second-order central difference operator, is the directional second-order central difference operator, is the directional virtual electric field, is the directional virtual electric field, is the n electric field in the direction at moment is the n electric field in the direction at moment is the electric field in the direction at moment is the n magnetic field in the direction at moment is the n magnetic field in the direction at moment is the magnetic field in the direction at moment is the n magnetic field in the direction at moment is the electric field in the direction at moment

[0090] When solving the discrete electric field with a uniform grid on both sides of the edge, the backward Euler method is used for discretization in the time domain, and the CDM method is used for discretization in the space domain. By modifying equations (8) and (9) again, the fully discrete equation of the electromagnetic field with second-order calculation accuracy can be obtained:

[0091] ,

[0092] , ,

[0093] ,

[0094] , ,

[0095] wherein, , and are respectively the index numbers of the discrete electromagnetic field at the spatial positions, is the virtual electric field in the x direction, is the virtual electric field in the y direction, is the virtual electric field in the z direction, is the electric field in the n direction at time x , is the electric field in the n direction at time y , is the electric field in the n direction at time z , is the magnetic field in the n direction at time x , is the magnetic field in the n direction at time y , is the magnetic field in the n direction at time z , is the electric field in the direction at time x , is the electric field in the direction at time y , is the electric field in the direction at time z , , , , , and are respectively the parameters of the CDM method in the x , y , z directions, and each direction satisfies Equation (4) at the same time. The corresponding grid sizes are and , , and They are the sizes of the larger grids on both sides of the interface of the non-uniform grid respectively.

[0096] When solving the "isolated" electromagnetic field at the interface between the coarse and fine grids, the CDM method is introduced. By selecting an appropriate discrete magnetic field and calculating the electromagnetic field at the interface, the calculation result of the electromagnetic field at this position has second-order calculation accuracy. By this method, the calculation accuracy is improved without reducing the calculation efficiency, ensuring that the calculation result has second-order accuracy. The present invention provides a new numerical calculation method for electromagnetic field simulation with a more accurate and efficient electromagnetic field simulation method, especially when dealing with calculation problems with complex geometric features and regions of different sizes.

[0097] Embodiment 2

[0098] This embodiment provides an electromagnetic field numerical simulation system based on multi-way tree grid meshing, including:

[0099] A calculation area meshing module, which is used to mesh the calculation area of the geoelectric model based on the multi-way tree grid method, including: meshing the entire calculation area of the geoelectric model to obtain a basic electromagnetic field sampling network; for the calculation area near the abnormal body, encrypting the grid of the basic electromagnetic field sampling network;

[0100] A sampling method determination module, which is used to determine the electromagnetic field sampling positions in the grid according to the multi-way tree grid layout after meshing the calculation area;

[0101] An electromagnetic field numerical simulation module, which is used to select non-adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling position when calculating the first-order partial derivative of the magnetic field at the interface where the adjacent grid sizes are not equal according to the electromagnetic field sampling positions in the calculation area, so that the magnetic field partial derivative at the boundary of different-sized grids has second-order calculation accuracy;

[0102] Assemble the calculation equations of all discrete electric and magnetic fields in the calculation area to obtain a fully discrete equation of the electromagnetic field with second-order calculation accuracy, and solve this equation to obtain the electric and magnetic fields at the sampling points at any time.

[0103] Since the embodiments in the system part correspond to the embodiments in the method part, please refer to the description of the embodiments in the method part for the embodiments in the system part, which will not be elaborated here. And it has the same beneficial effects as the above-mentioned electromagnetic field numerical simulation method based on multi-way tree grid meshing.

[0104] Embodiment 3

[0105] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps in the above-mentioned electromagnetic field numerical simulation method based on multi-way tree grid meshing.

[0106] Example 4

[0107] This embodiment provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps in the electromagnetic field numerical simulation method based on multi - fork tree grid dissection as described above are implemented.

[0108] Example 5

[0109] This embodiment provides a program product, which is a computer program product including a computer program. When the computer program is executed by a processor, the steps in the electromagnetic field numerical simulation method based on multi - fork tree grid dissection as described above are implemented.

[0110] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. The electromagnetic field numerical simulation method based on multi-tree grid generation is characterized by: The steps include: The calculation area of ​​the geoelectric model is divided based on the multi-branch tree grid method, including: dividing the entire calculation area of ​​the geoelectric model to obtain a basic electromagnetic field sampling network; for the calculation area near the abnormal body, the basic electromagnetic field sampling network is meshed; According to the multi-branch tree grid layout after the calculation area is divided, the electromagnetic field sampling position in the grid is determined; According to the sampling position of the electromagnetic field in the calculation area, when calculating the first-order partial derivative of the magnetic field at the interface of adjacent grids of unequal sizes, the non-adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling position are selected to make the partial derivatives of the magnetic field at the boundaries of grids of different sizes have second-order calculation accuracy; Assemble the calculation equations of all discrete electric and magnetic fields in the calculation area to obtain the fully discrete equation of the electromagnetic field with second-order calculation accuracy, and solve the equation to obtain the electric and magnetic fields at any sampling point at any time; The calculation formula of the partial derivative of the magnetic field at the boundary of different mesh sizes with second-order calculation accuracy is: ， The equation has second-order accuracy when the second term on the right side is zero. Let the distance be δ L and δ R The grid number where the discrete magnetic field is located is K 1 and K 2, then δ L and δ R The expression is: ， ,when δ L = δ R Sometimes: , in, represents the discrete magnetic field position in one-dimensional space, express y 0 grid size of the space to the left, Indicates along y Increment to the right of 0, Indicates along y Increment to the left of 0, express The first derivative of the magnetic field at , express The second derivative of the magnetic field at , express In magnetic field, express In magnetic field, express In magnetic field, and express and The grid number where the discrete magnetic field is located, express y 0 grid size of the space to the right, represents the higher-order error term with respect to the mesh size.

2. The electromagnetic field numerical simulation method based on multi-tree mesh generation according to claim 1, characterized in that: The coarse grid partitioning method is used to partition the entire calculation area of ​​the geoelectric model. Specifically, through the Yee grid scheme, the discrete electric field is sampled at the grid edges, the discrete magnetic field is sampled at the center of the grid surface, and the adjacent electric and magnetic fields have the same distance.

3. The electromagnetic field numerical simulation method based on multi-tree mesh generation according to claim 1, characterized in that: The grid encryption of the basic electromagnetic field sampling network for the calculation area near the abnormal body includes: For the calculation area near the anomaly, the basic electromagnetic field sampling network is further divided into a medium grid according to the coarse grid division method; when it is necessary to obtain the electromagnetic field change law at the boundary of the anomaly, the medium grid passing through the boundary of the anomaly is further encrypted to generate a fine grid according to the coarse grid division method, and the grid sizes of the same level are equal.

4. The electromagnetic field numerical simulation method based on multi-tree mesh generation according to claim 1, characterized in that: The electromagnetic field sampling positions in the grid are: based on the Yee unit cell, the spatial sampling positions of the electric field and the magnetic field in the multi-tree grid are determined, the electric field is located at the center of the unit cell edge, and the magnetic field is located at the center of each face of the unit cell.

5. The electromagnetic field numerical simulation method based on multi-tree mesh generation according to claim 1, characterized in that: The fully discrete equation of the electromagnetic field with second-order calculation accuracy is: ， ， ， ， ， ， In the formula, , and are the index numbers of the discrete electromagnetic fields in space, for x The virtual electric field in the direction of for y The virtual electric field in the direction of for z The virtual electric field in the direction of for n time x The electric field in the direction of for n time y The electric field in the direction of for n time z The electric field in the direction of for n time x Direction of the magnetic field, for n time y Direction of the magnetic field, for n time z Direction of the magnetic field, for time x The electric field in the direction of for time y The electric field in the direction of for time z The electric field in the direction of , , , , and The complementary derivative method is x , y , z Directional parameters, and each direction satisfies the formula , and the corresponding grid sizes are , , , , and , , and are the sizes of the medium and large grids on both sides of the non-uniform grid interface; , , , , μ and ε are the vacuum magnetic permeability and vacuum dielectric constant, respectively. σ is the conductivity, is the step time.

6. The electromagnetic field numerical simulation system based on multi-tree grid generation is characterized by: include: The calculation area partitioning module is used to partition the calculation area of ​​the geoelectric model based on the multi-tree grid method, including: partitioning the entire calculation area of ​​the geoelectric model to obtain a basic electromagnetic field sampling network; meshing the basic electromagnetic field sampling network for the calculation area near the anomaly; A sampling mode determination module is used to determine the electromagnetic field sampling position in the grid according to the multi-branch tree grid layout after the calculation area is divided; The electromagnetic field numerical simulation module is used to calculate the first-order partial derivatives of the magnetic field at the interface of adjacent grids of unequal sizes according to the sampling positions of the electromagnetic field in the calculation area, and select the non-adjacent and existing discrete magnetic fields on both sides of the interface of the spatial sampling position, so that the partial derivatives of the magnetic field at the boundaries of grids of different sizes have second-order calculation accuracy; Assemble the calculation equations of all discrete electric and magnetic fields in the calculation area to obtain the fully discrete equation of the electromagnetic field with second-order calculation accuracy, and solve the equation to obtain the electric and magnetic fields at any sampling point at any time; The calculation formula of the partial derivative of the magnetic field at the boundary of different mesh sizes with second-order calculation accuracy is: ， The equation has second-order accuracy when the second term on the right side is zero. Let the distance be δ L and δ R The grid number where the discrete magnetic field is located is K 1 and K 2, then δ L and δ R The expression is: ， ,when δ L = δ R Sometimes: , in, represents the discrete magnetic field position in one-dimensional space, express y 0 grid size of the space to the left, Indicates along y Increment to the right of 0, Indicates along y Increment to the left of 0, express The first derivative of the magnetic field at , express The second derivative of the magnetic field at , express In magnetic field, express In magnetic field, express In magnetic field, and express and The grid number where the discrete magnetic field is located, express y 0 grid size of the space to the right, represents the higher-order error term with respect to the mesh size.

7. The electromagnetic field numerical simulation system based on multi-tree grid generation according to claim 6, characterized in that: In the calculation area partitioning module, the coarse grid partitioning method is used to partition the entire calculation area of ​​the geoelectric model. Specifically, through the Yee grid scheme, the discrete electric field is sampled at the grid edges, the discrete magnetic field is sampled at the center of the grid surface, and the adjacent electric and magnetic fields have the same distance.

8. The electromagnetic field numerical simulation system based on multi-tree mesh generation according to claim 6, characterized in that: In the sampling method determination module, the electromagnetic field sampling positions in the grid are: based on the Yee unit cell, the spatial sampling positions of the electric field and the magnetic field in the multi-tree grid are determined, the electric field is located at the center of the unit cell edge, and the magnetic field is located at the center of each face of the unit cell.

9. A program product, the program product being a computer program product, comprising a computer program, characterized in that: When the computer program is executed by a processor, the steps of the electromagnetic field numerical simulation method based on multi-tree mesh generation as described in any one of claims 1 to 5 are implemented.

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