Numerical simulation method and system for electromagnetic response uncertainty quantization

Abstract

The invention provides a numerical simulation method and system for electromagnetic response uncertainty quantization, and the method comprises the following steps: 1, carrying out the initial mesh generation of a geometric model of a to-be-solved object, and obtaining a reference mesh; step 2, encrypting the reference grids to generate multi-level grids; step 3, generating corresponding random samples for the obtained multi-level grids respectively; 4, simulating each obtained random sample to obtain an electromagnetic response corresponding to each random sample; step 5, calculating an uncertainty quantitative index of the electromagnetic response; according to the method, the MLMC method of efficiently capturing the benchmark uncertainty through a large amount of sampling on the rough grid and correcting the result through a small amount of sampling on the fine grid is adopted, most repeated simulation work is transferred to the rough grid with light calculation burden, the calculation amount is reduced, and waste of the calculation burden is avoided.

Description

Technical Field

[0001] The present invention belongs to the field of computational electromagnetics, and in particular relates to a numerical simulation method and system for quantifying uncertainty of electromagnetic response. Background Art

[0002] Due to factors such as manufacturing process and measurement errors, there are uncertainties in the material parameters, loads, geometric dimensions and other conditions of actual electrical equipment. The classical electromagnetic simulation algorithm ignores this uncertainty and only performs simulation analysis of electrical equipment under deterministic input conditions. As a result, in the design and operation of electrical equipment, it is necessary to leave a large design margin based on the simulation prediction results to prevent the equipment response fluctuations caused by uncertainty from endangering the safety of the equipment. For example, due to the uncertainty of the material dielectric constant, the maximum electric field strength of the electrical equipment may further fluctuate upward based on the simulation prediction value, resulting in unexpected breakdown damage to the insulation structure. Therefore, quantifying the impact of the uncertainty of material parameters, loads, geometric dimensions and other conditions on the response of electrical equipment, and providing the statistical mean, variance and confidence interval of the equipment response are of great practical value in reducing the design margin of performance indicators and ensuring the safe operation and maintenance of equipment.

[0003] The existing uncertainty quantification algorithms mainly include Monte-Carlo (MC), Polynomial-Chaos and Stochastic methods. The MC method is intuitive and reliable, but the computational burden is heavy, and it requires thousands of electromagnetic forward modeling to obtain converged mean and variance; the polynomial chaos expansion method is only applicable to shorter time domain evolution processes and requires a small number of uncertain parameters, otherwise it will encounter the bottleneck of the so-called "dimensionality disaster"; the effect of the stochastic parameter method is highly dependent on the user's experience, and improper selection of algorithm parameters will lead to serious distortion of the results. To overcome the aforementioned bottleneck, some scholars have established the Multi-Level Monte-Carlo Finite-Difference Time-Domain (MLMC-FDTD) algorithm. The two key points of this algorithm are: 1) Introducing multi-level grids with different resolutions based on the MC method, capturing most of the uncertainties on the coarsest grid, and performing a small amount of sampling correction on the fine grid with a relatively heavy computational burden; 2) Using the FDTD method as the basic electromagnetic simulation algorithm. Since this method is based on orthogonal grid cells, it is very convenient to construct the multi-level grid division required for MLMC sampling.

[0004] The MLMC-FDTD algorithm greatly improves the convergence speed and efficiency of the MC method, but is limited by orthogonal grids, making this method inefficient for geometric modeling of electrical equipment with complex structures. On the other hand, the finite element method, which allows the use of unstructured grids with stronger geometric modeling capabilities, has low computational efficiency in the time domain, and there is no clear method for generating the multigrids required for MLMC based on the initial unstructured grid. Summary of the invention

[0005] The purpose of the present invention is to provide a numerical simulation method and system for quantifying uncertainty of electromagnetic response, so as to solve the defect of inaccurate experimental results in the existing electromagnetic response simulation experiments of electrical equipment.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: The present invention provides a numerical simulation method for quantifying uncertainty of electromagnetic response, comprising the following steps: Step 1, perform initial meshing on the geometric model of the object to be solved to obtain a reference mesh; Step 2, encrypting the reference grids to generate multi-level grids; Step 3, generating corresponding random samples for the obtained multi-level grids; Step 4, simulating each random sample to obtain an electromagnetic response corresponding to each random sample; Step 5: Calculate the uncertainty quantitative index of the electromagnetic response.

[0007] Preferably, in step 2, the reference grid is encrypted to generate a multi-level grid, and the specific method is: Generate the first-level grid by refining the base grid; Generate the secondary grid by encrypting the primary grid; The third-level grid is generated by refining the second-level grid, and so on to obtain multi-level grids.

[0008] Preferably, the encryption principle is: When the grid units of each level of grid are one-dimensional line segments, the endpoints and midpoints of each line segment unit are taken as the secondary unit vertices to generate an encrypted grid, and one line segment unit is encrypted into two secondary line segments; When the grid units of each level of grid are two-dimensional triangles, the vertices of each triangle and the midpoints of each edge are taken as the vertices of the secondary unit, and one triangle unit is encrypted into four secondary triangles; When the grid units of each level of grid are three-dimensional tetrahedrons, the vertices of the tetrahedron and the midpoints of its edges are taken as secondary unit vertices, and one tetrahedral unit is encrypted into four secondary tetrahedrons.

[0009] Preferably, in step 3, the random sample size corresponding to each level of grid is generated according to the following formula to obtain the random sample corresponding to each level of grid:

[0010] in, For the The random sample size corresponding to the level grid; is the random sample size corresponding to the 0th level grid; It is the ratio of the number of random samples between the coarse and fine grid cells of two adjacent levels.

[0011] Preferably, in step 4, each random sample is simulated to obtain an electromagnetic response corresponding to each random sample, and the specific method is: The random sample size corresponding to each level of grid is used as the input of electromagnetic simulation, and the DGTD algorithm is combined to perform M calculations to obtain the electromagnetic response corresponding to each level of grid.

[0012] Preferably, in step 5, the uncertainty quantitative index of the electromagnetic response is calculated, and the specific method is: The uncertainty quantitative index corresponding to each level of grid is calculated respectively using the electromagnetic response corresponding to each level of grid; The uncertainty quantitative index corresponding to the object to be solved is calculated using the uncertainty quantitative index corresponding to each level of grid.

[0013] A numerical simulation system for quantifying uncertainty of electromagnetic response, comprising: A mesh generation unit is used to perform initial mesh generation on the geometric model of the object to be solved to obtain a reference mesh; A grid encryption unit is used to encrypt the reference grids to generate multi-level grids; A sample generating unit is used to generate corresponding random samples from the obtained multi-level grids; An electromagnetic response calculation unit, used for simulating each obtained random sample to obtain an electromagnetic response corresponding to each random sample; The quantitative index calculation unit is used to calculate the uncertainty quantitative index of the electromagnetic response.

[0014] A computer device comprising: a processor suitable for executing a computer program; A computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the method described is performed.

[0015] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described above is implemented.

[0016] A computer program product, the computer program product comprising a computer program, the computer program implementing the method when executed by a processor Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a numerical simulation method for quantifying uncertainty of electromagnetic response. In the uncertainty quantification of time-domain electromagnetic response of electrical equipment, existing methods have inherent defects, namely, the polynomial chaos expansion method and the random parameter method have the bottleneck of "dimensionality disaster" and dependence on artificial parameter selection respectively; the classical Monte Carlo (MC) method is intuitive and reliable, but the required random sample capacity is large, and the converged mean and variance can only be obtained by repeating thousands of electromagnetic simulations under dense grid division, which has a heavy computational burden; while the present application adopts a multiple Monte Carlo (MLMC) method that performs random sampling on multi-level grids, captures most of the uncertainty on the coarsest grid, and only performs a small amount of sampling simulation correction results on dense grids with heavy computational burden, in addition, a multi-grid encryption generation rule for unstructured grid units is proposed, and a time-domain discontinuous Galerkin (DGTD) algorithm based on unstructured grids and with strong geometric modeling capabilities is introduced as a basic electromagnetic simulation method, and the MLMC-DGTD method finally established can efficiently handle the uncertainty of time-domain electromagnetic response of electrical equipment with complex geometric structures, and the numerical algorithm has the following advantages: First, the MLMC method uses a large number of samples on a coarse grid to efficiently capture the benchmark uncertainty and a small number of samples on a fine grid to correct the results. This transfers most of the repeated simulation work to the coarse grid with a lighter computational burden, reduces the amount of computation, and avoids the waste of computational burden. Second: As a basic electromagnetic simulation method, the DGTD method allows the use of unstructured grid units such as tetrahedrons, has strong geometric modeling capabilities and wide applicability; in addition, compared with existing electromagnetic simulation algorithms that support unstructured grids such as the finite element method, the DGTD method does not require the inversion of the high-dimensional mass matrix at each time step, which significantly improves the efficiency and memory consumption of time domain simulation of electrical equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The figure is a schematic diagram of the calculation flow of the algorithm proposed in the present invention.

[0018] Figure 2 Schematic diagram of multi-grid division of one-dimensional line segment grid cells.

[0019] Figure 3 Schematic diagram of multi-grid generation of two-dimensional triangular mesh elements.

[0020] Figure 4 Schematic diagram of multi-grid generation of three-dimensional tetrahedral mesh elements.

[0021] Figure 5This is a schematic diagram of the reference grid division of Example 1 of the present invention.

[0022] Figure 6 It is a schematic diagram of the subdivision of the reference grid after one encryption in Example 1 of the present invention. DETAILED DESCRIPTION

[0023] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0024] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or combinations thereof.

[0025] It should also be understood that the term “and / or” used in the specification and appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0026] As used in the specification and appended claims of this application, the term "if" can be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [described condition or event] is detected" or "in response to detecting [described condition or event]", depending on the context.

[0027] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0028] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0029] Example 1 This embodiment provides a numerical simulation method for quantifying the uncertainty of electromagnetic response, and proposes an MLMC-DGTD algorithm that combines MLMC sampling and the discontinuous Galerkin Time-Domain (DGTD) method. The DGTD method is an improvement on the classical finite element method. It can use unstructured grid units such as tetrahedrons, and there is no need to invert large matrices in time domain calculations, so the calculation efficiency is high. In addition, this embodiment proposes a multi-level grid generation method for unstructured grids based on grid unit edge center encryption. The MLMC-DGTD method finally established can realize efficient quantitative analysis of the uncertainty of electromagnetic response of complex structural electrical equipment with randomness in material properties, loads and boundary conditions.

[0030] As attached Figure 1 As shown, the specific steps include: Step 1: Generate a CAD model file for the geometric model of the object to be solved (such as a resonant cavity, transformer, cable); , the highest frequency of the electromagnetic field , the conductivity of the material and magnetic permeability ) Calculate the wavelength of electromagnetic waves and the skin depth of the material ,Pick and The smaller value of 1 / 20 is regarded as the characteristic scale of electromagnetic field phenomenon, and the smaller value of 2 N-1 Times (N is the preset grid level, generally 3) to obtain the maximum side length of the 0-level grid unit of the initial grid division. Enter this parameter into the grid division software to obtain the reference grid, and define the reference grid as the 0-level grid (L=0).

[0031] Step 2: Generate a multi-level grid based on the reference grid. The multi-level grid of one dimension, two dimension or three dimension is shown in the attached figure. Figure 2-4 As shown, the specific encryption principles are: The one-dimensional grid unit is a line segment. The endpoints and midpoints of each line segment unit are taken as secondary unit vertices to generate an encrypted grid. One line segment unit is encrypted into two secondary line segments. The two-dimensional grid unit is a triangle, and the vertices of each triangle and the midpoints of each edge are taken as the vertices of the secondary unit. One triangle unit is encrypted into 4 secondary triangles; The three-dimensional grid unit is a tetrahedron, and the vertices of the tetrahedron and the midpoints of its edges are taken as secondary unit vertices. One tetrahedron unit is encrypted into 8 secondary tetrahedrons.

[0032] The secondary grid obtained by encrypting the level 0 reference grid (L=0) is defined as the level 1 grid (L=1). The level 1 grid is further encrypted according to the above rules to obtain the level 2 grid (L=2), and so on. Taking the most commonly used three-level grid as an example (L=0, 1, 2), usually only the unit resolution of the densest grid (L=2) is required to meet the accuracy requirements of electromagnetic simulation (that is, the maximum side length of the grid unit is less than 1 / 20 of the smaller value of the electromagnetic wave wavelength and the material penetration depth). The average size (grid unit side length) of the level 0 and level 1 grid units can be expanded by 2 times and 4 times that of the level 2 grid, respectively.

[0033] Step 3: Generate random samples for each level of grid.

[0034] Taking the three-level grid as an example (L=0, 1, 2), the random sample size corresponding to each level of grid is given as M 0, M 1 and M 2, requiring a larger sample size on a coarse grid, i.e. M 0> M 1> M 2, and there is a positive integer greater than 1 S M So that: (1) in, For the The random sample size corresponding to the level grid; is the random sample size corresponding to the 0th level grid, and its value is set based on experience, generally 500-2000; It is the ratio of the number of random samples between two adjacent levels of coarse and fine grids, usually an integer between 2 and 10.

[0035] For each level of grid, generate random samples with corresponding capacity and in accordance with the expected distribution. For example, the relative dielectric constant of a certain power equipment If the parameter is uncertain and according to practical experience, it conforms to the normal distribution with a mean of 1 and a standard deviation of 0.05, the random number generator of MATLAB and other software can be used to input the mean, standard deviation and sample size. M etc., repeatedly extract M random numbers as sampling values, and the vector composed of all sampling values That is the required random sample, and the random number representing the relative dielectric constant sampling value obtained each time is (serial number i 1 to M An integer between ) is called a random sampling point.

[0036] Step 4: simulate and obtain the electromagnetic response of each random sampling point.

[0037] For each level of grid (random sample size is M ),by M Random sampling points are used as input parameters for electromagnetic simulation, and the DGTD algorithm is called M Calculate each time and record and store the result of each calculation.

[0038] Step 5: Calculate the uncertainty quantification index.

[0039] The uncertainty quantification indexes corresponding to each level of grid are calculated using the electromagnetic response corresponding to each level of grid. The uncertainty quantification indexes include the mean value and variance. (2) (3) in, and are the mean and variance estimates of the solution respectively; M is the random sample size, X The simulation result data set represents the quantity of interest (QoI) (which can be the original solved quantity such as electric field intensity, magnetic field intensity, or the physical quantity obtained by post-processing such as eddy current loss). The superscript MC indicates that equations (2) and (3) are the same as the calculation formulas for the mean and variance in the classical Monte Carlo method.

[0040] Based on the electromagnetic response data of each level of grid obtained in the previous step, the MLMC-DGTD algorithm estimates the mean and variance of QoI as follows: (5) (6) in Represents the grid level L = l , the random sample size isM l The simulation result dataset at that time.

[0041] Example 2 The object to be solved is a two-dimensional resonant cavity with a size of 2 m×2 m.

[0042] The reference mesh generation of a 2 m × 2 m two-dimensional resonant cavity is shown in the attached figure. Figure 5 As shown in the figure, the base level 0 grid (L=0) consists of 46 triangular units. The level 1 grid (L=1) encrypted on the basis of the base grid consists of 46×4=184 triangular units. Figure 6 As shown. The L=1 level grid is encrypted to obtain a level 2 grid (L=2) containing 184×4=736 triangular units, which are omitted in the display diagram due to the visual effect. The boundary condition of the resonant cavity is set to a perfect conductor boundary. A line current source with a differential Gaussian pulse in the +z direction and a time domain waveform is applied at the center point (0, 0) of the computational domain. The electric field intensity Ez at the random observation point at the coordinate (-0.4) is taken as the key physical quantity QoI, and its mean and variance are evaluated. In this example, the relative dielectric constant of the dielectric in the resonant cavity is a random variable with a mean of 2.2 and a standard deviation of 0.009.

[0043] The uncertainty of Ez at the observation point was evaluated by the MC-DGTD method (i.e., Monte Carlo sampling as uncertainty quantification method) and the MLMC-DGTD method of the present invention. For the MC-DGTD method, only 1000 random sampling and simulations were carried out under the densest grid division (L=2). For the MLMC-DGTD algorithm, the random sample sizes of the three-level grids were 1000 (L=0), 100 (L=1), and 10 (L=2), respectively.

[0044] Table 1 is a comparison of computing resource information of different algorithms in Example 1 of the present invention.

[0045]

[0046] Compared with the MC-DGTD method using classic Monte Carlo sampling, the MLMC-DGTD method transfers a large amount of random sampling and repeated calculations to the coarse grid with the lightest computational burden, and can achieve a speedup ratio of 2.87 and 10.31 times when using 2-level and 3-level grid divisions, respectively. In addition, as the number of grid levels increases, the average error of QoI also grows slowly, with only a relative error of 0.31% at 3-level grids, and although the variance error is more significant, the relative error level of 10% at 3-level grids is also within the acceptable range for general engineering applications.

[0047] Example 3 This embodiment provides a numerical simulation system for electromagnetic response uncertainty quantification, which is characterized by comprising: A mesh generation unit is used to perform initial mesh generation on the geometric model of the object to be solved to obtain a reference mesh; A grid encryption unit is used to encrypt the reference grids to generate multi-level grids; A sample generating unit is used to generate corresponding random samples from the obtained multi-level grids; An electromagnetic response calculation unit, used for simulating each obtained random sample to obtain an electromagnetic response corresponding to each random sample; The quantitative index calculation unit is used to calculate the uncertainty quantitative index of the electromagnetic response.

[0048] Example 4 This embodiment 4 provides a computer device, including: a memory for storing a computer program; and a processor for implementing the steps of a computer method when executing the computer program.

[0049] When the processor executes the computer program, the steps of the above computer method are implemented.

[0050] Alternatively, when the processor executes the computer program, the functions of each module in the above system are realized. The computer device may be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The computer device may include, but is not limited to, a processor and a memory. Those skilled in the art will appreciate that the above are examples of computer devices and do not constitute a limitation on computer devices. The computer device may include more components than the above, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0051] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the computer device, and uses various interfaces and lines to connect various parts of the entire computer device.

[0052] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the computer device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0053] The memory may mainly include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, a phone book, etc.), etc. In addition, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (SmartMediaCard, SMC), a secure digital (SecureDigital, SD) card, a flash card (FlashCard), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0054] Example 5 This embodiment 5 also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method described are implemented.

[0055] If the module / unit integrated in the computer system is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium.

[0056] Based on such understanding, the present invention implements all or part of the processes in the above method, and can also be completed by instructing related hardware through a computer program, and the computer program can be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above computer method can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or preset intermediate form, etc.

[0057] The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc.

[0058] It should be noted that the content contained in the computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable storage media do not include electrical carrier signals and telecommunication signals.

[0059] Example 6 This embodiment 6 provides a computer product, which includes a computer program, and the computer program is stored in a computer-readable storage medium; the processor of the computer device reads the computer program from the computer-readable storage medium, and the processor executes the computer program, so that the computer device can execute the method in embodiment 1, which will not be repeated here.

[0060] It should be noted that a person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0061] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A numerical simulation method for quantifying uncertainty of electromagnetic response, characterized in that: The following steps are involved: Step 1, performing initial meshing on the geometric model of the object to be solved to obtain a reference mesh; Step 2, encrypting the reference grids to generate multi-level grids; Step 3, generating corresponding random samples for the obtained multi-level grids; Step 4, simulating each random sample to obtain an electromagnetic response corresponding to each random sample; Step 5: Calculate the uncertainty quantitative index of the electromagnetic response.

2. A numerical simulation method for quantifying uncertainty of electromagnetic response according to claim 1, characterized in that: In step 2, the base grid is encrypted to generate a multi-level grid. The specific method is: Generate the first-level grid by encrypting the base grid; Generate the secondary grid by encrypting the primary grid; The third-level grid is generated by refining the second-level grid, and so on to obtain multi-level grids.

3. A numerical simulation method for quantifying uncertainty of electromagnetic response according to claim 2, characterized in that: The encryption principles are: When the grid units of each level of grid are one-dimensional line segments, the endpoints and midpoints of each line segment unit are taken as secondary unit vertices to generate an encrypted grid, and one line segment unit is encrypted into two secondary line segments; When the grid units of each level of grid are two-dimensional triangles, the vertices of each triangle and the midpoints of each edge are taken as the vertices of the secondary unit, and one triangle unit is encrypted into four secondary triangles; When the grid units of each level of grid are three-dimensional tetrahedrons, the vertices of the tetrahedron and the midpoints of its edges are taken as secondary unit vertices, and one tetrahedral unit is encrypted into four secondary tetrahedrons.

4. A numerical simulation method for quantifying uncertainty of electromagnetic response according to claim 1, characterized in that: In step 3, the random sample size corresponding to each level of grid is generated according to the following formula to obtain the random sample corresponding to each level of grid: in, For the The random sample size corresponding to the level grid; is the random sample size corresponding to the 0th level grid; It is the ratio of the number of random samples between the coarse and fine grid cells of two adjacent levels.

5. The numerical simulation method for quantifying uncertainty of electromagnetic response according to claim 1, characterized in that: In step 4, each random sample is simulated to obtain the electromagnetic response corresponding to each random sample. The specific method is: The random sample size corresponding to each level of grid is used as the input of electromagnetic simulation, and the DGTD algorithm is combined to perform M calculations to obtain the electromagnetic response corresponding to each level of grid.

6. A numerical simulation method for quantifying uncertainty of electromagnetic response according to claim 1, characterized in that: In step 5, the uncertainty quantitative index of the electromagnetic response is calculated. The specific method is: The uncertainty quantitative index corresponding to each level of grid is calculated respectively using the electromagnetic response corresponding to each level of grid; The uncertainty quantitative index corresponding to the object to be solved is calculated using the uncertainty quantitative index corresponding to each level of grid.

7. A numerical simulation system for quantifying uncertainty of electromagnetic response, characterized in that: include: A mesh generation unit is used to perform initial mesh generation on the geometric model of the object to be solved to obtain a reference mesh; A grid encryption unit is used to encrypt the reference grids to generate multi-level grids; A sample generating unit is used to generate corresponding random samples from the obtained multi-level grids; An electromagnetic response calculation unit, used for simulating each obtained random sample to obtain an electromagnetic response corresponding to each random sample; The quantitative index calculation unit is used to calculate the uncertainty quantitative index of the electromagnetic response.

8. A computer device, characterized in that: include: a processor suitable for executing a computer program; A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, and when the computer program is executed by the processor, the method according to any one of claims 1 to 6 is performed.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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