A method for analyzing approximation error of Lagrange polynomial based on sine wave

Abstract

The application discloses a Lagrange polynomial interpolation approximation error analysis method based on a sine wave, which comprises the following steps: taking a one-dimensional sine wave as an original function, calculating one-dimensional Lagrange polynomial interpolation under different interpolation node distribution conditions; analyzing the approximation error between the Lagrange polynomial interpolation under different interpolation node distribution conditions and the original function; establishing a two-dimensional sine wave original function according to the approximation error; establishing a two-dimensional irregular grid with different interpolation node distributions, and mapping the two-dimensional sine wave original function into the two-dimensional irregular grid to obtain a two-dimensional sine wave original wave field; calculating two-dimensional Lagrange polynomial interpolation approximation wave fields in different irregular grids according to the interpolation nodes with different distributions in the two-dimensional irregular grid; comparing the two-dimensional Lagrange polynomial interpolation approximation wave fields in the different irregular grids with the two-dimensional sine wave original wave field in the two-dimensional irregular grid to determine the Lagrange polynomial interpolation approximation error quantitative relationship. The method can effectively evaluate the relationship between the grid quality and the forward simulation precision without performing wave field forward simulation calculation.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of applied geophysical seismic wave field simulation technology, and in particular to a method for analyzing the approximate error of Lagrange polynomial interpolation based on sine waves. Background Technology

[0002] Numerical forward modeling of seismic wavefields is one of the main techniques in seismic exploration. By simulating the propagation and reflection of seismic waves in strata, it helps to understand the propagation patterns of wavefields within subsurface geological structures. Numerical forward modeling can not only predict seismic wave responses but also effectively assess subsurface lithology, structural characteristics, and other features, providing crucial information for oil and gas exploration, mineral exploration, and geological hazard early warning. The accuracy of the forward modeling directly affects the reliability of subsequent inversion interpretation and is an indispensable part of seismic data processing and interpretation.

[0003] Numerical simulation of wave fields can be categorized into various forward modeling methods based on different discretization methods of the wave equation, such as finite difference classification and finite element classification. Among these, the finite element classification seismic wave field forward modeling method has been widely used for simulating wave field propagation under complex geological conditions due to its flexibility in mesh generation and high computational accuracy. Finite element wave field simulation discretizes the solution domain (i.e., the seismic forward model) into a finite number of irregular discrete mesh elements, and the wave field values ​​are calculated at the nodes of these discrete irregular mesh elements.

[0004] In solving for wavefield values ​​on irregular mesh elements using the finite element method, the continuous wavefield within the irregular mesh must first be discretized into a discrete wavefield using Lagrange polynomial interpolation before numerical simulation can be performed. The approximate error accuracy of the discretization method within irregular meshes of varying quality directly affects the accuracy of the forward modeling. Therefore, simulation accuracy can be determined through approximate error analysis of the interpolation method.

[0005] Currently, methods for analyzing approximation errors in Lagrange interpolation primarily focus on understanding the deviation between the interpolating polynomial and the original function. These errors can generally be divided into two parts: truncation error and interpolation error. Truncation error is the function value approximation error caused by using a finite number of interpolation nodes. Specifically, when using Lagrange interpolation, we construct a polynomial to approximate the original function, but this polynomial may deviate from the original function in regions outside the interpolation nodes. Interpolation error refers to the difference between the interpolating polynomial and the original function in regions outside the interpolation nodes. This error is determined by both the properties of the interpolating polynomial itself (such as local approximation properties) and the choice of interpolation nodes. The analysis of interpolation error usually relies on a deep understanding of the properties of the interpolating polynomial, including its derivatives and extrema. In addition, the distribution and number of interpolation nodes also have a significant impact on the interpolation error. Currently, there is no generalized formula for calculating the error between Lagrange polynomial interpolation and the original function, making it difficult to obtain a generalized quantification error relationship. Summary of the Invention

[0006] To address the aforementioned technical problems, at least one embodiment of the present invention provides a method for analyzing the approximate error of Lagrange polynomial interpolation based on sine waves, thereby solving the problems.

[0007] In some optional embodiments, the method includes the following steps:

[0008] Using a one-dimensional sine wave as the primitive function, calculate the one-dimensional Lagrange polynomial interpolation under different interpolation node distributions;

[0009] Analyze the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions;

[0010] A two-dimensional sine wave primitive function is established based on the approximation error;

[0011] A two-dimensional irregular grid with different interpolation node distributions is established, and the original two-dimensional sine wave function is mapped onto the two-dimensional irregular grid to obtain the original two-dimensional sine wave field.

[0012] Based on the different distributions of interpolation nodes in a two-dimensional irregular grid, calculate the approximate wave field of two-dimensional Lagrange polynomial interpolation in different irregular grids;

[0013] By comparing the approximate wave field of the two-dimensional Lagrange polynomial interpolation in the different irregular grids with the original wave field of the two-dimensional sinusoidal wave in the two-dimensional irregular grids, the quantization relationship of the approximate error of the Lagrange polynomial interpolation is determined.

[0014] In some optional embodiments, the analysis of the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions includes:

[0015] Calculate the error curves between the Lagrange polynomial interpolation and the original sine wave function under different interpolation node distributions;

[0016] Calculate the maximum value of the error curve for each interpolation node distribution, and plot all the maximum error values ​​as a one-dimensional error curve;

[0017] The one-dimensional error curve is copied into two different spatial directions to obtain a two-way bidirectional cross error curve.

[0018] The two bidirectional cross error curves are added together to obtain the bidirectional error sum curve.

[0019] In some optional embodiments, establishing the original two-dimensional sine wave function based on the approximation error includes:

[0020] Based on the bidirectional error and curve, a two-dimensional sine wave primitive function is established.

[0021] In some optional embodiments, the length variation range in both directions of the original two-dimensional sine wave function is greater than or equal to the length variation range in both directions corresponding to the bidirectional error and curve.

[0022] In some optional embodiments, establishing a two-dimensional irregular mesh with different interpolation node distributions includes:

[0023] Establish two orthogonal meshes with equal side lengths in both directions;

[0024] While keeping the area constant, the orthogonality of the orthogonal mesh is changed by rotating one of the two directions, thereby creating irregular meshes of different mesh qualities, wherein the distribution of interpolation nodes is different in the irregular meshes of different mesh qualities.

[0025] In some optional embodiments, the step of calculating the two-dimensional Lagrange polynomial interpolation approximate wave field within different irregular grids based on the different distributions of interpolation nodes in the two-dimensional irregular grid includes:

[0026] Based on the interpolation nodes with different distributions in the two-dimensional irregular grid, the amplitude values ​​of the original two-dimensional sine wave function at the interpolation nodes are obtained as the original two-dimensional sine wave field values.

[0027] Based on the wave field values ​​of the two-dimensional sinusoidal wave field interpolation nodes, the approximate two-dimensional Lagrange polynomial interpolation wave field values ​​are obtained by using the Lagrange polynomial interpolation method.

[0028] In some optional embodiments, the step of comparing the approximate wave field of the two-dimensional Lagrange polynomial interpolation within the different irregular grids with the original two-dimensional sinusoidal wave field within the two-dimensional irregular grids to determine the quantization relationship of the Lagrange polynomial interpolation approximation error includes:

[0029] The interpolation approximation error quantization matrix is ​​obtained by subtracting the two-dimensional Lagrange polynomial interpolation approximation wave field value in the different irregular grids from the original two-dimensional sinusoidal wave field value in the two-dimensional irregular grids.

[0030] The maximum value of the interpolation approximation error quantization matrix is ​​extracted to characterize the Lagrange polynomial interpolation approximation error quantization relationship.

[0031] At least one embodiment of the present invention also provides an approximate error analysis device for Lagrange polynomial interpolation based on sine waves, characterized in that it includes:

[0032] The interpolation calculation module is used to calculate one-dimensional Lagrange polynomial interpolation with a one-dimensional sine wave as the original function, under different interpolation node distributions.

[0033] The error analysis module is used to analyze the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions.

[0034] A two-dimensional establishment module is used to establish a two-dimensional sine wave primitive function based on the approximation error.

[0035] The grid mapping module is used to establish a two-dimensional irregular grid with different interpolation node distributions, and to map the original two-dimensional sine wave function into the two-dimensional irregular grid to obtain the original two-dimensional sine wave field.

[0036] The wave field calculation module is used to calculate the approximate two-dimensional Lagrange polynomial interpolation wave field in different irregular grids based on the different distribution of interpolation nodes in the two-dimensional irregular grid.

[0037] The error quantization module is used to compare the approximate wave field of the two-dimensional Lagrange polynomial interpolation in different irregular grids with the original wave field of the two-dimensional sinusoidal wave in the two-dimensional irregular grids, and to determine the error quantization relationship of the Lagrange polynomial interpolation approximation.

[0038] At least one embodiment of the present invention also provides an electronic device, characterized in that it comprises:

[0039] At least one processor; and,

[0040] A memory communicatively connected to the at least one processor; wherein,

[0041] The memory stores instructions that can be executed by the at least one processor, which enables the at least one processor to perform the sinusoidal Lagrange polynomial interpolation approximation error analysis method as described above.

[0042] At least one embodiment of the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for approximate error analysis of sine wave-based Lagrange polynomial interpolation.

[0043] At least one embodiment of the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the sinusoidal Lagrange polynomial interpolation approximation error analysis method as described above.

[0044] Compared with the prior art, the Lagrange polynomial interpolation approximation error analysis method based on sine waves provided by the embodiments of the present invention has the following beneficial effects:

[0045] This invention provides a method for analyzing the approximate error of Lagrange polynomial interpolation based on sine waves. Addressing the difficulty in quantifying the approximate error of Lagrange polynomial interpolation, this method employs a concretized primitive function approach, using a sine wave as the primitive function carrier to calculate and obtain the specific quantitative relationship of the interpolation approximate error. In terms of quantifying the accuracy of wavefield numerical forward modeling, this method can effectively evaluate the relationship between mesh quality and forward modeling accuracy without performing wavefield forward modeling calculations, thus saving significant time for adjusting forward modeling calculation parameters and predicting forward modeling results. Attached Figure Description

[0046] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0047] Figure 1 This is a flowchart of the steps of the Lagrange polynomial interpolation approximation error analysis method based on sine waves in Embodiment 1 of the present invention;

[0048] Figure 2 This is a schematic diagram of the one-dimensional Lagrange interpolation approximation error in Embodiment 1 of the present invention;

[0049] Figure 3 This is a schematic diagram of the calculation of the approximate error of one-dimensional Lagrange polynomial interpolation in the x and z directions in Embodiment 1 of the present invention;

[0050] Figure 4 This is a schematic diagram of a two-dimensional irregular mesh with different interpolation node distributions according to Embodiment 1 of the present invention;

[0051] Figure 5 This is a schematic diagram of the original function of the two-dimensional sinusoidal wave field in Embodiment 2 of the present invention;

[0052] Figure 6 This is a schematic diagram of the original function of the two-dimensional sinusoidal wave field mapped onto an irregular grid in Embodiment 2 of the present invention;

[0053] Figure 7 This is a schematic diagram of the approximate wave field of two-dimensional Lagrange polynomial interpolation within different irregular grids in Embodiment 2 of the present invention;

[0054] Figure 8 This is a schematic diagram of the Lagrange polynomial interpolation approximation error quantization relation matrix according to Embodiment 2 of the present invention;

[0055] Figure 9 This is a schematic diagram of the quantization relationship curve of the approximate error of the Lagrange polynomial interpolation in Embodiment 2 of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0057] As mentioned earlier, in existing technologies, the main factor affecting the interpolation accuracy of Lagrange polynomial interpolation in finite element method numerical forward modeling is the mesh quality of the irregular mesh. Different mesh qualities result in different distributions of interpolation nodes. This invention focuses on the interpolation error caused by different distributions of interpolation nodes. It concretizes the original Lagrange polynomial function into a wave field function, or more generally, into a sine wave function. Based on the concretized sine wave function, the quantified error relationship is obtained by calculating the error value between the sine wave and its Lagrange polynomial interpolation.

[0058] The implementation details of the above method are described in detail below through examples. The following content is only for the convenience of understanding the implementation details and is not necessary for implementing this solution.

[0059] Example 1:

[0060] like Figure 1 As shown, this embodiment provides a method for analyzing the approximate error of Lagrange polynomial interpolation based on sine waves. The method mainly includes the following steps:

[0061] The first step is to perform one-dimensional Lagrange polynomial interpolation calculations.

[0062] In this step, a one-dimensional sine wave is used as the original function (e.g., Figure 2 (As shown by the black solid line in the image), calculate the interpolation nodes (such as...). Figure 2 Lagrange polynomial interpolation curves under different distribution conditions (as shown by the black dots in the image) Figure 2 (As shown by the black dashed line in the image).

[0063] The second step is to calculate the approximate error of the one-dimensional Lagrange polynomial interpolation.

[0064] In this step, Figure 2 The black dotted line in the middle and Figure 2 Subtract the corresponding portions of the black solid lines in the diagram to calculate the error curves between the Lagrange polynomial interpolation and the original sine wave function under different interpolation node distributions. Statistically calculate the maximum value of the error curve for each interpolation node distribution, and plot all the maximum error values ​​as a new curve, i.e., a one-dimensional error curve, as shown below. Figure 3 As shown by the solid black line, the one-dimensional error curve is copied to both x and z directions to obtain bidirectional cross-error curves in both directions. The bidirectional cross-error curves are then summed to calculate the bidirectional error sum curve (e.g., ...). Figure 3 (As shown by the black dashed line). It should be noted that the selection of the x and z directions is not fixed and can be adjusted according to actual needs during implementation. This invention does not limit this.

[0065] The third step is to establish the primitive function of the two-dimensional sinusoidal wave field.

[0066] In this step, the bidirectional error and curve are obtained through the second step calculation, and a two-dimensional sine wave primitive function is established, such that the length variation range of the two-dimensional sine wave primitive function in the x and z directions is greater than or equal to the length variation range in the x and z directions corresponding to the error and curve.

[0067] The fourth step is to establish a two-dimensional irregular grid with different interpolation node distributions, and then map the original function of the two-dimensional sinusoidal wave field established in the third step into the two-dimensional irregular grid.

[0068] In this step, an orthogonal mesh with equal side lengths in the x and z directions is first established (as shown in Figure 4). The orthogonal mesh has the highest mesh quality. Based on the orthogonal mesh, and while keeping the overall area of ​​the irregular mesh unchanged, the orthogonality of the mesh is changed by rotating the z-side, thereby creating irregular meshes of different qualities. Different mesh qualities result in different interpolation node distributions. Based on these different irregular meshes, the original two-dimensional sine wave function information contained within each irregular mesh is extracted.

[0069] The fifth step is to calculate the approximate wave field of two-dimensional Lagrange polynomial interpolation within different irregular grids.

[0070] In this step, based on the interpolation nodes with different distributions in the two-dimensional irregular grid established in step four, the amplitude values ​​of the original two-dimensional sine wave function at the interpolation nodes are obtained, i.e., the original two-dimensional sine wave field values. Based on the wave field amplitude values ​​of the two-dimensional sine wave field interpolation nodes, the two-dimensional approximate wave field amplitude values ​​are calculated using the Lagrange polynomial interpolation method.

[0071] The sixth step is to obtain the quantization relationship of the approximate error of the Lagrange polynomial interpolation.

[0072] In this step, the Lagrange polynomial interpolated wave field in different irregular grids obtained in step 5 is subtracted from the original two-dimensional sine wave field in the grid extracted in step 4 to obtain the interpolation approximation error quantization matrix. The maximum value of the error matrix is ​​extracted as the Lagrange polynomial interpolation approximation error quantization relationship.

[0073] This embodiment provides a method for analyzing the approximate error of Lagrange polynomial interpolation based on sinusoidal waves. The obtained quantitative relationship of the Lagrange polynomial interpolation approximate error can be directly used in the accuracy calculation of wavefield numerical forward modeling. By quantifying the error relationship of Lagrange polynomial interpolation within irregular grids of different qualities, the relationship between grid quality and forward modeling accuracy can be evaluated before the forward modeling operation. This saves a significant amount of time for adjusting forward modeling calculation parameters and predicting forward modeling results, and is of great significance for obtaining effective seismic wavefield numerical forward modeling results.

[0074] Example 2

[0075] The technical solution of the present invention and its beneficial effects will be further illustrated below with a specific example.

[0076] like Figure 5 As shown, the original function of the two-dimensional sinusoidal wave field used in this embodiment is 5m long in the x-direction and 2m long in the z-direction. The wave number of the sinusoidal wave is 0.5 and the amplitude is 1. Figure 5 This involves generating a three-dimensional wavefield plot (including amplitude representation) and a two-dimensional wavefield planar plot from a two-dimensional sinusoidal wavefield. Based on this two-dimensional sinusoidal wavefield, a two-dimensional irregular grid with different interpolation node distributions is constructed, and the original wavefield is mapped onto the irregular grid, such as... Figure 6 As shown; by using the wave field amplitude values ​​at the interpolation nodes and the Lagrange polynomial interpolation formula, the approximate two-dimensional Lagrange polynomial interpolation wave field in different irregular grids is calculated and obtained, such as... Figure 7 As shown; will Figure 7 The interpolated wave field obtained by calculation and Figure 6 The interpolation approximation error quantization matrix is ​​obtained by subtracting the corresponding original wavefields, such as... Figure 8 As shown; extract the maximum, average, and minimum values ​​of the error matrix, and use the maximum value as an approximate error relationship, as follows. Figure 9 As shown.

[0077] As can be seen from the above embodiments, the error relationship obtained by the sinusoidal Lagrange polynomial interpolation approximation error analysis method of the present invention shows that when the mesh quality is greater than 0.8, the error remains unchanged; when the mesh quality reaches 0.6, the error begins to rise slowly; and when the error quality reaches 0.4 or below, the error increases sharply. Therefore, this curve can be used to predict the relationship between mesh quality and forward modeling accuracy.

[0078] Example 3

[0079] Another embodiment of the present invention relates to a device for analyzing the approximate error of a sine wave-based Lagrange polynomial interpolation, comprising:

[0080] The interpolation calculation module is used to calculate one-dimensional Lagrange polynomial interpolation with a one-dimensional sine wave as the original function, under different interpolation node distributions.

[0081] The error analysis module is used to analyze the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions.

[0082] A two-dimensional establishment module is used to establish a two-dimensional sine wave primitive function based on the approximation error.

[0083] The grid mapping module is used to establish a two-dimensional irregular grid with different interpolation node distributions, and to map the original two-dimensional sine wave function into the two-dimensional irregular grid to obtain the original two-dimensional sine wave field.

[0084] The wave field calculation module is used to calculate the approximate two-dimensional Lagrange polynomial interpolation wave field in different irregular grids based on the different distribution of interpolation nodes in the two-dimensional irregular grid.

[0085] The error quantization module is used to compare the approximate wave field of the two-dimensional Lagrange polynomial interpolation in different irregular grids with the original wave field of the two-dimensional sinusoidal wave in the two-dimensional irregular grids, and to determine the error quantization relationship of the Lagrange polynomial interpolation approximation.

[0086] The present invention provides a technical solution for an approximate error analysis method based on sine waves using Lagrange polynomial interpolation. By specifying the original function as a sine wave, the interpolation error within different irregular grids is calculated, thus solving the problem of difficulty in quantifying interpolation errors. This method is applied to numerical forward modeling of seismic wavefields, improving the efficiency of evaluating grid quality and simulation accuracy, and is of great significance for optimizing computational parameters and predicting simulation results.

[0087] Example 4:

[0088] Another embodiment of the present invention relates to an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the sine wave-based Lagrange polynomial interpolation approximation error analysis method in the above embodiments.

[0089] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0090] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0091] Example 5:

[0092] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the sinusoidal Lagrange polynomial interpolation approximation error analysis method of the above embodiments.

[0093] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] Example 6

[0095] Another embodiment of the present invention relates to a computer program product, including a computer program that, when executed by a processor, implements the steps of the sine wave-based Lagrange polynomial interpolation approximation error analysis method of the above embodiments.

[0096] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for analyzing the approximate error of Lagrange polynomial interpolation based on sine waves, characterized in that, include: Using a one-dimensional sine wave as the primitive function, calculate the one-dimensional Lagrange polynomial interpolation under different interpolation node distributions; Analyze the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions; A two-dimensional sine wave primitive function is established based on the approximation error; A two-dimensional irregular grid with different interpolation node distributions is established, and the original two-dimensional sine wave function is mapped onto the two-dimensional irregular grid to obtain the original two-dimensional sine wave field. Based on the different distributions of interpolation nodes in a two-dimensional irregular grid, calculate the approximate wave field of two-dimensional Lagrange polynomial interpolation in different irregular grids; By comparing the approximate wave field of the two-dimensional Lagrange polynomial interpolation in the different irregular grids with the original wave field of the two-dimensional sinusoidal wave in the two-dimensional irregular grids, the quantization relationship of the approximate error of the Lagrange polynomial interpolation is determined.

2. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 1, characterized in that, The analysis of the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions includes: Calculate the error curves between the Lagrange polynomial interpolation and the original sine wave function under different interpolation node distributions; Calculate the maximum value of the error curve for each interpolation node distribution, and plot all the maximum error values ​​as a one-dimensional error curve; The one-dimensional error curve is copied into two different spatial directions to obtain a two-way bidirectional cross error curve. The two bidirectional cross error curves are added together to obtain the bidirectional error sum curve.

3. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 2, characterized in that, The step of establishing the original two-dimensional sine wave function based on the approximation error includes: Based on the bidirectional error and curve, a two-dimensional sine wave primitive function is established.

4. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 3, characterized in that, The range of length variation in the two directions of the original two-dimensional sine wave function is greater than or equal to the range of length variation in the two directions corresponding to the bidirectional error and curve.

5. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 1, characterized in that, The establishment of a two-dimensional irregular mesh with different interpolation node distributions includes: Establish two orthogonal meshes with equal side lengths in both directions; While keeping the area constant, the orthogonality of the orthogonal mesh is changed by rotating one of the two directions, thereby creating irregular meshes of different mesh qualities, wherein the distribution of interpolation nodes is different in the irregular meshes of different mesh qualities.

6. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 1, characterized in that, The step of calculating the approximate wave field of two-dimensional Lagrange polynomial interpolation in different irregular grids based on the different distribution of interpolation nodes in the two-dimensional irregular grid includes: Based on the interpolation nodes with different distributions in the two-dimensional irregular grid, the amplitude values ​​of the original two-dimensional sine wave function at the interpolation nodes are obtained as the original two-dimensional sine wave field values. Based on the wave field values ​​of the two-dimensional sinusoidal wave field interpolation nodes, the approximate two-dimensional Lagrange polynomial interpolation wave field values ​​are obtained by using the Lagrange polynomial interpolation method.

7. The method for approximate error analysis of Lagrange polynomial interpolation based on sine waves according to claim 6, characterized in that, The step of comparing the approximate wave field of the two-dimensional Lagrange polynomial interpolation within the different irregular grids with the original two-dimensional sinusoidal wave field within the two-dimensional irregular grids to determine the quantization relationship of the Lagrange polynomial interpolation approximation error includes: The interpolation approximation error quantization matrix is ​​obtained by subtracting the two-dimensional Lagrange polynomial interpolation approximation wave field value in the different irregular grids from the original two-dimensional sinusoidal wave field value in the two-dimensional irregular grids. The maximum value of the interpolation approximation error quantization matrix is ​​extracted to characterize the Lagrange polynomial interpolation approximation error quantization relationship.

8. A device for analyzing approximate errors in Lagrange polynomial interpolation based on sine waves, characterized in that, include: The interpolation calculation module is used to calculate one-dimensional Lagrange polynomial interpolation with a one-dimensional sine wave as the original function, under different interpolation node distributions. The error analysis module is used to analyze the approximation error between the Lagrange polynomial interpolation and the original function under different interpolation node distributions. A two-dimensional establishment module is used to establish a two-dimensional sine wave primitive function based on the approximation error. The grid mapping module is used to establish a two-dimensional irregular grid with different interpolation node distributions, and to map the original two-dimensional sine wave function into the two-dimensional irregular grid to obtain the original two-dimensional sine wave field. The wave field calculation module is used to calculate the approximate two-dimensional Lagrange polynomial interpolation wave field in different irregular grids based on the different distribution of interpolation nodes in the two-dimensional irregular grid. The error quantization module is used to compare the approximate wave field of the two-dimensional Lagrange polynomial interpolation in different irregular grids with the original wave field of the two-dimensional sinusoidal wave in the two-dimensional irregular grids, and to determine the error quantization relationship of the Lagrange polynomial interpolation approximation.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the sine wave-based Lagrange polynomial interpolation approximation error analysis method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for approximate error analysis of Lagrange polynomial interpolation based on sine waves as described in any one of claims 1 to 7.

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