A two-dimensional grid generation method and system based on poisson equation iterative optimization

Abstract

The application discloses a two-dimensional grid generation method and system based on Poisson equation iteration optimization, belongs to the field of computational fluid dynamics and scientific calculation, and comprises the following steps: acquiring boundary coordinate data of a complex geometric shape; adopting a node simplification algorithm and an adaptive encryption algorithm to perform smoothing processing on the boundary coordinate data of the complex geometric shape, so as to form an outer boundary of the complex geometric shape; based on the boundary coordinate data of the complex geometric shape, adopting a geometric centerline extraction algorithm and a control line generation algorithm to generate a plurality of control lines; introducing a grid correction amount into a Poisson equation, combining the outer boundary of the complex geometric shape and the plurality of control lines, iteratively solving and optimizing the grid correction amount, and finally generating a two-dimensional grid. The application is suitable for high-precision fluid dynamics numerical simulation of a complex geometric shape region, improves orthogonality of the two-dimensional grid, adaptive sparsity control capability and calculation stability, and provides high-quality two-dimensional grid support for numerical calculation of the complex geometric shape region.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics and scientific computing, specifically relating to a two-dimensional mesh generation method and system based on iterative optimization of the Poisson equation. Background Technology

[0002] Mesh generation is a core foundation for numerical simulations in computational fluid dynamics (CFD) and environmental hydrology, and its quality directly affects the computational accuracy and efficiency of physical fields (such as flow velocity, concentration, and temperature). While traditional mesh generation methods (such as those based on the Laplace equation) can generate uniform meshes, they have significant limitations when dealing with complex geometric boundaries (such as irregular channels and multi-connected domains). For example, meshes generated by the Laplace equation are difficult to control in terms of density distribution, leading to insufficient resolution in high-gradient regions (such as boundary layers and separated flow regions), thus affecting the simulation accuracy of key parameters such as flow velocity. Furthermore, traditional methods lack sufficient orthogonality control in complex three-dimensional domains, easily leading to numerical instability and limiting their application in large-scale engineering problems.

[0003] To overcome the aforementioned limitations, mesh generation techniques based on the Poisson equation have gradually become a research hotspot. The Poisson equation, by introducing source terms to actively adjust the distribution density and orthogonality of mesh nodes, can better adapt to complex geometries. For example, in the numerical simulation of the hydrodynamic field of the Yangtze River estuary, existing techniques, by comparing the generation effects of the Laplace equation and the Poisson equation, have found that the Poisson equation exhibits greater flexibility in fitting complex boundaries (such as islands and meandering channels), generating meshes with controllable density and good orthogonality, significantly improving the accuracy of multi-connected domain simulations. Similarly, other existing techniques in the generation of 3D meshes for turbine blades have achieved a refined distribution of the mesh near the boundary by adjusting the source terms of the Poisson equation, and have improved computational stability by utilizing improved difference schemes, solving the iterative divergence problem caused by excessively large source terms in traditional methods.

[0004] In recent years, with the deep integration of dynamic models and numerical methods, Poisson equation mesh generation technology based on dynamic models has further expanded its application scenarios. For example, the PhyGeoNet framework proposed in related technologies combines elliptical coordinate transformation with convolutional neural networks to achieve adaptive mapping from irregular physical domains to regular reference domains by solving parameterized Poisson equations, generating high-precision meshes without the need for labeled data. This method not only inherits the advantages of Poisson equations in boundary fitting and orthogonal control, but also enhances the adaptive capability of mesh generation through deep learning, providing new ideas for dynamic systems and large-scale parameterized problems. However, it still suffers from problems such as insufficient orthogonality of two-dimensional meshes under complex geometries, unreasonable density distribution, and poor computational stability.

[0005] Therefore, it is necessary to design a two-dimensional mesh generation method and system based on iterative optimization of the Poisson equation to address the above problems. Summary of the Invention

[0006] This invention addresses the problems of insufficient orthogonality, unreasonable density distribution, and poor computational stability of two-dimensional meshes under complex geometries. It provides a two-dimensional mesh generation method based on iterative optimization of the Poisson equation, which performs smoothing processing through node simplification and adaptive density algorithms, and numerically solves the Poisson equation with introduced mesh corrections. This method is suitable for high-precision numerical simulation of fluid dynamics in complex geometric regions, improving the orthogonality, adaptive density control capability, and computational stability of the two-dimensional mesh, and providing high-quality two-dimensional mesh support for numerical calculations of complex geometries.

[0007] According to one aspect of this specification, a two-dimensional mesh generation method based on iterative optimization of the Poisson equation is provided, comprising:

[0008] S1. Obtain the boundary coordinate data of complex geometric shapes;

[0009] S2. Based on the boundary coordinate data of complex geometries, a node simplification algorithm is used to eliminate redundant nodes, and an adaptive encryption algorithm is used for smoothing to form the outer boundary of the complex geometries.

[0010] S3. Based on the boundary coordinate data of complex geometric shapes, the spatial distribution characteristics are analyzed using the geometric centerline extraction algorithm, and multiple control lines are generated using the control line generation algorithm.

[0011] S4. Introduce the mesh correction into the Poisson equation, and combine the complex geometric outer boundary and multiple control lines to iteratively solve the mesh correction, finally generating a two-dimensional mesh.

[0012] Further, S2 includes:

[0013] A node simplification algorithm is used to equalize the boundary coordinate data of the complex geometry;

[0014] An adaptive encryption algorithm is used to scatter and encrypt the boundary coordinate data after the equalization process, forming an outer boundary with a complex geometric shape.

[0015] Further, S3 includes:

[0016] Based on the boundary coordinate data of the complex geometry, a reference curve is generated using a geometric midline extraction algorithm;

[0017] Based on the reference curve, a control line generation algorithm is used to generate multiple control lines perpendicular to the outer boundary of the complex geometry.

[0018] Furthermore, the mesh correction is introduced into the Poisson equation to construct a mapping relationship between the physical domain and the reference domain;

[0019] The grid correction is iteratively solved and the grid size is adjusted to generate grid point coordinates;

[0020] The coordinates of the grid points are plotted to form a two-dimensional grid; the Poisson equation expression, which incorporates grid correction, is as follows:

[0021]

[0022]

[0023] in,( , () represents the coordinates of the reference domain, ( , () represents the coordinates of the physical domain. Indicates along Grid correction amount in direction, Indicates along Grid correction amount in direction, , They represent , A measure of the degree of local mesh stretching in a given direction. express , The degree of coupling between directions.

[0024] Furthermore, an adaptive encryption algorithm is used to perform scatter point encryption on the averaged boundary coordinate data, including:

[0025] A smoothness control factor is introduced into the adaptive encryption algorithm, and interpolation points are dynamically inserted through the smoothness control factor to generate a smooth boundary representation;

[0026] Based on the smooth boundary representation, the outer boundary of the complex geometric shape is formed; the smoothness control factor adopts the exponential weighted moving average method to control the weight distribution of the previous scatter point coordinates and the current scatter point coordinates.

[0027] Furthermore, the method also includes: re-iterating and generating a two-dimensional mesh by adjusting multiple control lines.

[0028] According to one aspect of this specification, a two-dimensional mesh generation system based on iterative optimization of the Poisson equation is provided, comprising:

[0029] The data acquisition module is used to acquire boundary coordinate data of complex geometric shapes;

[0030] The boundary formation module is used to form the outer boundary of complex geometries based on boundary coordinate data. It uses a node simplification algorithm to eliminate redundant nodes and an adaptive encryption algorithm for smoothing.

[0031] The control line generation module is used to analyze the spatial distribution characteristics based on boundary coordinate data of complex geometric shapes, and to generate multiple control lines using a geometric midline extraction algorithm.

[0032] The mesh generation module incorporates the mesh correction factor into the Poisson equation, and combines the complex geometric outer boundary and multiple control lines to iteratively solve the mesh correction factor, ultimately generating a two-dimensional mesh.

[0033] According to one aspect of this specification, an electronic device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the two-dimensional mesh generation method based on the iterative optimization of the Poisson equation.

[0034] According to one aspect of this specification, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the two-dimensional mesh generation method based on the iterative optimization of the Poisson equation.

[0035] According to one aspect of the present invention, a computer program product containing instructions is provided, which, when run on a computer, causes the computer to perform the steps of the two-dimensional mesh generation method based on the iterative optimization of the Poisson equation.

[0036] Compared with the prior art, the beneficial effects of the present invention are:

[0037] 1. This invention improves the geometric fitting accuracy of the mesh boundary by performing smoothing processing through node simplification algorithm and adaptive encryption algorithm, and reduces the total number of mesh cells while ensuring calculation accuracy, effectively reducing the consumption of computing resources and memory requirements.

[0038] 2. This invention achieves higher precision boundary fitting by numerically solving the Poisson equation with introduced mesh correction, generating a mesh while ensuring mesh quality, thereby improving computational efficiency and reducing the human resources and time costs of engineering simulation.

[0039] 3. This invention improves the computational efficiency and boundary fitting accuracy of numerical simulation by dynamically optimizing the mesh density distribution, and supports user-defined mesh resolution parameters, providing a flexible and scalable high-quality mesh generation framework for multi-scale fluid dynamics modeling. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of water system boundary point extraction according to an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of water system scatter point encryption and boundary smoothing according to an embodiment of the present invention;

[0044] Figure 4 This is a schematic diagram of control line generation according to an embodiment of the present invention;

[0045] Figures 5(a)-5(d) This is a schematic diagram of two-dimensional mesh generation according to an embodiment of the present invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] like Figure 1 As shown, this embodiment of the invention provides a two-dimensional mesh generation method based on iterative optimization of the Poisson equation, including: S1, obtaining boundary coordinate data of a complex geometric shape; S2, based on the boundary coordinate data of the complex geometric shape, using a node simplification algorithm to eliminate redundant nodes and using an adaptive encryption algorithm for smoothing, forming the outer boundary of the complex geometric shape; S3, based on the boundary coordinate data of the complex geometric shape, using a geometric midline extraction algorithm to analyze spatial distribution characteristics and using a control line generation algorithm to generate multiple control lines; S4, introducing the mesh correction amount into the Poisson equation, combining the outer boundary of the complex geometric shape and multiple control lines, iteratively solving the mesh correction amount, and finally generating a two-dimensional mesh.

[0048] Specifically, this embodiment of the invention also provides the specific content of S1, which involves first depicting the boundary outline of a complex geometric shape on a satellite map; after the depiction is completed, the information of the boundary outline is converted into general non-topological vector data (shp file). Then, the shp file is converted into a series of scattered coordinates using a professional geographic information system software platform (ArcGIS). , Finally, these scattered point coordinate data are extracted and saved as DAT files as boundary coordinate data, providing basic data support for subsequent related operations.

[0049] Specifically, this embodiment of the invention also provides the specific content of S2, which uses a node simplification algorithm to process scattered coordinate data, compressing the number of scattered points to 1 / n of the original number based on a preset adjustable compression coefficient n. This process is not a simple random deletion, but rather based on in-depth analysis of the distribution characteristics and topological relationships of the scattered points. Through intelligent judgment and screening, redundant nodes that have little impact on the overall boundary shape are eliminated. By adjusting a specific equalization coefficient, the number of output equalized scattered points can be controlled, thereby minimizing the amount of data and improving the efficiency of subsequent processing while ensuring that the basic shape of the boundary remains unchanged. The equalized scattered coordinate data effectively smooths out local minor undulations, laying a good foundation for subsequent encryption processing. Then, an adaptive encryption algorithm is used to further optimize the equalized scattered points. By introducing a smoothness control factor, the strength and effect of encryption are dynamically adjusted according to actual needs. Based on the smoothness control factor, interpolation points are dynamically inserted between the equalized scattered points, and precise calculations and adjustments are made according to the curvature changes and smoothness requirements of the boundary. In this way, the boundary smoothness can be guaranteed while preserving the original features of the boundary as much as possible. The smoothness control factor employs the concept of an exponentially weighted moving average to control the weighting of historical data and current observations. The recursive formula is as follows:

[0050] (1)

[0051] (2)

[0052] in Represents historical data. For the current observation value, The weights represent the weights and increase dynamically with each iteration. This represents the smoothness control factor. This non-static weight design is suitable for the progressive smoothing of non-stationary geological boundary data.

[0053] Specifically, this embodiment of the invention also provides the specific content of S3. Based on the input boundary coordinate data, a geometric centerline extraction algorithm is used to deeply analyze the spatial distribution characteristics of the boundary coordinate data and calculate and generate a reference curve located at the center of the boundary. During the calculation process, the program fully considers factors such as the curvature and length variation of the boundary to ensure that the generated reference curve can accurately reflect the geometric center position of the boundary, providing a reliable reference for the subsequent generation of control lines. After the centerline is generated, a series of perpendicular line segments perpendicular to the boundary direction are generated based on the reference curve using a control line generation algorithm. The number of perpendicular line segments, n, is an adjustable integer parameter. In practical applications, the value of n can be reasonably adjusted according to specific needs, such as engineering accuracy requirements and data processing scale. When higher control accuracy is required, the value of n can be appropriately increased to increase the number of perpendicular line segments, thereby making the control lines denser and able to describe the boundary changes more meticulously. Conversely, when the accuracy requirements are relatively low or the data processing scale is large, the value of n can be decreased to reduce the number of perpendicular line segments, thereby improving processing efficiency.

[0054] Specifically, this embodiment of the invention also provides the specific content of S4, which introduces a correction amount based on mesh features into the Poisson equation to drive the dynamic adjustment of the spatial configuration of mesh points. Combining the outer boundary of the complex geometry and multiple control lines, the correction amount based on mesh features is solved iteratively until a predetermined convergence criterion is met, ultimately obtaining the mesh point coordinates and providing a geometric basis for subsequent high-precision simulation of the physical field. The expression of the Poisson equation with the mesh correction amount is:

[0055] (3)

[0056] (4)

[0057] Equations (3) and (4) are elliptic partial differential equations used to construct the coordinate mapping relationship between the physical domain (Ωp) and the reference domain (Ωr). By solving the equations, the forward mapping can be determined, mapping the coordinates (ξ, η) of the regular reference domain to the coordinates (x, y) of the irregular physical domain. Fx represents the mesh correction along the x-direction, and Fy represents the mesh correction along the y-direction. By adjusting the distribution of mesh nodes, it is ensured that the generated mesh conforms to the boundary of complex geometry in the physical domain, while maintaining the regularity of the reference domain. In addition, the elliptic nature of the equations ensures that the generated mesh is smooth and non-intersecting, making it suitable for numerical calculations. The correlation coefficient is calculated as follows:

[0058] (5)

[0059] (6)

[0060] (7)

[0061] Where α and γ represent the measures of local mesh stretching in the η and ξ directions, respectively; if α is large, the mesh spacing along the η direction in the physical domain is small, corresponding to high gradient regions (such as boundary layers). β represents the degree of coupling between the η and ξ directions, reflecting the non-orthogonality of coordinate transformation; if β=0, the mesh is locally orthogonal.

[0062] Specifically, after obtaining the coordinates of the grid points, the grid points are drawn to form a two-dimensional grid; in addition, the grid can be regenerated iteratively by adjusting the control lines of the boundary.

[0063] Specifically, this invention also provides Embodiment 1, which extracts water system coordinates based on the DEM digital elevation data of the watershed to obtain the watershed water system structure layer, such as... Figure 2 The diagram shows the extraction of coordinates for boundary points of the Xiluodu main stream system. The obtained river boundary coordinates are saved as four DAT files, which are used to store the coordinate data of the upper boundary, lower boundary, left boundary, and right boundary points, respectively.

[0064] Specifically, the above process played a significant role in addressing the issue of uneven river boundaries. First, the built-in averaging program is invoked to average the scatter coordinate set of the original boundary. This step quickly smooths out minor local undulations, making the boundary shape more regular. Subsequently, the encryption program densifies the averaged scatter points, forming a smoother outer boundary, such as... Figure 3 As shown. By default, the smoothness control factor is set to 0.8. This value has been verified through extensive experimentation and can achieve good smoothing results in most cases. The smoothness control factor can be adjusted according to actual needs to obtain a boundary shape that better meets the requirements.

[0065] Specifically, to make the mesh more regular, control line data files are generated through a centerline generation program and a control line generation program. The centerline generation program, based on the input original boundary coordinate data, uses a geometric centerline extraction algorithm to generate a reference curve located at the center of the boundary. Subsequently, the control line generation module uses this as a reference to generate n perpendicular line segments perpendicular to the boundary direction; this integer parameter n can be adjusted as needed, thereby achieving flexible control of the control line density (here, n is set to 36). Figure 4 As shown.

[0066] Specifically, based on the Poisson equation with introduced grid correction, the grid correction is iteratively solved. The default grid size is 30m x 30m. The first iteration involves 100,000 iterations, taking 40-60 minutes. The second, more refined iteration involves 2,000 iterations, taking 30-50 minutes. Adjusting the grid size will change the iteration time. The final output includes a grid x-coordinate data file (X.DAT) and a grid y-coordinate data file (Y.DAT), representing the coordinates of the grid points. In this embodiment, the grid size is 30m x 30m, resulting in 53,333 grid cells (2807 x 19). Figures 5(a)-5(d) As shown, the orthogonality and regularity of the corresponding two-dimensional mesh meet the requirements, whether in the region where the boundary turns or in the region where it is straight.

[0067] The implementation of the various embodiments of this invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of this invention provide a two-dimensional mesh generation system based on Poisson equation iterative optimization. This system is used to execute a two-dimensional mesh generation method based on Poisson equation iterative optimization from the above method embodiments.

[0068] The system includes: a data acquisition module for acquiring boundary coordinate data of complex geometries; a boundary formation module for forming the outer boundary of complex geometries by using a node simplification algorithm to eliminate redundant nodes and an adaptive encryption algorithm for smoothing based on the boundary coordinate data of complex geometries; a control line generation module for generating multiple control lines by using a geometric midline extraction algorithm to analyze spatial distribution characteristics based on the boundary coordinate data of complex geometries; and a mesh generation module for iteratively solving the mesh correction by incorporating the mesh correction into the Poisson equation and combining the outer boundary of the complex geometries and multiple control lines to finally generate a two-dimensional mesh.

[0069] The two-dimensional mesh generation system based on iterative optimization of the Poisson equation provided in this invention addresses the problems of insufficient orthogonality, unreasonable density distribution, and poor computational stability of two-dimensional meshes under complex geometries in existing technologies. It employs several modules and uses node simplification and adaptive densification algorithms for smoothing, improving the geometric fitting accuracy of mesh boundaries. While maintaining computational accuracy, it reduces the total number of mesh elements, effectively lowering computational resource consumption and memory requirements. By numerically solving the Poisson equation with introduced mesh corrections, it generates meshes while ensuring mesh quality, achieving higher-precision boundary fitting effects, improving computational efficiency, and reducing the human resource and time costs of engineering simulations.

[0070] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize a two-dimensional mesh generation method based on iterative optimization of the Poisson equation as proposed in the above embodiments.

[0071] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, this program overcomes the problems of insufficient orthogonality, unreasonable density distribution, and poor computational stability of two-dimensional meshes under complex geometries. It is suitable for high-precision numerical simulation of fluid dynamics in complex geometric regions, improves the orthogonality, adaptive density control capability, and computational stability of two-dimensional meshes, and provides high-quality two-dimensional mesh support for numerical calculations in complex geometric regions.

[0072] The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, or optical disk, used to store computer program code and necessary data files. The stored computer program includes: a data acquisition module, a boundary formation module, a control line generation module, and a mesh generation module.

[0073] This invention also provides a computer program product containing instructions that, when run on a computer, generate, in whole or in part, the two-dimensional mesh generation method based on iterative optimization of the Poisson equation as proposed in the above embodiments. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0074] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A two-dimensional mesh generation method based on iterative optimization of the Poisson equation, characterized in that, include: S1. Obtain the boundary coordinate data of complex geometric shapes; S2. Based on the boundary coordinate data of complex geometries, a node simplification algorithm is used to eliminate redundant nodes, and an adaptive encryption algorithm is used for smoothing to form the outer boundary of the complex geometries. S3. Based on the boundary coordinate data of the complex geometric shape, a geometric midline extraction algorithm is used to analyze the spatial distribution characteristics, and a control line generation algorithm is used to generate multiple control lines; S3 includes: based on the boundary coordinate data of the complex geometric shape, a geometric midline extraction algorithm is used to generate a reference curve; based on the reference curve, a control line generation algorithm is used to generate multiple control lines perpendicular to the outer boundary of the complex geometric shape. S4. Introduce the mesh correction factor into the Poisson equation, and iteratively solve the mesh correction factor by combining the outer boundary of the complex geometry and multiple control lines to finally generate a two-dimensional mesh; S4 includes: By incorporating mesh corrections into the Poisson equation, a mapping relationship between the physical domain and the reference domain is constructed. The grid correction is iteratively solved and the grid size is adjusted to generate grid point coordinates; The coordinates of the grid points are plotted to form a two-dimensional grid; the Poisson equation expression, which incorporates grid correction, is as follows: ， ， in,( , () represents the coordinates of the reference domain, ( , () represents the coordinates of the physical domain. Indicates along directional grid correction amount, Indicates along directional grid correction amount, , They represent , A measure of the degree of local mesh stretching in a given direction. express , The degree of coupling between directions.

2. The two-dimensional mesh generation method based on iterative optimization of the Poisson equation according to claim 1, characterized in that, The S2 includes: A node simplification algorithm is used to equalize the boundary coordinate data of the complex geometry; An adaptive encryption algorithm is used to scatter and encrypt the boundary coordinate data after the equalization process, forming an outer boundary with a complex geometric shape.

3. The two-dimensional mesh generation method based on iterative optimization of the Poisson equation according to claim 2, characterized in that, An adaptive encryption algorithm is used to perform scatter point encryption on the averaged boundary coordinate data, including: A smoothness control factor is introduced into the adaptive encryption algorithm, and interpolation points are dynamically inserted through the smoothness control factor to generate a smooth boundary representation; Based on the smooth boundary representation, the outer boundary of the complex geometric shape is formed; the smoothness control factor adopts the exponential weighted moving average method to control the weight distribution between the previous scatter point coordinates and the current scatter point coordinates.

4. The two-dimensional mesh generation method based on iterative optimization of the Poisson equation according to claim 1, characterized in that, The method further includes: re-iterating and generating a two-dimensional mesh by adjusting multiple control lines.

5. A two-dimensional mesh generation system based on iterative optimization of the Poisson equation, used to implement the two-dimensional mesh generation method based on iterative optimization of the Poisson equation as described in any one of claims 1 to 4, characterized in that, include: The data acquisition module is used to acquire boundary coordinate data of complex geometric shapes; The boundary formation module is used to form the outer boundary of complex geometries based on boundary coordinate data. It uses a node simplification algorithm to eliminate redundant nodes and an adaptive encryption algorithm for smoothing. The control line generation module is used to analyze the spatial distribution characteristics based on boundary coordinate data of complex geometric shapes, and to generate multiple control lines using a geometric midline extraction algorithm. The mesh generation module incorporates mesh corrections into the Poisson equation, and iteratively solves for the mesh corrections by combining the complex geometric outer boundary and multiple control lines, ultimately generating a two-dimensional mesh.

6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the two-dimensional mesh generation method based on iterative optimization of the Poisson equation as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the two-dimensional mesh generation method based on the iterative optimization of the Poisson equation as described in any one of claims 1 to 4.

8. A computer program product containing instructions, characterized in that, When it is run on a computer, it causes the computer to perform the steps of the two-dimensional mesh generation method based on the iterative optimization of the Poisson equation as described in any one of claims 1 to 4.

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