Electromagnetic field numerical calculation method based on prior knowledge of physical field and related device

Abstract

The invention belongs to the field of computational electromagnetics and numerical simulation, and discloses an electromagnetic field numerical calculation method based on physical field priori knowledge and a related device, and the method comprises the steps: carrying out the mesh generation of a geometric calculation model of a to-be-calculated electromagnetic structure, carrying out the type division of a plurality of mesh units, and determining the unit type of each mesh unit; generating a discontinuous bit function interpolation function based on the enhanced enrichment function fused with the prior knowledge of the physical field; based on the unit type of each grid unit, a non-continuity bit function interpolation function is combined, and a unit stiffness matrix of each grid unit is obtained through calculation; combining the element stiffness matrix of each grid element, and constructing a multi-scale finite element discrete equation; solving the multi-scale finite element discrete equation to obtain an electromagnetic field numerical calculation result of the electromagnetic structure to be calculated; according to the method, the calculation precision of bit function distribution and field distribution near the medium interface is remarkably improved, and the physical fidelity of interface calculation is fundamentally improved.

Description

Technical Field

[0001] This invention belongs to the field of computational electromagnetics and numerical simulation technology, and specifically relates to a numerical calculation method and related apparatus for electromagnetic fields based on prior knowledge of physical fields. Background Technology

[0002] In numerous engineering applications such as motor design, microwave devices, and electromagnetic compatibility, numerical calculations of electromagnetic fields for complex multi-scale structures (such as composite materials, periodic microstructures, and thin conductors) are crucial for accurately determining the electromagnetic field distribution of such structures. This has a central impact on the performance and reliability of related products. Therefore, accurately obtaining the electromagnetic field distribution is essential for optimizing design and improving product performance.

[0003] As one of the mainstream numerical calculation methods for electromagnetic fields, the finite element method typically employs an interface-compatible mesh generation method. This requires that the boundaries of the mesh elements be strictly fitted to the interfaces between different media. This significantly increases the difficulty of mesh generation for complex structures with multi-scale complex structures, moving interfaces, and randomly distributed media. Not only is the computation cost high, but the workload of preprocessing is also greatly increased, resulting in low efficiency of the entire calculation process and making it difficult to meet the needs of rapid and efficient acquisition of electromagnetic field distribution in practical engineering.

[0004] To overcome the aforementioned bottlenecks, advanced techniques such as the Extended Finite Element Method (XFEM) and the Multiscale Finite Element Method (MSFEM) have emerged. The core of the XFEM and MSFEM is to decouple mesh generation from the physical interface, allowing the medium interface to pass through the interior of the mesh. By introducing additional enrichment functions to correct the standard form function, local characteristics such as abrupt changes in field quantity at the medium interface can be captured in the coarse-scale mesh entropy. To a certain extent, this addresses the difficulties of the ordinary finite element method in the mesh generation process, improves computational efficiency, and provides a new approach for handling electromagnetic field distribution tasks with complex multi-scale structures.

[0005] However, in practical applications, existing extended finite element methods (EPM) and multi-scale finite element methods often exhibit significant errors in calculating field distributions near media interfaces. To achieve the required engineering accuracy, mesh refinement is still necessary to some extent, failing to fully realize the potential of multi-scale finite element methods. Specifically, the enrichment functions used in existing EPM and multi-scale finite element methods, such as jump functions based on Heaviside functions or enrichment functions based on absolute value functions, are mostly general-purpose mathematical functions. While general-purpose functions are designed to describe the discontinuities of field quantities, they cannot deeply integrate the specific physical field laws that must be satisfied at the media interface, leading to significant errors in field distribution calculations. For example, in constant magnetic field problems, the physical fields on both sides of the media interface must strictly satisfy the boundary conditions of Ampere's law and the continuity of the normal component of magnetic flux density. Although general-purpose enrichment functions can construct jumps in the solution space, these jumps are free and do not establish a mandatory relationship with the constitutive parameters of the material (such as magnetic permeability and electrical conductivity), resulting in the inability to accurately and intrinsically satisfy the above physical constraints, leading to significant errors in field distribution calculations near the interface. Summary of the Invention

[0006] To address the technical problems existing in the prior art, this invention provides a numerical calculation method and related apparatus for electromagnetic fields based on prior knowledge of physical fields, in order to solve the technical problem that existing extended finite element method and multi-scale finite element method often have significant errors in the calculation of field distribution near the medium interface.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a numerical calculation method for electromagnetic fields based on prior knowledge of physical fields, comprising: Based on a meshing strategy that does not depend on the geometric features of the medium interface, the geometric computational model of the electromagnetic structure to be computed is meshed to obtain spatial discrete mesh results; wherein, the spatial discrete mesh results include several mesh cells and the cell node information of each mesh cell; Based on the pre-generated interface level set function and spatial discrete mesh results, several mesh elements are classified into types to determine the element type of each mesh element; among them, the element types of mesh elements include enriched elements, mixed elements and ordinary elements; Based on a pre-constructed enhanced enrichment function that integrates prior knowledge of physical fields, a discontinuous potential function interpolation function is generated. Based on the element type of each grid element and combined with the discontinuous potential function interpolation function, the element stiffness matrix of each grid element is calculated. The element stiffness matrices of each mesh element are combined to obtain the overall stiffness matrix; based on the overall stiffness matrix, multi-scale finite element discrete equations are constructed. The multi-scale finite element discrete equations are solved to obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

[0008] Furthermore, the pre-constructed enhanced enrichment function that integrates prior knowledge of the physical field is a second type of enrichment function that embeds prior knowledge of the physical field; wherein, the prior knowledge of the physical field includes boundary continuity conditions, field quantity conservation relations, or dielectric / magnetic properties constraints of the medium.

[0009] Furthermore, the discontinuous bit interpolation function is as follows:

[0010] in, It is a discontinuous bit interpolation function; and These are all shape functions in the ordinary multi-scale finite element method; This represents the node potential; For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; For enriched nodes in enriched cells Additional degrees of freedom.

[0011] Furthermore, the construction process of the pre-constructed enhanced enrichment function that integrates prior knowledge of the physical field is as follows: Based on the physical field continuity condition at the medium interface, a constraint relationship between material parameters and field distribution is established. By introducing a correction factor to optimize the function, a pre-constructed enhanced enrichment function integrating prior physical field knowledge is obtained. The pre-constructed enhanced enrichment function integrating prior physical field knowledge is as follows:

[0012]

[0013]

[0014] in, For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; This is the enrichment function in the ordinary multi-scale finite element method; As a correction factor; For Herveside step function; For the pre-generated interface level set function The physical field correction function of the region; For the pre-generated interface level set function The physical field correction function of the region; For the pre-generated interface level set function; For nodes under the ordinary multi-scale finite element method Shape function at the location; For nodes The level set function value at that location; The set of enriched nodes in all enriched units; This is the set of nodes in all enriched units.

[0015] Furthermore, based on the element type of each mesh element and combined with the discontinuous potential function interpolation function, the process of calculating the element stiffness matrix of each mesh element is as follows: Determine whether the cell type of the mesh element is an enriched cell; If the element type of the mesh is enriched element, the enriched element is divided into different material property regions according to the medium interface, and each material property region is divided into several sub-elements of a preset shape based on the isoparametric element principle. The element stiffness matrix of the enriched element is calculated based on the Hammer spatial integration method and the discontinuous potential function interpolation function.

[0016] Furthermore, if the element type of the mesh element is a common element, the element stiffness matrix of the common element is calculated based on the common finite element method and in combination with the discontinuous potential function interpolation function.

[0017] This invention also provides a numerical calculation system for electromagnetic fields based on prior knowledge of physical fields, comprising: The mesh discretization module is used to perform mesh partitioning on the geometric computational model of the electromagnetic structure to be computed based on a mesh partitioning strategy that does not depend on the geometric features of the medium interface, and obtain spatially discrete mesh results. The spatially discrete mesh results include several mesh cells and the cell node information of each mesh cell. The cell partitioning module is used to classify several grid cells based on the pre-generated interface level set function and spatial discrete grid results, and to determine the cell type of each grid cell; the cell types of the grid cells include enriched cells, mixed cells and ordinary cells; The function generation module is used to generate discontinuous potential function interpolation functions based on pre-built enhanced enrichment functions that incorporate prior knowledge of physical fields. The matrix calculation module is used to calculate the element stiffness matrix of each grid element based on its element type and in conjunction with the discontinuous potential function interpolation function. The equation construction module is used to combine the element stiffness matrices of each mesh element to obtain the overall stiffness matrix; based on the overall stiffness matrix, multi-scale finite element discrete equations are constructed. The equation solving module is used to solve the multi-scale finite element discrete equations and obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

[0018] The present invention also provides an electronic device, comprising: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the electromagnetic field numerical calculation method based on prior knowledge of physical fields.

[0019] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the electromagnetic field numerical calculation method based on prior knowledge of physical fields.

[0020] The present invention also provides a computer program product, characterized in that the computer program product includes a computer program, which, when executed by a processor, implements the electromagnetic field numerical calculation method based on prior knowledge of physical fields.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: The electromagnetic field numerical calculation method based on prior physical field knowledge provided by this invention utilizes a pre-constructed enhanced enrichment function that integrates prior physical field knowledge to generate a discontinuous potential function interpolation function. By incorporating prior physical field knowledge at the medium-substrate interface into the enrichment function, it achieves high-precision fitting of the electromagnetic field variation law at the medium-substrate interface on a large-scale grid cell, ensuring that the numerical solution strictly satisfies the physical laws at the medium-substrate interface in structure. This significantly improves the calculation accuracy of the potential function distribution and field distribution near the medium-substrate interface, fundamentally enhancing the physical fidelity of the interface calculation. Specifically, the introduction of prior physical field knowledge at the medium-substrate interface into the pre-constructed enhanced enrichment function ensures that the enrichment function contains a precise mathematical description of the medium-substrate interface. This allows the multi-scale finite element solution to approximate the true solution more quickly, achieving higher computational accuracy at the same mesh density and effectively improving the convergence performance of the method. Secondly, the coarse meshing strategy decoupled from the medium interface avoids the complex and time-consuming interface mesh generation process in the traditional finite element method, greatly simplifying the preprocessing flow and maintaining the mesh generation flexibility advantage of the multi-scale finite element method. The idea of ​​improving the enrichment function based on prior knowledge of the physical field has universality. By adapting to different interface physical constraints, it can be applied to different types of electromagnetic field problems such as eddy current fields and electromagnetic wave propagation, exhibiting good versatility and scalability. It is suitable for accurate simulation analysis in engineering fields such as electrical equipment, integrated circuits, and electromagnetic compatibility, which contain complex internal medium interfaces.

[0022] The electromagnetic field numerical calculation system, electronic device, computer-readable storage medium, and computer program product based on prior knowledge of physical fields provided by this invention possess all the advantages of the aforementioned electromagnetic field numerical calculation method based on prior knowledge of physical fields. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application 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 this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A flowchart of the electromagnetic field numerical calculation method based on prior knowledge of physical fields provided in Example 1; Figure 2 This is a schematic diagram of the classification results of different categories of grid cells in Example 1; Figure 3 This is a schematic diagram of the structure of a long, straight conductor with uniformly charged two-dimensional parallel planar field in Example 1; Figure 4 This is a comparison diagram of different meshing models used under the ordinary multi-scale finite element method and the method in Example 1; among them, Figure 4 a is a diagram of the meshed model under the ordinary multi-scale finite element method. Figure 4 b is a diagram of the subdivision model under the method of Example 1; Figure 5 This is a distribution diagram of the interface level set function in Example 1; Figure 6 This is a schematic diagram of the enriched cells and ordinary cells identified using the interface level set function in Example 1; Figure 7 This is a schematic diagram of the sub-unit partitioning process of a certain enrichment unit in Example 1; Figure 8 This is a comparison chart of the radial vector magnetic potential distribution curves and analytical solutions obtained by the multi-scale finite element method before and after the improvement of the enrichment function in Example 1; where, Figure 8 a is a comparison of the radial vector magnetic potential distribution curves obtained by the multi-scale finite element method before and after the improvement of the enrichment function; Figure 8 b is a magnified view of the numerical and analytical solutions of the x-coordinates obtained by multi-scale finite element method before and after the improvement of the enrichment function in the interval (1.2, 2.2); Figure 8 c is a magnified view of the numerical and analytical solutions of the x-coordinates obtained by the multi-scale finite element method before and after the improvement of the enrichment function in the interval (3.5, 4.5). Figure 8d is a local magnified view of the numerical and analytical solutions of the x-coordinates obtained by the multi-scale finite element method before and after the improvement of the enrichment function in the interval (5.5, 6.5); Figure 9 This is an error distribution diagram comparing the vector magnetic potential calculation results before and after the improvement of the enrichment function with the analytical solution in Example 1; wherein, Figure 9 Figure a shows a comparison of the absolute errors between the vector magnetic potential calculation results and the analytical solution before and after the improvement of the enrichment function. Figure 9 b is a comparison of the relative errors between the vector magnetic potential calculation results and the analytical solution before and after the enrichment function is improved; Figure 10 This is a structural block diagram of the electromagnetic field numerical calculation system based on prior knowledge of physical fields provided in Example 2; Figure 11 This is a structural block diagram of the electronic device provided in Example 3. Detailed Implementation

[0025] To make the technical problems, technical solutions, and beneficial effects solved by this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0026] This invention provides a numerical calculation method for electromagnetic fields based on prior knowledge of physical fields, comprising the following steps: Step 100: Based on a meshing strategy that does not depend on the geometric features of the medium interface, the geometric computation model of the electromagnetic structure to be computed is meshed to obtain spatial discrete mesh results; wherein, the spatial discrete mesh results include several mesh cells and the cell node information of each mesh cell.

[0027] Step 200: Based on the pre-generated interface level set function and spatial discrete grid results, classify several grid cells into types and determine the cell type of each grid cell; wherein, the cell type of the grid cell includes enriched cells, mixed cells and ordinary cells.

[0028] Step 300: Generate discontinuous potential function interpolation function based on the pre-constructed enhanced enrichment function that integrates prior knowledge of physical fields.

[0029] Step 400: Based on the element type of each grid element and combined with the discontinuous potential function interpolation function, calculate the element stiffness matrix of each grid element.

[0030] Step 500: Combine the element stiffness matrices of each grid element to obtain the overall stiffness matrix; based on the overall stiffness matrix, construct the multi-scale finite element discrete equations.

[0031] Step 600: Solve the multi-scale finite element discrete equations to obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

[0032] In the above embodiments, by adopting a meshing strategy that does not rely on the geometric features of the medium interface, the difficulty of meshing complex structures with multiple scales is reduced, computational costs and preprocessing workload are decreased, and computational efficiency is improved. Simultaneously, based on a pre-constructed enhanced enrichment function that integrates prior knowledge of the physical field, a discontinuous potential function interpolation function is generated. This pre-constructed enhanced enrichment function deeply incorporates specific physical field laws at the medium interface, overcoming the problem in existing extended finite element methods and multi-scale finite element methods where the general enrichment function cannot be forcibly correlated with material constitutive parameters, leading to significant errors in the calculation of field distribution near the medium interface. This method can more accurately satisfy physical constraints, thereby significantly improving the accuracy of electromagnetic field distribution calculations for complex structures with multiple scales, better meeting the needs of rapid, efficient, and accurate acquisition of electromagnetic field distributions in practical engineering. This invention introduces an enhanced enrichment function that integrates prior knowledge of the physical field, thus enabling high-precision analysis on large-scale meshes. It is suitable for accurate simulation analysis in engineering fields such as electrical equipment, integrated circuits, and electromagnetic compatibility, which contain complex internal medium interfaces.

[0033] The following specific embodiments further explain and illustrate the electromagnetic field numerical calculation method based on prior knowledge of physical fields provided by this invention: Example 1 As attached Figure 1 As shown, this embodiment 1 provides a numerical calculation method for electromagnetic fields based on prior knowledge of physical fields, including the following steps: Step 1: Based on a meshing strategy that does not depend on the geometric features of the medium interface, the geometric computational model of the electromagnetic structure to be computed is meshed to obtain a spatially discrete mesh result. The spatially discrete mesh result includes several mesh elements and the element node information for each mesh element.

[0034] Specifically, a geometric computational model of the electromagnetic structure to be calculated is modeled using pre-defined finite element analysis software. This electromagnetic structure may include, for example, electrical equipment, integrated circuits, or electromagnetic compatibility structures containing complex internal media interfaces. Then, based on a meshing strategy independent of the geometric features of the media interfaces—that is, allowing a single mesh cell to contain multiple different material media—the geometric computational model of the electromagnetic structure to be calculated is meshed to obtain spatially discrete mesh results. In the spatial discretization process of the finite element problem for electromagnetic field numerical calculation, a large-scale meshing strategy independent of the geometric features of material interfaces is adopted to obtain meshing results that ignore material differences, thereby reducing the dependence on fine geometric structures and lowering the complexity of mesh generation. Preferably, the large-scale meshing strategy independent of the geometric features of material interfaces employs unstructured mesh generation technology, where the mesh size is not limited by the geometric features of the material interfaces.

[0035] Step 2: Based on the pre-generated interface level set function and spatial discrete mesh results, classify several mesh elements into different types to determine the element type of each mesh element. The element types include enriched elements, hybrid elements, and ordinary elements.

[0036] Specifically, the steps are as follows: Step 21: Based on the location of the medium interface in the electromagnetic structure to be calculated, fit the medium interface using a distance function to generate the interface level set function, thus obtaining the pre-generated interface level set function. The pre-generated interface level set function is used to locate the medium interfaces of different materials and, based on the interface level set function, determine the relationship between the medium interface and the mesh elements, thereby classifying the mesh elements.

[0037] Step 22: Based on the pre-generated interface level set function, calculate the level set function values ​​at the element nodes in all grid cells; based on the positional relationship between the level set function at the element nodes and the medium interface, classify the grid cells into three different types, determining the element type of each grid cell; the element types of the grid cells include enriched elements, mixed elements, and ordinary elements, as shown in the appendix. Figure 2As shown; specifically, mesh elements with a medium interface passing through them are classified as enriched elements, i.e., mesh elements with a medium interface passing through them are considered enriched elements; the nodes contained in the enriched elements are called enriched nodes, and the material properties of the enriched elements are discontinuously distributed; mesh elements without a medium interface passing through them but containing at least one enriched node are classified as mixed nodes, i.e., mesh elements without a medium interface passing through them but containing at least one enriched node are considered mixed elements, and the mixed elements do not directly contact the medium interface but are adjacent to the enriched elements; mesh elements without a medium interface passing through them and without any enriched nodes are classified as ordinary elements.

[0038] Step 3: Based on the pre-constructed enhanced enrichment function that integrates prior knowledge of the physical field, generate a discontinuous potential function interpolation function. The discontinuous potential function interpolation function is as follows:

[0039] in, It is a discontinuous bit interpolation function; and These are all shape functions in the ordinary multi-scale finite element method; This represents the node potential; For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; For enriched nodes in enriched cells Additional degrees of freedom.

[0040] The pre-constructed enhanced enrichment function integrating prior knowledge of physical fields is a type II enrichment function embedded with prior knowledge of physical fields; wherein, the prior knowledge of physical fields includes boundary continuity conditions, field conservation relations, or dielectric / magnetic property constraints of the medium; specifically, the construction process of the pre-constructed enhanced enrichment function integrating prior knowledge of physical fields is as follows: Based on the physical field continuity condition at the medium interface, a constraint relationship between material parameters and field distribution is established. By introducing a correction factor to optimize the function, a pre-constructed enhanced enrichment function integrating prior physical field knowledge is obtained. The pre-constructed enhanced enrichment function integrating prior physical field knowledge is as follows:

[0041]

[0042]

[0043] in, For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; This is the enrichment function in the ordinary multi-scale finite element method; As a correction factor; The Herveside step function is used to distinguish different material regions based on the positive or negative function value of the pre-generated interface level set function; when Take 1, Take 0 at the time; For the pre-generated interface level set function The physical field correction function of the region is based on the pre-generated interface level set function. The material parameters and physical field continuity conditions of the region are constructed; For the pre-generated interface level set function The physical field correction function of the region is based on the pre-generated interface level set function. The material parameters and physical field continuity conditions of the region are constructed; For the pre-generated interface level set function; For nodes under the ordinary multi-scale finite element method Shape function at the location; For nodes The level set function value at that location; The set of enriched nodes in all enriched units; This is the set of nodes in all enriched units.

[0044] It should be noted that in the multi-scale finite element method calculation process, based on the principle of the unit decomposition method, an enhanced enrichment function that integrates prior physical field knowledge is introduced to improve the ordinary multi-scale finite element method. This is done to increase the weak discontinuities and construct an approximate interpolation expression for the potential function, thus obtaining the discontinuous potential function interpolation function. Specifically, in the construction of the enhanced enrichment function integrating prior physical field knowledge, prior physical field knowledge is embedded into a second type of enrichment function. This introduces prior physical field knowledge, including boundary continuity conditions, field conservation relationships, or dielectric / magnetic permeability constraints, into the second type of enrichment function. Furthermore, based on the physical field continuity conditions at the interface, a constraint relationship between material parameters and field distribution is established, and an optimization function is introduced by introducing a correction factor. The second type of enrichment function uses the absolute value method to handle physical scenarios where the field quantity is continuous but the derivative is discontinuous at the medium interface (such as the sudden strain change at the interface of two materials in elasticity, the discontinuity of the electric field strength derivative caused by the jump in the dielectric constant in the electromagnetic field, etc.). It is essentially a mathematical construction method for weak discontinuity, but it does not take into account physical laws (such as boundary conditions related to material parameters). In this embodiment 1, for the electromagnetic field problem of the electromagnetic structure to be calculated, when constructing the enrichment function, the prior knowledge of the local physical information of the medium interface, such as the boundary continuity conditions derived from Maxwell's equations, the conservation relationship of field quantity, and the dielectric / magnetic permeability constraints of the medium, is compiled into physical constraints and introduced into the second type of enrichment function to form a physically consistent improved enrichment function.

[0045] Step 4: Based on the element type of each mesh element and in conjunction with the discontinuous potential function interpolation function, calculate the element stiffness matrix of each mesh element. Specifically, determine whether the element type of the mesh element is an enriched element; if the element type is an enriched element, divide the enriched element into different material property regions according to the medium interface, and divide each material property region into several sub-elements of a preset shape based on the isoparametric element principle; calculate the element stiffness matrix of the enriched element using the Hammer spatial integration method and in conjunction with the discontinuous potential function interpolation function; if the element type of the mesh element is a normal element, calculate the element stiffness matrix of the normal element using the ordinary finite element method and in conjunction with the discontinuous potential function interpolation function.

[0046] It should be noted that in the process of calculating the element stiffness matrix of each mesh element, the Galerkin method is used, combined with the approximate solution of the discontinuous potential function interpolation function, to derive the weighted residual of the finite element method and obtain the element expression of the element stiffness matrix. In ordinary elements and hybrid elements, due to the characteristics of the enrichment function, the approximate solution expression will automatically degenerate into the traditional finite element approximate solution form; while in enriched elements, its weak discontinuity characteristics will be maintained.

[0047] Specifically, for mesh elements that are not crossed by the medium-material interface, i.e., ordinary elements that contain only one material and whose material properties do not change abruptly, the element stiffness matrix is ​​calculated using the traditional finite element method. For mesh elements that are crossed by the medium-material interface, i.e., enriched elements that contain more than one material and whose material properties change abruptly, it is necessary to divide the elements into sub-elements according to the location of the medium-material interface, and apply different material property coefficients to calculate the element stiffness matrix in different material regions within the element.

[0048] In particular, the presence of irregularly shaped sub-elements in the enriched elements caused by the partitioning of different media interfaces will affect the integral calculation of the integral results in the solution domain during the calculation of the stiffness matrix using the finite element functional method. In this case, the isoparametric element method theory is used to transform the irregularly shaped sub-elements in the enriched elements into regions that are equivalent to regular element shapes that are easy to calculate. By combining the spatial integration method, the irregular regions are integrated in blocks, and the finite element energy functional is calculated to obtain the element stiffness matrix under the enriched elements.

[0049] Step 5: Combine the element stiffness matrices of each mesh element to obtain the overall stiffness matrix; based on the overall stiffness matrix, construct the multi-scale finite element discretization equations. The multi-scale finite element discretization equations are as follows:

[0050] in, Let be the self-stiffness matrix of all finite element nodes; and Let be the mutual stiffness matrix between all finite element nodes and enriched nodes, and let be the transpose of . Let be the self-stiffness matrix of all enriched nodes; Let be the regular degree of freedom vector for all finite element nodes; Let be the enriched degree of freedom vector for all enriched nodes; The load vector for all finite element nodes; This is the load vector for all enriched nodes.

[0051] It is worth noting that the element stiffness matrix of all elements is calculated and then synthesized into a global stiffness matrix, which is then solved. Since additional degrees of freedom are added to the enriched nodes, the final global stiffness matrix includes the additional degrees of freedom.

[0052] Step 6: Solve the multi-scale finite element discrete equations to obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

[0053] The electromagnetic field numerical calculation method based on prior knowledge of physical fields described in Embodiment 1 obtains a mesh partitioning result that ignores material differences through spatial discretization and organizes the unit node information; according to the position of the medium interface, a level set function of the interface is fitted and generated; the level set function of the interface is used to divide the entire solution domain into different sub-regions, representing different material medium regions; combining the level set function of the interface and the spatially discretized mesh results, the level set function values ​​on each unit node are calculated to distinguish between enriched units, mixed units, and ordinary units in the entire solution domain, and to count the enriched units and enriched nodes; by introducing pre-constructed... An enhanced enrichment function incorporating prior knowledge of physical fields is used to generate discontinuous potential function interpolation functions to express the potential function distribution characteristics, including abrupt material changes. Based on the spatial discrete mesh results, the element stiffness matrix is ​​calculated using the Galerkin method in different elements. For ordinary elements, since there is no interface between the medium and the element contains only one material, the material properties within the element do not change abruptly, and the element stiffness matrix is ​​calculated directly using the same method as the traditional finite element method. For enriched elements, since there is an interface between the medium and the element contains more than one material, the material properties within the element will change abruptly. A sudden change occurs; at this point, the first step is to divide the material into sub-elements. Within the enriched element, several sub-regions are divided at both ends of the material interface, represented by the interface level set function. Based on the isoparametric element principle, the Jacob matrix is ​​used to perform isoparametric element transformations between the global and local coordinate systems. Irregular regions formed by the sub-region divisions in the global coordinate system are transformed into regular regions in the local coordinate system, facilitating subsequent calculations. Next, the Hammer numerical integration method is used to calculate the spatial integration results in the local coordinate system. Finally, the Jacob matrix is ​​used to transform the calculation results back to the global coordinate system, thus completing the enriched element transformation. The element stiffness matrix of the set element is calculated; the element stiffness matrix of all elements is calculated and then synthesized into a global stiffness matrix, which is then solved; the global stiffness matrix includes the original vector magnetic potential degrees of freedom at the nodes and the additional potential degrees of freedom at the enriched nodes; the solution for all degrees of freedom is obtained, and the distribution of vector magnetic potential within the enriched element satisfies the previously mentioned discontinuous interpolation function; since the material medium can pass through the medium interface, the number of nodes and elements generated by spatial discretization is less, and the calculation speed is faster, which is especially suitable for electromagnetic field analysis problems of models with diverse material properties or containing dense thin layers.

[0054] Example explanation: In this embodiment 1, taking the calculation of vector magnetic potential under two-dimensional material media distribution as an example, the electromagnetic field numerical calculation method based on prior knowledge of physical fields described in the above embodiment 1 is explained in detail as follows: In this example, the electromagnetic structure to be calculated is a long, straight, uniformly charged conductor in a two-dimensional parallel planar field, i.e., a space with a radius of... A long, straight cylindrical conductor, such as the attached Figure 3 As shown; where the permeability of the long straight cylindrical conductor is the same as the permeability of free space. A long, straight cylindrical conductor carrying a uniform current density The goal of this example is to solve for the magnetic vector potential distribution inside and outside a long straight cylindrical conductor.

[0055] There exists a standard analytical solution to the problem of finding the magnetic vector potential distribution inside and outside a long straight cylindrical conductor. Assume the size of the outer air domain boundary is... In radius Less than Within a certain range, the vector magnetic potential exhibits a quadratic function-like distribution with respect to radius; in Greater than Less than Within this range, the vector magnetic potential distribution exhibits logarithmic function characteristics; at this time, the actual analytical solution function expression is as follows:

[0056] in, For the interior of a cylindrical conductor ( The vector magnetic potential distribution function of the region; The vacuum permeability; Uniform current density; Let be the radius of the long, straight cylindrical conductor; The size of the outer air domain boundary; This is the radial distance from the field point to the axis of the cylinder; For the interior of a cylindrical conductor ( The vector magnetic potential distribution function of the region.

[0057] Spatial discretization was performed using both the conventional multi-scale finite element method and the method in Example 1, resulting in spatial discretization models suitable for the conventional finite element method and spatial discretization meshes suitable for the method described in Example 1, i.e., mesh generation results for multi-scale finite element method that ignore material differences, as shown in the appendix. Figure 4 As shown; from the appendix Figure 4 It can be clearly seen that the number of mesh nodes and the number of mesh nodes used in the multi-scale finite element method are reduced.

[0058] Based on the location of the medium interface, a level set function for the interface is fitted and generated. This level set function is then used to divide the entire solution domain of the long, straight cylindrical conductor into two regions, as shown in the attached diagram. Figure 5 As shown; in the appendix Figure 5In the diagram, the negative values ​​of the level set represent the conductor material region, and the positive values ​​represent the air region outside the conductor. The red dashed line represents the location of the zero level set line, i.e., the interface between the two materials. By calculating the level set function values ​​at each element node, all elements are classified into enriched elements and ordinary elements, as shown in the appendix. Figure 6 As shown; in the appendix Figure 6 In the diagram, red cells represent enriched cells, green cells represent ordinary cells, and red dashed lines indicate the positions of the zero-level set isopotential lines, i.e., the media interface positions.

[0059] In this example, the discontinuous potential interpolation function is the discontinuous vector magnetic potential interpolation function in the two-dimensional case, as follows:

[0060]

[0061]

[0062] in, This is an approximate solution expression for the vector magnetic potential distribution in a two-dimensional plane. For the standard finite element shape function on the finite element node; The vector magnetic potential degrees of freedom at conventional nodes; For the finite element shape function on the enriched nodes; An enhanced enrichment function that incorporates prior physical knowledge; For enriched nodes in enriched cells Additional degrees of freedom; This is the enrichment function in the ordinary multi-scale finite element method; As a correction factor; For use in building The shape function can usually be selected from the standard shape function of the finite element method; For nodes i The level set function value at that location; , These are the spatial coordinates in a two-dimensional plane.

[0063] By solving the analytical solution of the actual analytical solution function, it can be seen that in the region where the horizontal set function of the interface is less than 0, i.e., in the conductor region, the vector magnetic potential distribution satisfies the following: .

[0064] Therefore, when the level set function of the interface is less than 0, the correction factor Select as About x , y The quadratic function form is used as the correction function, for example:

[0065] in, and All of these are undetermined coefficients, which will be determined based on information such as the location of the interface.

[0066] Similarly, in the region where the level set function of the interface is greater than 0, i.e., in the air domain, the vector magnetic potential distribution satisfies the following: .

[0067] Therefore, when the level set function of the interface is greater than 0, the correction factor... Select as About x , y The logarithmic form of the function is used as a correction function, for example:

[0068] in, These are coefficients to be determined.

[0069] Based on the element type of each mesh element, the element stiffness matrix is ​​calculated in both the spatial discretization model applicable to ordinary finite element methods and the spatial discretization mesh results applicable to the method described in Example 1. For ordinary elements, the element stiffness matrix is ​​calculated directly using the same method as in traditional finite element methods. For enriched elements, element sub-division is first performed. Within the enriched element, several sub-regions are divided at both ends of the material interface represented by the level set function. The sub-division result of a certain enriched element is shown in the attached figure. Figure 7 As shown, each sub-element contains only one type of material after partitioning, which facilitates subsequent integration calculations. Based on the isoparametric element principle, the Jacob matrix is ​​used to transform the isoparametric elements in the global coordinate system and the local coordinate system, which facilitates subsequent calculations. The Hammer spatial integration method is used to calculate the spatial integration results in the local coordinate system, and the calculation results are transformed to the global coordinate system using the Jacob matrix to complete the calculation of the element stiffness matrix of the enriched element.

[0070] The element stiffness matrix of all elements is calculated and synthesized to obtain the overall stiffness matrix. Based on the overall stiffness matrix, a multi-scale finite element discrete equation is constructed. The multi-scale finite element discrete equation is solved to obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

[0071] Example results are explained below: Due to the symmetry in solving the problem of magnetic vector potential distribution inside and outside a long straight cylindrical conductor, the vector magnetic potential can be extracted. x The trends of change along the axis are compared to verify the accuracy of different calculation methods; as shown in the appendix. Figure 8As shown in Figure a, the curves calculated based on the analytical solution (denoted as AS), the results calculated using the ordinary multi-scale finite element method (denoted as MSFEM), and the results calculated using the method described in Example 1 (denoted as the novel MSFEM) are plotted and compared. A local magnification of the overall vector magnetic potential distribution curve is shown in the attached figure. Figure 8 As shown in b, 8c, and 8d; from the appendix Figure 8 As can be seen from a-8d, the calculation results using the method described in Example 1, i.e., the novel multi-scale finite element method utilizing the enhanced enrichment function, are significantly better than those using the ordinary multi-scale finite element method, i.e., the multi-scale finite element method without the enhanced enrichment function, and are closer to the analytical solution results. Meanwhile, the error between the example problem before and after the enrichment function improvement and the analytical solution is shown in the attached figure. Figure 9 The error comparison chart shown below; among them, the attached... Figure 9 Figure a shows a comparison of the absolute errors between the vector magnetic potential calculation results and the analytical solution before and after the improvement of the enrichment function. Figure 9 b is a comparison of the relative errors between the vector magnetic potential calculation results and the analytical solution before and after the enrichment function improvement; from the appendix Figure 9 In a and 9b, we can quantitatively see the effect of the improved enrichment function on improving computational accuracy.

[0072] The electromagnetic field numerical calculation method based on prior knowledge of physical fields described in Embodiment 1 employs a large-scale meshing strategy that does not rely on the geometric features of material interfaces during the spatial discretization process of the finite element problem in electromagnetic field numerical calculation. This allows a single computational unit to contain multiple different material media, thereby reducing dependence on fine geometric structures and lowering mesh generation complexity. During spatial identification, a level set function is introduced to accurately locate the interfaces between different material media. Based on the relative relationship between the medium interface and the mesh unit, the computational units are classified into enriched units, ordinary units, and hybrid units. Enriched units are mesh units that directly cross the medium interface, where material properties are discontinuously distributed. Ordinary units are mesh units located entirely within a single medium region, where material properties are uniformly continuous. Hybrid units are mesh units that, although not directly in contact with the interface, are adjacent to enriched units.

[0073] In this embodiment 1, considering the presence of multiple materials and discontinuous distribution of material properties within the enriched unit, an enhanced enrichment function integrating prior knowledge of the physical field is constructed. By introducing prior knowledge of local physical information, the traditional local numerical solution is corrected and optimized, thereby compensating for the field distribution characterization deviation caused by material discontinuities and improving the adaptability and accuracy of the enrichment function to complex multi-scale electromagnetic structures. Secondly, isoparametric element transformation technology is used to handle complex geometries. Within the enriched unit, the unit is divided into regions with different material properties based on the medium interface, and irregularly shaped regions with different material properties are further divided into multiple sub-unit shapes according to certain rules. Specifically, in the two-dimensional problem, the sub-unit shape is a triangular region, and in the three-dimensional problem, the sub-unit shape is a tetrahedral region. The Hammer numerical integration method is used to calculate... The element stiffness matrix within the enriched element is used to establish a multi-scale finite element computation framework for electromagnetic fields based on prior knowledge of physical fields. An enhanced enrichment function incorporating prior knowledge of physical fields is used to construct approximate solutions for multi-scale finite elements, thereby enabling the assembly and solution of multi-scale finite element equations globally. This achieves a high-precision, fast numerical algorithm for electromagnetic field computation, particularly suitable for electromagnetic field numerical computation in scenarios such as periodic media or finely geometric thin layers. Furthermore, by employing element subdivision techniques, isoparametric element transformation techniques, and higher-order Hammer numerical integration techniques, the integral results of the integrand within the enriched element, composed of various functional forms including shape functions, enhanced enrichment functions, partial derivatives of shape functions, and partial derivatives of enhanced enrichment functions, are accurately calculated. This allows for accurate calculation of numerical integration results within materials with different properties under complex geometric boundaries.

[0074] Example 2 As attached Figure 10 As shown, this embodiment 2 provides an electromagnetic field numerical calculation system based on prior knowledge of physical fields, including a grid discretization module, a cell partitioning module, a function generation module, a matrix calculation module, an equation construction module, and an equation solving module.

[0075] The system comprises the following modules: a mesh discretization module, a spatial discrete meshing module, and an equation construction module. The former uses a meshing strategy independent of the geometric features of the medium interface to discretize the geometric model of the electromagnetic structure to be computed, resulting in a spatial discrete mesh. The spatial discrete mesh includes several mesh elements and their node information. The latter uses an element partitioning module to classify the mesh elements based on a pre-generated interface level set function and the spatial discrete mesh, determining the element type of each element. Element types include enriched elements, hybrid elements, and ordinary elements. The former uses a function generation module to generate a discontinuous potential function interpolation function based on a pre-constructed enhanced enrichment function that incorporates prior knowledge of the physical field. The latter uses a matrix calculation module to calculate the element stiffness matrix of each mesh element based on its element type and the discontinuous potential function interpolation function. The former combines the element stiffness matrices of each mesh element to obtain the overall stiffness matrix. Based on the overall stiffness matrix, a multi-scale finite element discrete equation is constructed. The latter solves the multi-scale finite element discrete equation to obtain the numerical computation results of the electromagnetic field of the electromagnetic structure.

[0076] Example 3 As attached Figure 11 As shown, this embodiment 3 provides an electronic device, including: a memory for storing a computer program; a processor for executing the computer program to implement the steps of a numerical calculation method for electromagnetic fields based on prior knowledge of physical fields; or, the processor executing the computer program to implement the functions of each module in the above-mentioned numerical calculation system for electromagnetic fields based on prior knowledge of physical fields.

[0077] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the electronic device.

[0078] The electronic device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of electronic devices and do not constitute a limitation on the electronic device. It may include more components than described above, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0079] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor, or any conventional processor, etc. The processor is the control center of the electronic device, connecting various parts of the entire electronic device through various interfaces and lines.

[0080] The memory can be used to store the computer program and / or module, and the processor implements various functions of the electronic device by running or executing the computer program and / or module stored in the memory, and by calling the data stored in the memory.

[0081] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart memory cards, secure digital cards, flash memory cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0082] Example 4 This embodiment 4 also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the electromagnetic field numerical calculation method based on prior knowledge of physical fields.

[0083] If the modules / units integrated in the electromagnetic field numerical calculation system based on prior knowledge of physical fields are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0084] Based on this understanding, the present invention can implement all or part of the processes in the above-mentioned electromagnetic field numerical calculation method based on prior knowledge of physical fields. This can also be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of the above-mentioned electromagnetic field numerical calculation method based on prior knowledge of physical fields. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0085] The computer-readable storage medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0086] Example 5 This embodiment 5 provides a computer product, which includes a computer program stored in a computer-readable storage medium. The processor of the electronic device reads the computer program from the computer-readable storage medium and executes the computer program, so that the electronic device can execute the electromagnetic field numerical calculation method based on prior knowledge of physical fields as described in embodiment 1, which will not be repeated here.

[0087] It should be noted that those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above methods.

[0088] The electromagnetic field numerical calculation method based on prior knowledge of physical fields described in this invention overcomes the shortcomings of existing multi-scale finite element methods in handling multi-medium electromagnetic field problems, which suffer from insufficient accuracy in enrichment function calculations. By improving the enrichment function based on prior knowledge of physical fields during multi-scale finite element electromagnetic field calculations, an enhanced enrichment function incorporating prior knowledge of physical fields is obtained to more accurately characterize the changing characteristics at the medium interface. During spatial discretization, a large-scale meshing strategy independent of the geometric features of the material interface is employed, and the enhanced enrichment function incorporating prior knowledge of physical fields is introduced to capture local physical field changes at the interface. Based on the interface level set function... The spatial relationship between numerical feature identification units and medium interfaces is determined, and mesh units are divided into three categories: enriched units that directly pass through the medium interface, ordinary units located entirely within a single medium region, and hybrid units that are adjacent to enriched units but do not directly contact the interface. To address the discontinuous distribution of material parameters within enriched units, an enhanced enrichment function integrating prior physical field knowledge is constructed to describe the variation characteristics of potential functions at the interface. Isoparametric element transformation techniques are used to handle complex geometries, and the Hammer numerical integration method is combined to calculate the element stiffness matrix containing the enhanced enrichment function. Finally, a novel multi-scale finite element calculation framework for electromagnetic fields based on prior physical field knowledge is established.

[0089] This invention achieves high-precision fitting of the electromagnetic field variation law at the medium interface on a large-scale grid by incorporating the physical constraints at the interface into the enrichment function construction process, thus realizing a novel multi-scale finite element method for high-precision analysis on a large-scale grid. Specifically, by deeply embedding prior knowledge of the physical field into the enrichment function construction process, the numerical solution strictly satisfies the physical laws at the interface in structure, significantly improving the calculation accuracy of the potential function distribution and field distribution near the interface, fundamentally enhancing the physical fidelity of the interface calculation. Furthermore, because the enhanced enrichment function incorporating prior knowledge of the physical field contains a precise mathematical description of the physical field at the interface, the multi-scale finite element solution can approximate the true solution faster, achieving higher calculation accuracy at the same grid density, effectively improving the convergence performance of the method. Secondly, due to the integration of prior knowledge... The enhanced enrichment function, which incorporates prior knowledge of the physical field, contains an accurate mathematical description of the physical field at the interface. This allows the multi-scale finite element solution to approximate the true solution more quickly and achieve higher computational accuracy at the same mesh density, effectively improving the convergence performance of the method. Furthermore, the coarse meshing strategy, decoupled from the material interface, avoids the complex and time-consuming interface mesh generation process in traditional finite element methods, greatly simplifying the preprocessing workflow and maintaining the mesh generation flexibility advantage of multi-scale finite element methods. The method described in this invention is universal and can be applied to different types of electromagnetic field problems, such as eddy current fields and electromagnetic wave propagation, by adapting to different interface physical constraints. It has good versatility and scalability and is suitable for accurate simulation analysis in engineering fields such as electrical equipment, integrated circuits, and electromagnetic compatibility, which contain complex internal media interfaces.

[0090] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

Claims

1. A numerical calculation method for electromagnetic fields based on prior knowledge of physical fields, characterized in that, include: Based on a meshing strategy that does not depend on the geometric features of the medium interface, the geometric computational model of the electromagnetic structure to be computed is meshed to obtain spatial discrete mesh results; wherein, the spatial discrete mesh results include several mesh cells and the cell node information of each mesh cell; Based on the pre-generated interface level set function and spatial discrete mesh results, several mesh elements are classified into types to determine the element type of each mesh element; among them, the element types of mesh elements include enriched elements, mixed elements and ordinary elements; Based on a pre-constructed enhanced enrichment function that integrates prior knowledge of physical fields, a discontinuous potential function interpolation function is generated. Based on the element type of each grid element and combined with the discontinuous potential function interpolation function, the element stiffness matrix of each grid element is calculated. The element stiffness matrices of each mesh element are combined to obtain the overall stiffness matrix; based on the overall stiffness matrix, multi-scale finite element discrete equations are constructed. The multi-scale finite element discrete equations are solved to obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

2. The numerical calculation method for electromagnetic fields based on prior knowledge of physical fields according to claim 1, characterized in that, The pre-constructed enhanced enrichment function that integrates prior knowledge of physical fields is a second type of enrichment function that embeds prior knowledge of physical fields; wherein, the prior knowledge of physical fields includes boundary continuity conditions, field quantity conservation relations or dielectric / magnetic properties constraints of the medium.

3. The numerical calculation method for electromagnetic fields based on prior knowledge of physical fields according to claim 1, characterized in that, The discontinuous bit interpolation function is as follows: in, It is a discontinuous bit interpolation function; and These are all shape functions in the ordinary multi-scale finite element method; This represents the node potential; For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; For enriched nodes in enriched cells Additional degrees of freedom.

4. The numerical calculation method for electromagnetic fields based on prior knowledge of physical fields according to claim 1, characterized in that, The construction process of the pre-built enhanced enrichment function that integrates prior knowledge of physical fields is as follows: Based on the physical field continuity condition at the medium interface, a constraint relationship between material parameters and field distribution is established. By introducing a correction factor to optimize the function, a pre-constructed enhanced enrichment function integrating prior physical field knowledge is obtained. The pre-constructed enhanced enrichment function integrating prior physical field knowledge is as follows: in, For pre-constructed enhanced enrichment functions that integrate prior knowledge of physical fields; This is the enrichment function in the ordinary multi-scale finite element method; As a correction factor; For Herveside step function; For the pre-generated interface level set function The physical field correction function of the region; For the pre-generated interface level set function The physical field correction function of the region; For the pre-generated interface level set function; For nodes under the ordinary multi-scale finite element method Shape function at the location; For nodes The level set function value at that location; The set of enriched nodes in all enriched units; This is the set of nodes in all enriched units.

5. The numerical calculation method for electromagnetic fields based on prior knowledge of physical fields according to claim 1, characterized in that, The process of calculating the element stiffness matrix of each mesh element based on its element type and using a discontinuous potential function interpolation function is as follows: Determine whether the cell type of the mesh element is an enriched cell; If the element type of the mesh is enriched element, the enriched element is divided into different material property regions according to the medium interface, and each material property region is divided into several sub-elements of a preset shape based on the isoparametric element principle. The element stiffness matrix of the enriched element is calculated based on the Hammer spatial integration method and the discontinuous potential function interpolation function.

6. The numerical calculation method for electromagnetic fields based on prior knowledge of physical fields according to claim 5, characterized in that, If the element type of the mesh element is a normal element, the element stiffness matrix of the normal element can be calculated by using the ordinary finite element method and combining the discontinuous potential function interpolation function.

7. A numerical calculation system for electromagnetic fields based on prior knowledge of physical fields, characterized in that, include: The mesh discretization module is used to perform mesh partitioning on the geometric computational model of the electromagnetic structure to be computed based on a mesh partitioning strategy that does not depend on the geometric features of the medium interface, and obtain spatially discrete mesh results. The spatially discrete mesh results include several mesh cells and the cell node information of each mesh cell. The cell partitioning module is used to classify several grid cells based on the pre-generated interface level set function and spatial discrete grid results, and to determine the cell type of each grid cell; the cell types of the grid cells include enriched cells, mixed cells and ordinary cells; The function generation module is used to generate discontinuous potential function interpolation functions based on pre-built enhanced enrichment functions that incorporate prior knowledge of physical fields. The matrix calculation module is used to calculate the element stiffness matrix of each grid element based on its element type and in conjunction with the discontinuous potential function interpolation function. The equation construction module is used to combine the element stiffness matrices of each mesh element to obtain the overall stiffness matrix; based on the overall stiffness matrix, multi-scale finite element discrete equations are constructed. The equation solving module is used to solve the multi-scale finite element discrete equations and obtain the numerical calculation results of the electromagnetic field of the electromagnetic structure to be calculated.

8. An electronic device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the electromagnetic field numerical calculation method based on prior knowledge of physical fields as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the electromagnetic field numerical calculation method based on prior knowledge of physical fields as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the electromagnetic field numerical calculation method based on prior knowledge of physical fields as described in any one of claims 1-6.

Images