Adaptive grid division method for modeled polyhedron and related equipment

Abstract

The invention provides a self-adaptive grid division method for a modeled polyhedron and related equipment. The method comprises the following steps of: performing the following grid division operation on each round: dividing the polyhedron; determining a primary function coefficient conversion matrix corresponding to the target sub-polyhedron; determining an error of an electric field function corresponding to the target sub-polyhedron for solving the electromagnetic problem; in response to determining that the error of the electric field function determined by at least one grid division operation of the current round is greater than or equal to a preset convergence error, taking a target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the preset convergence error as a polyhedron in the next grid division operation, and executing the next grid division operation; and in response to determining that the errors of all the electric field functions determined by the grid division operation of the current round are smaller than the preset convergence error, exiting at least one round of grid division operation, thereby solving the technical problem that the grid division of the polyhedron is not accurate in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, and in particular to a modeling multi-faceted adaptive meshing method and related equipment. BACKGROUND

[0002] The electromagnetic simulation of the multi-faceted is based on the electromagnetic field theory to construct a model, simulates the propagation, radiation, scattering and other phenomena of electromagnetic waves in a specific environment (such as circuits, antennas, microwave devices, etc.) through numerical calculation method, predicts electromagnetic performance, and provides basis for design optimization and shortens the development cycle. With the development of modern electromagnetic equipment towards high frequency, integration and multi-function, electromagnetic simulation is facing the severe challenges of multi-scale, wide frequency band and complex medium coupling. When dealing with electromagnetic problems, the traditional finite element method usually adopts a fixed meshing strategy. This single resolution discretization method is not accurate for meshing the multi-faceted, and it is difficult to balance the local field strength mutation and the global field distribution characteristics. Inaccurate multi-faceted partitioning will increase the deviation between the modeled model and the actual structure, resulting in distortion of the electromagnetic field distribution calculation results. SUMMARY

[0003] Therefore, the purpose of the present application is to provide a modeling multi-faceted adaptive meshing method and related equipment to overcome all or part of the deficiencies in the prior art.

[0004] To achieve the above purpose, the present application provides a modeling multi-faceted adaptive meshing method, which comprises: performing at least one round of meshing operation on the multi-faceted, each round of meshing operation being performed as follows: dividing the multi-faceted to obtain a plurality of initial sub-multi-facets corresponding to the multi-faceted and a plurality of target sub-multi-facets corresponding to each initial sub-multi-faceted; for each target sub-multi-faceted, determining a basis function coefficient conversion matrix corresponding to the target sub-multi-faceted based on the target sub-multi-faceted, the initial sub-multi-faceted corresponding to the target sub-multi-faceted and a predetermined requirement; determining the error of the electric field function for solving electromagnetic problems corresponding to the target sub-multi-faceted based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-multi-faceted corresponding to the target sub-multi-faceted which is constructed in advance; in response to determining that there is at least one electric field function error determined by the meshing operation of the current round of meshing operation is greater than or equal to the predetermined convergence error, the target sub-multi-faceted corresponding to the electric field function error greater than or equal to the predetermined convergence error is taken as the multi-faceted in the next round of meshing operation, and the next round of meshing operation is performed; in response to determining that all electric field function errors determined by the meshing operation of the current round of meshing operation are less than the predetermined convergence error, the at least one round of meshing operation is exited.

[0005] Optionally, the dividing the polyhedron to obtain a plurality of initial sub-polyhedrons corresponding to the polyhedron and a plurality of target sub-polyhedrons corresponding to each initial sub-polyhedron comprises: performing coarse division on the polyhedron to obtain a plurality of initial sub-polyhedrons corresponding to the polyhedron; and performing fine division on each initial sub-polyhedron to obtain a plurality of target sub-polyhedrons corresponding to the initial sub-polyhedron, wherein a division precision of the coarse division is less than a division precision of the fine division.

[0006] Optionally, the determining the basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, an initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement comprises: determining a function order corresponding to the target sub-polyhedron according to the predetermined requirement; constructing a basis function corresponding to the target sub-polyhedron and a basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron based on the function order; and determining the basis function coefficient conversion matrix based on the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron.

[0007] Optionally, the basis function corresponding to the target sub-polyhedron comprises a first first-order basis function and a first second-order basis function, and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron comprises a second first-order basis function and a second second-order basis function; and the constructing the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron based on the function order comprises: in response to determining that the function order is first order, constructing the first first-order basis function corresponding to the target sub-polyhedron and the second first-order basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron; and in response to determining that the function order is second order, constructing the first second-order basis function corresponding to the target sub-polyhedron and the second second-order basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron.

[0008] Optionally, the determining the error of the electric field function for solving an electromagnetic problem corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and an initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance comprises: determining a conversion matrix corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance; and determining the error of the electric field function corresponding to the target sub-polyhedron based on the conversion matrix.

[0009] Optionally, the determining the conversion matrix corresponding to the target sub-polyhedron based on the base function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron comprises: obtaining a total number of times that the target sub-polyhedron has completed the mesh division operation; performing at least one round of subdivision operation on the base function coefficient conversion matrix based on the total number of times, each round of subdivision operation performing the following: in response to a round number corresponding to a current round of subdivision operation being less than or equal to the total number of times, converting the base function coefficient conversion matrix to obtain a target base function coefficient conversion matrix, taking the target base function coefficient conversion matrix as a base function coefficient conversion matrix in a next round of subdivision operation, and performing the next round of subdivision operation; in response to the round number corresponding to the current round of subdivision operation being greater than the total number of times, exiting the at least one round of subdivision operation; and calculating the conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix.

[0010] Optionally, the initial matrix comprises a first initial matrix and a second initial matrix, and the conversion matrix comprises a first conversion matrix and a second conversion matrix; and the calculating the conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix comprises: calculating the first conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the first initial matrix; and calculating the second conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the second initial matrix.

[0011] Based on the same inventive concept, the application further provides a device for adaptive meshing of a modeled polyhedron, comprising: performing at least one round of meshing operation on the polyhedron, each round of meshing operation being performed as follows: a division module configured to divide the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron; a first determination module configured to determine, for each target sub-polyhedron, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, an initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement; a second determination module configured to determine an error of an electric field function for solving an electromagnetic problem corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and an initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance; and a third determination module configured to, in response to determining that there is at least one error of the electric field function determined by the meshing operation of the current round being greater than or equal to a predetermined convergence error, take the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error as the polyhedron in the next round of meshing operation and perform the next round of meshing operation; and the third determination module is further configured to, in response to determining that all errors of the electric field function determined by the meshing operation of the current round are less than the predetermined convergence error, exit the at least one round of meshing operation.

[0012] Based on the same inventive concept, the application further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor implements the method described above when executing the computer program.

[0013] Based on the same inventive concept, the application further provides a non-transitory computer-readable storage medium storing computer instructions for causing a computer to execute the method described above.

[0014] It can be seen from the above that the adaptive mesh generation method for the modeled polyhedron and the related device provided by the application comprises: performing at least one round of mesh generation operation on the polyhedron, and each round of mesh generation operation is performed as follows: the polyhedron is divided to obtain a plurality of initial child polyhedrons corresponding to the polyhedron and a plurality of target child polyhedrons corresponding to each initial child polyhedron, thereby improving the division efficiency of the polyhedron. For each target child polyhedron, a basis function coefficient conversion matrix corresponding to the target child polyhedron is determined based on the target child polyhedron, the initial child polyhedron corresponding to the target child polyhedron, and a predetermined requirement, so as to accurately determine the conversion relationship between the target child polyhedron and the initial child polyhedron corresponding to the target child polyhedron. The error of an electric field function for solving an electromagnetic problem corresponding to the target child polyhedron is determined based on the basis function coefficient conversion matrix and an initial matrix of the initial child polyhedron corresponding to the target child polyhedron, which is constructed in advance, thereby avoiding large-scale calculation directly on a fine mesh or a complex basis function, and improving the determination efficiency and accuracy of the error of the electric field function corresponding to the target child polyhedron. In response to determining that the error of the electric field function determined by at least one current round of mesh generation operation is greater than or equal to a predetermined convergence error, the target child polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error is taken as the polyhedron in the next round of mesh generation operation, and the next round of mesh generation operation is performed, so as to ensure the accuracy of the mesh generation of the polyhedron. In response to determining that all the errors of the electric field functions determined by the current round of mesh generation operation are less than the predetermined convergence error, the at least one round of mesh generation operation is exited, and the mesh generation of the polyhedron is accurate. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the application or related art, the following will briefly introduce the drawings needed to be used in the embodiments or related art description. Obviously, the drawings in the following description are only embodiments of the application, and other drawings can be obtained by those skilled in the art without creative effort.

[0016] Figure 1 The flowchart of the adaptive mesh generation method for the modeled polyhedron in the embodiment of the application;

[0017] Figure 2 The schematic diagram of the coarse division of the polyhedron in the embodiment of the application;

[0018] FIG. 3(a) is a composition schematic diagram of all sub-first-order basis functions corresponding to the initial child polyhedron in the embodiment of the application;

[0019] FIG. 3(b) is a composition schematic diagram of all sub-first-order basis functions corresponding to the target child polyhedron in the embodiment of the application;

[0020] Fig. 4(a) is a schematic diagram of the composition of all sub-quadratic basis functions corresponding to the initial sub-polyhedron of the embodiment of the present application;

[0021] Fig. 4(b) is a schematic diagram of the composition of all sub-quadratic basis functions corresponding to the target sub-polyhedron of the embodiment of the present application;

[0022] Figure 5 Fig. 5 is a schematic diagram of the model of the polyhedron 1 after meshing of the embodiment of the present application;

[0023] Figure 6 Fig. 6 is a schematic diagram of the mesh distribution of the polyhedron 1 at the non-conformal mesh interface between the regions of the embodiment of the present application;

[0024] Figure 7 Fig. 7 is a schematic diagram of the relative error of the tangential electric field at the regions of the polyhedron of the embodiment of the present application;

[0025] Figure 8 Fig. 8 is a schematic diagram of the model of the polyhedron 2 of the embodiment of the present application;

[0026] Figure 9 Fig. 9 is a schematic diagram of the convergence results of the method provided by the embodiment of the present application and the HFSS algorithm.

[0027] Figure 10 Fig. 10 is a schematic diagram of the structure of the adaptive meshing device of the modeled polyhedron of the embodiment of the present application;

[0028] Figure 11 Fig. 11 is a schematic diagram of the hardware structure of the electronic device of the embodiment of the present application. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the specific embodiments and the accompanying drawings.

[0030] It should be noted that, unless otherwise defined, technical terms or scientific terms used in the embodiments of the present application shall be understood as having the common meaning to those skilled in the art to which the embodiments of the present application belong. The terms "first", "second", and similar terms used in the embodiments of the present application do not denote any order, quantity, or importance, but are only used to distinguish different components. The terms "include", "contain", and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "upper", "lower", "left", "right", and the like are only used to represent relative positional relationships, and when the absolute positions of the described objects change, the relative positional relationships can also change accordingly.

[0031] As described in the background section, the electromagnetic simulation of the polyhedron is based on the electromagnetic field theory to build a model, simulate the propagation, radiation, scattering, and other phenomena of electromagnetic waves in a specific environment (such as circuits, antennas, microwave devices, etc.) through numerical calculation methods, and the modeled polyhedron can flexibly approximate the real structure, accurately describe the geometric characteristics of the object, facilitate subsequent grid division to calculate the electromagnetic field and predict electromagnetic performance, provide a basis for design optimization, and shorten the development cycle. With the development of modern electromagnetic equipment towards high frequency, integration and multi-function, electromagnetic field numerical simulation faces severe challenges of multi-scale, wide frequency band and complex medium coupling. When dealing with electromagnetic problems, the traditional finite element method usually adopts a fixed grid division strategy. The polyhedron has complex and diverse geometric shapes, and the fixed grid division strategy is difficult to fit the irregular boundaries and curved surfaces, and is prone to generate distorted elements at sharp features, affecting the calculation accuracy and stability. In addition, the fixed grid division strategy is not effective in dealing with complex boundary conditions, and it is difficult to accurately simulate electromagnetic phenomena on the boundary of the polyhedron, resulting in a large deviation between the final calculation results and the actual situation. For example, in the electromagnetic simulation of an antenna, if the grid division of the antenna is not accurate, the calculation error of key performance parameters such as the antenna's radiation pattern and gain is large, and the antenna performance cannot be accurately evaluated. The above single resolution discretization method is not accurate for grid division of the polyhedron, and it is difficult to balance the local field strength mutation and global field distribution characteristics of the electromagnetic field.

[0032] In addition, when a non-conformal region involving multi-physical field coupling or composite medium structure is involved, the existing adaptive mesh technology is not accurate in meshing polyhedrons, which will cause the following problems: first, the mesh optimization strategy based on global error estimation cannot effectively handle the field strength discontinuity characteristics at the interface of different materials, resulting in a decrease in interface field calculation accuracy; second, the traditional h-type adaptive method needs to repeatedly reconstruct the mesh in wideband scanning, significantly increasing the calculation redundancy; third, the existing non-structured mesh generation algorithm is difficult to ensure the coordination of adjacent region meshes when processing non-conformal subdomains, which is easy to cause numerical instability. Although the p-type adaptive method developed in recent years has improved the local calculation accuracy, it still faces the problem of high-order basis function selection and frequency variation characteristics matching when dealing with anisotropic media or multi-scale problems.

[0033] Therefore, the embodiment of the present application proposes a modeling polyhedron adaptive meshing method, which refers to Figure 1 , comprising the following steps:

[0034] Step 101, for the polyhedron, at least one round of meshing operation is performed, and each round of meshing operation is executed as follows: the polyhedron is divided to obtain a plurality of initial sub-polyhedrons corresponding to the polyhedron and a plurality of target sub-polyhedrons corresponding to each initial sub-polyhedron.

[0035] In this step, in electromagnetic simulation, for some electromagnetic structures with complex geometric shapes, the modeling polyhedron can more accurately represent the physical structure. For example, in the electromagnetic simulation design of a permanent magnet, if the shape of the permanent magnet is complex, using a polyhedron for geometric modeling can more accurately simulate its shape and size, and thus more accurately analyze key physical quantities such as magnetic field distribution and magnetic field strength. As a geometric model, the electromagnetic field inside and on the boundary of the polyhedron is also continuously distributed. By meshing the polyhedron, it is divided into many small, discrete units (such as tetrahedrons, hexahedrons, etc.), which can convert the continuous electromagnetic field problem into a numerical calculation problem on these discrete units. Therefore, in electromagnetic simulation, meshing the polyhedron is particularly important.

[0036] The polyhedron is a three-dimensional figure surrounded by multiple planar polygons, for example, the polyhedron is a tetrahedron. Since the meshing of the polyhedron is only performed once, the meshing may not be accurate, which may result in low calculation accuracy of electromagnetic simulation using the meshed polyhedron. Therefore, at least one round of meshing operation is performed on the polyhedron to ensure the accuracy of the meshing of the polyhedron. Each round of meshing operation is performed as follows: the polyhedron is divided to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron. Performing meshing on the polyhedron only once will result in low meshing efficiency, therefore, the meshing includes two meshing processes, i.e. first meshing and second meshing. The first meshing of the polyhedron can obtain a plurality of initial sub-polyhedra, and the second meshing of each initial sub-polyhedron can obtain a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron. Since the parallel second meshing is performed on the initial sub-polyhedra, the meshing efficiency of the polyhedron is improved.

[0037] In step 102, for each target sub-polyhedron, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron is determined based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and the predetermined requirement.

[0038] In this step, it is determined whether the target sub-polyhedron obtained after meshing can meet the electromagnetic simulation requirement. First, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron is determined based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and the predetermined requirement. The determination method of the basis function coefficient conversion matrix includes multiple methods, and one method is determined according to the predetermined requirement. Since the target sub-polyhedron is obtained by performing second meshing on the initial sub-polyhedron, the volume of the target sub-polyhedron is smaller than that of the initial sub-polyhedron. In subsequent calculation, the calculation data of the target sub-polyhedron can be determined by using the initial sub-polyhedron corresponding to the target sub-polyhedron, therefore, it is necessary to determine the basis function coefficient conversion matrix between the target sub-polyhedron and the initial sub-polyhedron. By determining the basis function coefficient conversion matrix, the conversion relationship between the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron is accurately determined.

[0039] In step 103, an error of an electric field function for solving an electromagnetic problem corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and an initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron which is constructed in advance.

[0040] In this step, unlike traditional a posteriori error estimation algorithms, the present application is a target-oriented error estimation, which needs to determine the error of the target parameter. Generally, the target parameter can be various parameters in electromagnetic simulation, such as the S parameter of the port or the gain of the antenna in a certain direction, the RCS of the far field, etc. Obviously, these parameters can be expressed according to the electric field, that is, they are all electric field functions. The error of the electric field function solved for the electromagnetic problem can reflect whether the division of the target sub-polyhedron is reasonable. A reasonable grid should make the error converge uniformly with encryption. If the division is unreasonable (such as grid distortion, insufficient density or topology error), the error distribution of the electric field function is uneven or stagnant, indicating that the current division cannot effectively improve the solution accuracy, and the grid strategy needs to be adjusted. Among them, the electromagnetic problem is a problem of solving the electric field distribution for the divided polyhedron. The error of the electric field function can reveal the approximation ability of the division to complex electromagnetic physical mechanisms, so even if the electromagnetic problem is relatively complex, the quantitative and qualitative characteristics of the error of the electric field function can still reflect the advantages and disadvantages of the division. The error of the electric field function can verify the rationality of the polyhedron division. For example, if the division is unreasonable, such as the grid is too sparse, it may lead to inaccurate simulation of the charge distribution on the surface of the sphere, and then the deviation of the current electric field distribution of the metal sphere from the true electric field distribution is significantly increased. This deviation can be reflected by the error of the electric field function. Therefore, the error of the electric field function corresponding to the target sub-polyhedron needs to be determined. Since the volume of the target sub-polyhedron is smaller than the volume of the initial sub-polyhedron, the target sub-polyhedron is relatively fine, and directly determining the error of the electric field function corresponding to the target sub-polyhedron requires relatively large amount of calculation, therefore, the error of the electric field function corresponding to the target sub-polyhedron can be indirectly determined by means of the initial sub-polyhedron and the basis function coefficient conversion matrix. Since the basis function coefficient conversion matrix can determine the accurate relationship between the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron, based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance, the error of the electric field function corresponding to the target sub-polyhedron is determined, which avoids large-scale calculation directly on fine grids or complex basis functions, and improves the determination efficiency and accuracy of the error of the electric field function corresponding to the target sub-polyhedron.

[0041] The error of the electric field function corresponding to the target sub-polyhedron is determined by the following process:

[0042] The discretization error of the finite element occurs on the truncation after the field expansion. Define the error as the difference between the approximate electric field and the theoretical electric field , the error can be quantified as: Formula one.

[0043] The vector wave equation of the electric field is expressed as a numerical linear functional operator equation expression, and the variational equation can be obtained as:

[0044]

[0045] in, It is an electromagnetic excitation source. basis functions In a complete vector function space, the above variational equation can be represented by a transformation matrix, expressed as given by M. e and N e The matrix equation is in the form of the matrix.

[0046] Unlike traditional posterior error estimation algorithms, target-oriented error estimation requires the error of the target parameters. These parameters can be determined based on the electric field. This means that they are all electric fields. The functional of the objective parameters. Constructing the functional expression for the objective parameters is equivalent to constructing the electric field function. At this point, the objective parameters are defined with respect to... The functional expression is:

[0047]

[0048] Where g is The density function. Substituting the error function from Formula 1 into the equation, we obtain the error function for the target parameter as:

[0049]

[0050] To evaluate the impact of the error on the multi-objective parameters of each cell in the grid, it is necessary to utilize the adjoint problem of the original problem to obtain the influence factor of the error of each cell on the objective parameters. Furthermore, because in actual solving the adjoint problem, the adjoint solution... Similarly, it is difficult to obtain; only approximate solutions can be found. Therefore, the adjoint equation is constructed, and the expression for the adjoint problem can be derived from... Accompanying forms * Written as:

[0051]

[0052] in, basis functions A complete vector function space.

[0053] When port excitation is applied in the electromagnetic finite element model, the variational equation can be written as:

[0054]

[0055] Formula Six

[0056] Where B is a bilinear functional operator. ε r μ is the relative permittivity.r is the relative permeability, k0 is the wave number in free space, j is the imaginary unit, and Z0 is the wave impedance in free space, is the outer normal vector of the port surface, is the Hamiltonian operator. is the tangential component of the incident field at the i-th port, is the propagation constant at the i-th port, is the impressed current source excitation. Similarly, the above variational equation can be expressed in the form of a matrix equation by the conversion matrix determined in the present application, represented as M e and N e . The variational equation participates in the calculation of the error of the electric field function. The approximate solution of the S ij parameters calculated by the finite element analysis is denoted as The error of the electric field function is The specific expression is:

[0057]

[0058] According to the error of the electric field function, the adjoint equation is constructed, and the error of the electric field function is solved by using the adjoint equation, so that the right end term of the adjoint equation is determined as:

[0059]

[0060] After the complete adjoint equation with the port S parameter as the target parameter is constructed, the S parameter represents the function of the electric field. The adjoint solution of the adjoint equation is obtained The weighted element residual is obtained after the adjoint solution of the adjoint equation is obtained, the element residual is weighted by using the adjoint weighted residual method, which is used as the index of grid refinement, and the element to be refined is marked according to the weighted element residual, and the specific expression of the weighted element residual is:

[0061]

[0062] Formula nine,

[0063] where N k is the number of volume elements, N f is the number of surface elements, is the electromagnetic excitation source. The volume residual R v and the surface residual R f are respectively represented as:

[0064]

[0065] where K i is the calculation domain of the i-th tetrahedral element in the grid, is the current density, f m ​For the m-th face in the computational domain, the superscripts (1), (2) represent the adjacent elements, denotes the normal vector at the common face pointing from element 1 to element 2, Γ s denotes the PEC boundary condition, Γ c denotes the Cauchy boundary condition.

[0066] The functional expression of the target parameter is constructed, the target parameter is set, and the adjoint equation is constructed. The element residual is weighted by using the adjoint weighted residual method as an index of grid refinement. According to the weighted element residual, the element needing refinement is marked, and the grid optimization is performed.

[0067] In step 104, in response to determining that there is at least one error of the electric field function determined by the grid division operation of the current round greater than or equal to the predetermined convergence error, the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error is taken as a polyhedron in the next round of grid division operation, and the next round of grid division operation is performed.

[0068] In this step, in the case where it is determined that there is at least one error of the electric field function determined by the grid division operation of the current round greater than or equal to the predetermined convergence error, it is indicated that the target sub-polyhedron obtained after division has a division problem, and the division of the polyhedron is not accurate, and the target sub-polyhedron needs to be continuously divided. The predetermined convergence error is determined according to historical experience. Therefore, the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error is taken as a polyhedron in the next round of grid division operation, and the next round of grid division operation is performed, so as to ensure the accuracy of the grid division of the polyhedron.

[0069] In step 105, in response to determining that all errors of the electric field function determined by the grid division operation of the current round are less than the predetermined convergence error, the at least one round of grid division operation is exited.

[0070] In this step, in the case where all errors of the electric field function determined by the grid division operation of the current round are less than the predetermined convergence error, it is indicated that the target sub-polyhedron obtained after division has no division problem, and the grid division of the polyhedron has accuracy. At this time, the grid division operation does not need to be continuously performed, and the at least one round of grid division operation is exited.

[0071] The application can be used for wideband electromagnetic problems, adopt non-conformal grid (grid units do not need to be strictly matched), and can adaptively adjust the grid according to the electromagnetic field change, improve the calculation precision and efficiency, and more accurately simulate electromagnetic phenomena. By improving the treatment of the base function at the interface of the polyhedron and introducing the error estimation oriented to the error of the electric field function, the technical problems of inaccurate adaptive grid division and low division efficiency in the prior art are solved, and the electromagnetic calculation precision is improved. Through the division algorithm and the base function processing, the tangential continuity of the electric field on the non-conformal interface is ensured, the field discontinuity problem of the non-conformal grid in adaptive finite element analysis is effectively solved, the calculation result error is avoided, the local grid division strategy is adopted, the consumption of calculation resources is reduced, the applicability of the method is enhanced, the method is suitable for efficient numerical simulation of complex electromagnetic structures, and has wide application prospect.

[0072] Through the above scheme, at least one round of grid division operation is performed on the polyhedron. Each round of grid division operation is performed as follows: the polyhedron is divided to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron, thereby improving the division efficiency of the polyhedron. For each target sub-polyhedron, based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement, a base function coefficient conversion matrix corresponding to the target sub-polyhedron is determined, and the conversion relationship between the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron is accurately determined. Based on the base function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance, the error of the electric field function for solving the electromagnetic problem corresponding to the target sub-polyhedron is determined, thereby avoiding large-scale calculation directly on a fine grid or a complex base function, improving the determination efficiency and accuracy of the error of the electric field function corresponding to the target sub-polyhedron. In response to determining that the error of the electric field function determined by at least one current round of grid division operation is greater than or equal to a predetermined convergence error, the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error is taken as the polyhedron in the next round of grid division operation, and the next round of grid division operation is performed, thereby ensuring the accuracy of the grid division of the polyhedron. In response to determining that all the errors of the electric field functions determined by the current round of grid division operation are less than the predetermined convergence error, the at least one round of grid division operation is exited, and the grid division of the polyhedron is accurate.

[0073] In some embodiments, the dividing the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron comprises: coarsely dividing the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron; and finely dividing each initial sub-polyhedron to obtain a plurality of target sub-polyhedra corresponding to the initial sub-polyhedron, wherein a division precision of the coarse division is less than a division precision of the fine division.

[0074] In the present embodiment, coarse division of the polyhedron can obtain a plurality of initial sub-polyhedra corresponding to the polyhedron. In the preliminary calculation stage, using large elements can greatly reduce the number of nodes and equations required for calculation, thereby reducing the calculation complexity and accelerating the calculation speed. The large element is a relatively large sub-polyhedron obtained after the polyhedron is divided. The division precision of the coarse division is less than the predetermined division precision. For example, in the case of a tetrahedron, the tetrahedron is coarsely divided to generate a sub-tetrahedron. Figure 2 Figure 2 Fig. 1 is a schematic diagram of coarse division of a polyhedron according to an embodiment of the present application. The midpoint of each edge of a tetrahedral element is taken, and then the midpoints in the same triangular face are connected. This cuts four sub-tetrahedrons similar to the tetrahedron at the tetrahedron vertex, and an octahedron is retained in the interior of the tetrahedron. For the internal octahedron, three division surfaces can be determined, and another four sub-tetrahedrons are formed by cutting according to the three diagonal lines. The node order of the sub-tetrahedral element after the division should be consistent with that of the tetrahedral element, following the counterclockwise principle. Since the division precision of the coarse division is not fine enough, it cannot meet the division requirements of the polyhedron. When the polyhedron structure is complex and local features (such as sharp corners, small protrusions, etc.) exist, the coarse division cannot adjust the grid density according to these local features. Therefore, the initial sub-polyhedron needs to be finely divided to obtain a plurality of target sub-polyhedra corresponding to the initial sub-polyhedron. The division precision of the coarse division is less than the division precision of the fine division, and the division precision of the fine division is greater than or equal to the predetermined division precision. Based on the coarse division, the initial sub-polyhedron is finely divided to achieve the purpose of more accurate division of the polyhedron. In addition, when each initial sub-polyhedron is finely divided, each initial sub-polyhedron is divided in parallel. Compared with only fine division of the polyhedron, the coarse and fine division of the polyhedron according to the present application greatly improves the division efficiency of the polyhedron and the calculation efficiency of the electromagnetic simulation of the polyhedron.

[0075] ​For example, when simulating electromagnetic field distribution of a large polyhedron, if the polyhedron is directly finely divided, there can be millions or even tens of millions of units, resulting in extremely long calculation time. If the polyhedron is first coarsely divided into several thousand units, and the approximate distribution of the field is preliminarily calculated, and then the regions after coarse division are finely divided, the initial calculation amount can be significantly reduced, and the overall calculation time can be shortened.

[0076] In some embodiments, the determining, based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and the predetermined requirement, the basis function coefficient conversion matrix corresponding to the target sub-polyhedron comprises: determining the function order corresponding to the target sub-polyhedron according to the predetermined requirement; constructing the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron based on the function order; and determining the basis function coefficient conversion matrix based on the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron.

[0077] In this embodiment, the basis function is needed to determine the basis function coefficient conversion matrix of the target sub-polyhedron. Since the basis functions are different when the orders of the basis functions are different, the function order corresponding to the target sub-polyhedron is first determined according to the predetermined requirement. After the function order is determined, the basis function corresponding to the target sub-polyhedron is constructed based on the function order, and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron is constructed. The basis function corresponding to the target sub-polyhedron can accurately represent the target sub-polyhedron, and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron can accurately represent the initial sub-polyhedron. Therefore, the conversion relationship between the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron can be accurately determined based on the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron, that is, the basis function coefficient conversion matrix can be accurately determined.

[0078] It should be noted that the predetermined requirement is the same when the same modeled polyhedron is subjected to the mesh division operation.

[0079] In the case of a first-order function, a first-order basis function is constructed, that is, a first-order stacked vector basis function is constructed. At this time, only an edge basis function is included, and the edge basis function corresponding to the initial sub-polyhedron can be linearly represented by the edge basis function corresponding to the target sub-polyhedron. For example, the following relationship is defined:

[0080]

[0081] wherein, respectively represent the i-th sub-primary basis function corresponding to the initial sub-polyhedron, as shown in FIG. 3(a), which is a schematic diagram of the composition of all sub-primary basis functions corresponding to the initial sub-polyhedron according to an embodiment of the present application. All sub-primary basis functions corresponding to the initial sub-polyhedron constitute the primary basis function corresponding to the initial sub-polyhedron. respectively represent the i-th sub-primary basis function corresponding to the target sub-polyhedron, as shown in FIG. 3(b), which is a schematic diagram of the composition of all sub-primary basis functions corresponding to the target sub-polyhedron according to an embodiment of the present application. All sub-primary basis functions corresponding to the target sub-polyhedron constitute the primary basis function corresponding to the target sub-polyhedron. i,j is the element at the position (i, j) of the basis function coefficient conversion matrix C. The role of C is to linearly express all basis functions of the initial sub-polyhedron by using the basis functions of the target sub-polyhedron, and the focus is how to obtain the elements in the matrix C. Take a point on the first edge of the target sub-polyhedron, define the vector basis function at the point, and take the unit direction vector of the edge as Take the inner product of both sides of the equation, according to the characteristics of the edge vector basis function: the edge vector basis function only has a tangent component on the edge where the basis function is defined, and the tangent component is a constant, and has no tangent component on the remaining edges. Then the expression can be written as:

[0082]

[0083] In this way, c 1,1 , c 2,1 and c 3,1 in C can be solved. Obviously, c 1,1 is a constant, and the values of c 2,1 and c 3,1 are zero, which indicates that the first edge basis function of the surface only couples with the edge basis function corresponding to the main surface. By systematically applying the field matching condition, the corresponding coefficients of the remaining edges can be sequentially solved.

[0084] ​In the case of the function order being two, a two-order basis function is constructed, i.e., a two-order stacking vector basis function is constructed. At this time, the edge basis function and the surface basis function are contained. For example, two edge basis functions are defined on each edge, and two surface basis functions are defined on each triangular surface. Therefore, as shown in FIG. 4(a), which is a schematic diagram of the composition of all sub two-order basis functions corresponding to the initial sub polyhedron of the embodiment of the present application, the all sub two-order basis functions corresponding to the initial sub polyhedron contain six edge basis functions and two surface basis functions. As shown in FIG. 4(b), which is a schematic diagram of the composition of all sub two-order basis functions corresponding to the target sub polyhedron of the embodiment of the present application, the all sub two-order basis functions corresponding to the target sub polyhedron contain eighteen edge basis functions and eight surface basis functions. The relationship expression of the basis functions defined on the initial sub polyhedron and the target sub polyhedron at the non-conformal interface can be written as:

[0085]

[0086] The solving strategy follows the basic principles of the first-order case: the field matching condition is established from the first edge of the surface, and the unit tangent vector is defined as Equation fourteen and The inner product is done to obtain:

[0087]

[0088] The calculation process of the elements in matrix C is consistent with the methodology of the low-order case.

[0089] In some embodiments, the basis functions corresponding to the target sub polyhedron include first one-order basis functions and first two-order basis functions, and the basis functions corresponding to the initial sub polyhedron of the target sub polyhedron include second one-order basis functions and second two-order basis functions; the constructing, based on the function order, of the basis functions corresponding to the target sub polyhedron and the basis functions corresponding to the initial sub polyhedron of the target sub polyhedron includes: in response to determining that the function order is one, constructing the first one-order basis functions corresponding to the target sub polyhedron and the second one-order basis functions corresponding to the initial sub polyhedron of the target sub polyhedron; and in response to determining that the function order is two, constructing the first two-order basis functions corresponding to the target sub polyhedron and the second two-order basis functions corresponding to the initial sub polyhedron of the target sub polyhedron.

[0090] In the embodiment, the base functions are constructed based on the function order because the base functions are different due to different function orders. In the case of the function order being one order, the first one-order base function corresponding to the target sub-polyhedron is constructed, and the second one-order base function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron is constructed. In the case of the function order being two orders, the first two-order base function corresponding to the target sub-polyhedron is constructed, and the second two-order base function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron is constructed. The base functions of the target sub-polyhedron and the initial sub-polyhedron are connected through a linear relationship on the non-conformal interface of the polyhedron. The linear relationship of the base functions of the target sub-polyhedron and the initial sub-polyhedron is derived for the one-order and two-order base functions. The linear interpolation method corresponding to the linear relationship ensures the tangential continuity of the electric field on the non-conformal interface. The base functions of the target sub-polyhedron and the initial sub-polyhedron are accurately constructed through the function order.

[0091] In some embodiments, the error of the electric field function of the target sub-polyhedron for solving the electromagnetic problem is determined based on the base function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron pre-constructed, including: the conversion matrix of the target sub-polyhedron is determined based on the base function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron pre-constructed; and the error of the electric field function of the target sub-polyhedron is determined based on the conversion matrix.

[0092] In the embodiment, the number of target sub-polyhedrons is greater than the number of initial sub-polyhedrons because the initial sub-polyhedrons are twice divided to obtain the target sub-polyhedrons. Therefore, the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron pre-constructed is used to determine the conversion matrix of the target sub-polyhedron, and the number of initial matrices constructed is relatively small. Because the base function coefficient conversion matrix can accurately connect the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron, the conversion matrix of the target sub-polyhedron is determined by using the base function coefficient conversion matrix and the initial matrix, and the efficiency of determining the conversion matrix is improved. The error of the electric field function of the target sub-polyhedron is determined based on the conversion matrix. The error of the electric field function can be calculated through a formula, and the conversion matrix is used to calculate the error of the electric field function. Because the efficiency of determining the conversion matrix is improved, the efficiency of determining the error of the electric field function is also improved.

[0093] It should be noted that according to the linear relationship of the basis function, the conversion matrix corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron. The system matrix corresponding to the polyhedron is first composed of a plurality of initial matrices, and each initial matrix is replaced with its corresponding conversion matrix. When constructing the system matrix, it is necessary to first assemble all the initial matrices into the system matrix according to the global number, and the conversion matrix needs to be changed by the basis function coefficient conversion matrix C to be correctly assembled into the system matrix.

[0094] In some embodiments, the determining the conversion matrix corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron pre-constructed, comprises: obtaining the total number of times corresponding to the target sub-polyhedron that have completed the mesh division operation; based on the total number of times, at least one round of subdivision operation is performed on the basis function coefficient conversion matrix, and each round of subdivision operation is executed as follows: in response to the round corresponding to the current round of subdivision operation being less than or equal to the total number of times, the basis function coefficient conversion matrix is converted to obtain a target basis function coefficient conversion matrix, the target basis function coefficient conversion matrix is taken as the basis function coefficient conversion matrix in the next round of subdivision operation, and the next round of subdivision operation is executed; in response to the round corresponding to the current round of subdivision operation being greater than the total number of times, the at least one round of subdivision operation is exited; based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix, the conversion matrix is calculated.

[0095] In this embodiment, since the region where the target sub-polyhedron is located within the polyhedron may have undergone multiple meshing operations, the scale of the basis function coefficient transformation matrix is ​​not adapted to the total number of meshing operations. Therefore, it is necessary to scale the basis function coefficient transformation matrix based on the total number of meshing operations to facilitate subsequent comparison and analysis with the predetermined convergence error corresponding to the error of the electric field function. The total number of meshing operations corresponding to the target sub-polyhedron is obtained, and based on this total number, at least one round of subdivision operation is performed on the basis function coefficient transformation matrix. Each round of subdivision operation is performed as follows: if the round number corresponding to the current subdivision operation is less than or equal to the total number of operations, it indicates that the scale of the basis function coefficient transformation matrix is ​​not adapted to the total number of meshing operations. The basis function coefficient transformation matrix is ​​then scaled to obtain the target basis function coefficient transformation matrix, which is used as the basis function coefficient transformation matrix in the next round of subdivision operation. If the number of rounds corresponding to the current meshing operation is greater than the total number of rounds, it indicates that the scale of the basis function coefficient transformation matrix is ​​appropriate for the total number of meshing operations already performed, and at least one round of meshing operations should be exited. Based on the target basis function coefficient transformation matrix and the initial matrix corresponding to each round of meshing operations, the transformation matrix is ​​calculated. Since the scale of the target basis function coefficient transformation matrix is ​​appropriate for the total number of meshing operations already performed, the accuracy of the transformation matrix calculated using the target basis function coefficient transformation matrix corresponding to each round of meshing operations is ensured.

[0096] In some embodiments, the initial matrix includes a first initial matrix and a second initial matrix, and the transformation matrix includes a first transformation matrix and a second transformation matrix; calculating the transformation matrix based on the target basis function coefficient transformation matrix corresponding to each round of partitioning operation and the initial matrix includes: calculating the first transformation matrix based on the target basis function coefficient transformation matrix corresponding to each round of partitioning operation and the first initial matrix; and calculating the second transformation matrix based on the target basis function coefficient transformation matrix corresponding to each round of partitioning operation and the second initial matrix.

[0097] In this embodiment, an initial matrix is ​​constructed from different predetermined dimensions, and the initial matrix includes a first initial matrix A. e Second initial matrix B e The set of basis functions defined on this unit is The transformation matrix after the initial matrix is ​​transformed is defined as the first transformation matrix M. e Second transformation matrix N e Its expression is derived from C and the transpose of C. T The common expression is:

[0098]

[0099] In the finite element adaptive process, the mesh elements of polyhedron often need to be subdivided for many times, at this time the affiliation of polyhedron may be progressive layer by layer, with multi-layer structure, for example, edge a is subordinate to edge b, and edge b is subordinate to edge c, and so on. Based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the first initial matrix, the first conversion matrix is calculated; based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the second initial matrix, the second conversion matrix is calculated, which ensures the accuracy of the calculation of the conversion matrix. At this time, the conversion matrix is written as:

[0100]

[0101] Wherein, C i represents the i-th layer target basis function coefficient conversion matrix, is the transpose matrix of C i .

[0102] In another embodiment provided in the present application, the method provided in the present application is used for test simulation, and a wideband adaptive sweep frequency result f L (s) is drawn.

[0103] 1. Simulation conditions and contents:

[0104] The hardware platform of the simulation experiment is: windows 10 operating system, the computer main frequency is 2.9GHz, and the corresponding CPU model is Xeon 6248R. The software platform of the simulation experiment is: the simulation calculation environment is visual studio 2017+intelvisual fortran 2020.

[0105] Simulation one, the model of the polyhedron 1 simulated in the present application is divided into five areas after multiple mesh divisions, as shown in Figure 5 , the mesh in each area is divided for different times, wherein area one is the original mesh, area two is divided once on the basis of the original mesh, area three is divided twice, and area four is divided three times. The mesh distribution of the polyhedron 1 at the non-conformal mesh interface between each area is shown in Figure 6 . The port is excited by the main mode, sampling points are taken on each area, the tangential component of electric field of different areas at the sampling points is calculated, and the relative error of the tangential component of electric field on both sides is compared. Because the tangential component of electric field is a complex number, the relative error of real part and imaginary part needs to be calculated respectively. The relative error comparison chart of tangential electric field of each area of the polyhedron is shown in Figure 7 , wherein the horizontal coordinate is the total number of sampling points taken on each area, and the vertical coordinate is the corresponding relative error of electric field function. It can be found that the method proposed in the present patent has high solving accuracy for electromagnetic problems.

[0106] In the simulation two, the model of the polyhedron 2 simulated by the application is shown in Figure 8 As shown in the figure, the antenna is composed of three parts, i.e., a dielectric substrate, a feed line and a ground plane. The double-frequency resonance of the antenna is realized by etching some rectangular and trapezoidal slots on the ground plane. The antenna uses a lumped port feed. The relative dielectric constant of the dielectric substrate of the antenna is 4.4. Exemplarily, the dimensions of the dielectric substrate can be a = 3 mm, b = 18 mm, c = 3 mm, d = 9 mm, e = 30 mm, f = 14 mm, g = 3 mm, h = 1.6 mm, m = 15 mm, n = 6 mm, L = 35 mm and W = 30 mm. Figure 9 , Figure 9 The comparison diagram between the convergence results of the method provided by the application and the HFSS algorithm is shown in the figure. The horizontal coordinate represents frequency, and the vertical coordinate represents S parameter. The sweep frequency range is 1 GHz to 7 GHz. 101 frequency points are uniformly taken. The initial mesh and the final convergence results after the adaptive completion are recorded respectively, and are compared with the convergence results of the HFSS (High Frequency Structural Simulator) algorithm. The solution frequency of the HFSS is set to 5 GHz, and the convergence error is set to 0.02. The convergence error of the application is also set to 0.02. The convergence results are almost consistent with the convergence results of the HFSS. In the part where the S parameter is lower than -10 dB, the two are very close. The patent realizes the efficient solution of complex electromagnetic problems by proposing an efficient tetrahedral element refinement algorithm, a non-conformal interface base function processing method and a target-oriented error estimation strategy. The results of multiple numerical examples verify the feasibility and effectiveness of the proposed method, which shows that the method can significantly reduce the consumption of computing resources while ensuring the calculation accuracy, and provides an effective solution for the numerical simulation of complex electromagnetic problems.

[0107] It should be noted that the method of the application embodiment can be executed by a single device, such as a computer or a server. The method of the embodiment can also be applied to a distributed scenario, and completed by multiple devices in cooperation. In the distributed scenario, one of the multiple devices can only execute one or more steps in the method of the application embodiment, and the multiple devices can interact with each other to complete the method.

[0108] It is to be understood that the foregoing description is directed to embodiments of the application. Various embodiments can be devised without departing from the scope of the application. Some aspects of the application can be implemented in different embodiments and expressions can be used interchangeably to illustrate different aspects of embodiments of this application. Additionally, the description is not intended to limit the scope of the application to the specific embodiments described. The description is intended to cover any grant, file, or application that can be filed by the inventor or assignee of this application or in connection with this application, and any patent that issues on or after the priority date of this application, including but not limited to any continuations, continuations-in-part, patent applications, or patents that arise for this application and any corresponding foreign priority applications.

[0109] Based on the same inventive concept, the application also provides a device for adaptive mesh generation of a modeled polyhedron corresponding to any of the above-mentioned embodiments.

[0110] Reference Figure 10 , the device for adaptive mesh generation of a modeled polyhedron comprises:

[0111] At least one round of mesh generation operation is performed for the polyhedron, and each round of mesh generation operation is performed as follows:

[0112] The division module 10 is configured to divide the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron;

[0113] The first determination module 20 is configured to determine, for each target sub-polyhedron, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, an initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement;

[0114] The second determination module 30 is configured to determine an error of an electric field function for solving an electromagnetic problem corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and an initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance;

[0115] The third determination module 401 is configured to, in response to determining that the error of the electric field function determined by at least one current round of mesh generation operation is greater than or equal to a predetermined convergence error, take the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error as the polyhedron in the next round of mesh generation operation, and perform the next round of mesh generation operation;

[0116] The third determination module 402 is further configured to, in response to determining that all errors of the electric field functions determined by the current round of mesh generation operation are less than the predetermined convergence error, exit the at least one round of mesh generation operation.

[0117] The device is used for the polyhedron, and at least one round of grid division operation is performed. Each round of grid division operation is performed as follows: the polyhedron is divided to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron, and the division efficiency of the polyhedron is improved. For each target sub-polyhedron, based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron is determined, and the conversion relationship between the target sub-polyhedron and the initial sub-polyhedron corresponding to the target sub-polyhedron is accurately determined. Based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance, the error of the electric field function for solving the electromagnetic problem corresponding to the target sub-polyhedron is determined, direct large-scale calculation in a fine grid or a complex basis function is avoided, and the determination efficiency and accuracy of the error of the electric field function corresponding to the target sub-polyhedron are improved. In response to determining that the error of the electric field function determined by at least one current round of grid division operation is greater than or equal to a predetermined convergence error, the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error is taken as the polyhedron in the next round of grid division operation, and the next round of grid division operation is performed, so that the grid division of the polyhedron has accuracy. In response to determining that all the errors of the electric field functions determined by the current round of grid division operation are less than the predetermined convergence error, the at least one round of grid division operation is exited, and the grid division of the polyhedron has accuracy.

[0118] In some embodiments, the division module 10 is further configured to perform coarse division on the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron; and perform fine division on each initial sub-polyhedron to obtain a plurality of target sub-polyhedra corresponding to the initial sub-polyhedron, wherein the division accuracy of the coarse division is less than the division accuracy of the fine division.

[0119] In some embodiments, the first determination module 20 is further configured to determine the function order corresponding to the target sub-polyhedron according to the predetermined requirement; construct the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron based on the function order; and determine the basis function coefficient conversion matrix based on the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron.

[0120] In some embodiments, the base function corresponding to the target sub-polyhedron includes a first first-order base function and a first second-order base function, and the base function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron includes a second first-order base function and a second second-order base function; the first determining module 20 is further configured to, in response to determining that the function order is first order, construct the first first-order base function corresponding to the target sub-polyhedron, and construct the second first-order base function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron; in response to determining that the function order is second order, construct the first second-order base function corresponding to the target sub-polyhedron, and construct the second second-order base function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron.

[0121] In some embodiments, the second determining module 30 is further configured to determine the conversion matrix corresponding to the target sub-polyhedron based on the base function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron pre-constructed, and determine the error of the electric field function corresponding to the target sub-polyhedron based on the conversion matrix.

[0122] In some embodiments, the second determining module 30 is further configured to obtain the total number of times that the target sub-polyhedron has completed the mesh division operation, and perform at least one round of subdivision operation on the base function coefficient conversion matrix based on the total number, each round of subdivision operation being performed as follows: in response to the round corresponding to the current round of subdivision operation being less than or equal to the total number, converting the base function coefficient conversion matrix to obtain a target base function coefficient conversion matrix, taking the target base function coefficient conversion matrix as the base function coefficient conversion matrix in the next round of subdivision operation, and performing the next round of subdivision operation; in response to the round corresponding to the current round of subdivision operation being greater than the total number, exiting the at least one round of subdivision operation; and calculating the conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix.

[0123] In some embodiments, the initial matrix includes a first initial matrix and a second initial matrix, and the conversion matrix includes a first conversion matrix and a second conversion matrix; the second determining module 30 is further configured to calculate the first conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the first initial matrix, and calculate the second conversion matrix based on the target base function coefficient conversion matrix corresponding to each round of subdivision operation and the second initial matrix.

[0124] For the convenience of description, the above apparatus is described in various modules in the description. Of course, the functions of the modules can be implemented in one or more software and / or hardware in the implementation of the present application.

[0125] The device of the above embodiment is used to implement the adaptive mesh generation method of the corresponding modeled polyhedron in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which are not described here again.

[0126] Based on the same inventive concept, the present application also provides an electronic device corresponding to the method of any of the above embodiments, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the adaptive mesh generation method of the modeled polyhedron according to any of the above embodiments when executing the program.

[0127] Figure 11 A more specific hardware structure schematic diagram of an electronic device provided by the present embodiment is shown, which can include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are connected to each other through the bus 1050 for communication within the device.

[0128] The processor 1010 can be implemented in the form of a general-purpose CPU (Central Processing Unit), a microprocessor, an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits, etc., for executing related programs to implement the technical solutions provided by the present embodiment.

[0129] The memory 1020 can be implemented in the form of a ROM (Read Only Memory), a RAM (Random Access Memory), a static storage device, a dynamic storage device, etc. The memory 1020 can store an operating system and other application programs, and when the technical solutions provided by the present embodiment are implemented by software or firmware, the related program codes are saved in the memory 1020 and executed by the processor 1010.

[0130] The input / output interface 1030 is used to connect input / output modules to realize information input and output. The input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. The input device can include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device can include a display, a speaker, a vibrator, an indicator light, etc.

[0131] The communication interface 1040 is configured to connect a communication module (not shown in the figure) to realize the communication interaction between the device and other devices. The communication module can realize communication through wired mode (such as USB, network cable, etc.), or can realize communication through wireless mode (such as mobile network, WIFI, Bluetooth, etc.).

[0132] The bus 1050 includes a path for transmitting information between various components (such as the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040) of the device.

[0133] It should be noted that although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040, and the bus 1050, in the specific implementation process, the device can also include other components necessary for normal operation. In addition, those skilled in the art can understand that the above device can also only contain the components necessary for the implementation of the embodiments of the present application, and does not have to contain all the components shown in the figure.

[0134] The electronic device of the above embodiment is used to implement the adaptive mesh generation method of the corresponding modeled polyhedron in any of the preceding embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0135] Based on the same inventive concept, corresponding to the method of any of the above embodiments, the present application also provides a non-transitory computer readable storage medium storing computer instructions for causing the computer to execute the adaptive mesh generation method of the modeled polyhedron according to any of the above embodiments.

[0136] The computer readable medium of the present embodiment includes permanent and non-permanent, removable and non-removable media, which can be realized by any method or technology to store information. The information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device.

[0137] The storage medium of the above embodiments stores computer instructions for causing the computer to perform the adaptive mesh generation method of the modeled polyhedron as described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which are not described here again.

[0138] Based on the same concept, corresponding to the method of any of the above embodiments, the present application also provides a computer program product comprising computer program instructions, which, when executed on a computer, cause the computer to perform the adaptive mesh generation method of the modeled polyhedron as described in any of the above embodiments, with the beneficial effects of the corresponding method embodiments, which are not described here again.

[0139] It should be noted that the embodiments of the present application can also be further described in the following way:

[0140] It can be understood that before using the technical solutions of various embodiments in the present disclosure, the type of personal information involved, the scope of use, the use scenario, etc. will be informed to the user in an appropriate manner, and the user's authorization will be obtained.

[0141] For example, in response to receiving the user's active request, the user is sent prompt information to explicitly prompt the user that the operation requested to be performed will require the acquisition and use of the user's personal information. Thus, the user can choose whether to provide personal information to the software or hardware such as electronic devices, application programs, servers, or storage media that perform the technical solutions of the present disclosure according to the prompt information.

[0142] As an optional but not limited implementation manner, in response to accepting the user's active request, the way of sending prompt information to the user may, for example, be a pop-up window manner, in which the prompt information can be presented in the form of text. In addition, the pop-up window can also carry selection controls for the user to select "agree" or "disagree" to provide personal information to the electronic device.

[0143] It can be understood that the above notification and user authorization process is only illustrative, and does not limit the implementation of the present disclosure, and other ways that meet the relevant laws and regulations can also be applied to the implementation of the present disclosure.

[0144] Those skilled in the art will understand that the discussion of any of the above embodiments is only exemplary and is not intended to imply that the scope of the present application is limited to these examples; under the idea of the present application, the above embodiments or technical features in different embodiments can also be combined, the steps can be implemented in any order, and there are many other changes of different aspects of the embodiments of the present application as described above. In order to be brief, they are not provided in detail.

[0145] Additionally, to simplify the description and discussion, and so as not to obscure the embodiments of the application being presented, the well-known functions or constructions of integrated circuit (IC) chips and other components can or can not be shown in the figures and will be omitted as not to unnecessarily obscure the embodiments of the application being presented. Moreover, the devices can be shown in block diagram form in order to avoid obscuring the embodiments of the application, and this also acknowledges the fact that the details in regards to the implementation of such block devices are highly dependent on the platform upon which the embodiments of the application are being implemented (i.e., these details should be well within the purview of one of ordinary skill in the art). Where specific details are set forth in order to describe an illustrative embodiment of the application, it will be apparent to one of ordinary skill in the art that the embodiments of the application can be practiced without, or with variation of, these specific details. Thus, the description is to be considered as illustrative and not restrictive, and the scope of the application should be determined not with reference to the above description, but should be given to the appended claims.

[0146] While the application has been described in connection with specific embodiments thereof, many alternatives, modifications and variations will be apparent to those skilled in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) can use the embodiments discussed.

[0147] Embodiments of the application are intended to cover all such alternatives, modifications and variations as falling within the scope of the application. Accordingly, any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the application should be included in the scope of protection of the application.

Claims

1. A method of adaptive mesh refinement of a modelled polyhedron, characterized in that, The method comprises the following steps: performing at least one round of mesh division operation on the polyhedron, each round of mesh division operation being performed as follows: dividing the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron; for each target sub-polyhedron, determining a basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, an initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement; determining an error of an electric field function for solving an electromagnetic problem corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and an initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron which is constructed in advance; in response to determining that there is at least one error of the electric field function determined by the mesh division operation of the current round being greater than or equal to a predetermined convergence error, regarding the target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error as the polyhedron in the next round of mesh division operation, and performing the next round of mesh division operation; in response to determining that all errors of the electric field function determined by the mesh division operation of the current round are less than the predetermined convergence error, exiting the at least one round of mesh division operation.

2. The method of claim 1, wherein, The step of dividing the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron comprises the following steps: coarsely dividing the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron; for each initial sub-polyhedron, finely dividing the initial sub-polyhedron to obtain a plurality of target sub-polyhedra corresponding to the initial sub-polyhedron, wherein the division precision of the coarse division is less than the division precision of the fine division.

3. The method of claim 1, wherein, The step of determining the basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, the initial sub-polyhedron corresponding to the target sub-polyhedron, and the predetermined requirement comprises the following steps: determining the order of function corresponding to the target sub-polyhedron according to the predetermined requirement; based on the order of function, constructing the basis function corresponding to the target sub-polyhedron, and constructing the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron; based on the basis function corresponding to the target sub-polyhedron and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron, determining the basis function coefficient conversion matrix.

4. The method of claim 3, wherein, The basis function corresponding to the target sub-polyhedron comprises a first first-order basis function and a first second-order basis function, and the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron comprises a second first-order basis function and a second second-order basis function. The step of constructing the basis function corresponding to the target sub-polyhedron and constructing the basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron based on the order of function comprises the following steps: in response to determining that the order of function is first order, constructing the first first-order basis function corresponding to the target sub-polyhedron, and constructing the second first-order basis function corresponding to the initial sub-polyhedron corresponding to the target sub-polyhedron; In response to determining that the function order is two, a first two-order basis function corresponding to the target sub-polyhedron is constructed, and a second two-order basis function corresponding to an initial sub-polyhedron corresponding to the target sub-polyhedron is constructed.

5. The method of claim 1, wherein, The error of the electric field function for solving the electromagnetic problem corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and an initial matrix of an initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance, and the error of the electric field function for solving the electromagnetic problem corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance. The conversion matrix corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance. The error of the electric field function corresponding to the target sub-polyhedron is determined based on the conversion matrix.

6. The method of claim 5, wherein, The conversion matrix corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance, and the conversion matrix corresponding to the target sub-polyhedron is determined based on the basis function coefficient conversion matrix and the initial matrix of the initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance. The total number of times that the mesh division operation has been completed corresponding to the target sub-polyhedron is obtained. At least one round of subdivision operation is performed on the basis function coefficient conversion matrix based on the total number of times, and each round of subdivision operation is performed as follows: In response to the round corresponding to the current round of subdivision operation being less than or equal to the total number of times, the basis function coefficient conversion matrix is converted to obtain a target basis function coefficient conversion matrix, and the target basis function coefficient conversion matrix is used as the basis function coefficient conversion matrix in the next round of subdivision operation to perform the next round of subdivision operation. In response to the round corresponding to the current round of subdivision operation being greater than the total number of times, the at least one round of subdivision operation is exited. The conversion matrix is calculated based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix.

7. The method of claim 6, wherein, The initial matrix includes a first initial matrix and a second initial matrix, and the conversion matrix includes a first conversion matrix and a second conversion matrix. The conversion matrix is calculated based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix, and the conversion matrix is calculated based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the initial matrix. The first conversion matrix is calculated based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the first initial matrix. The second conversion matrix is calculated based on the target basis function coefficient conversion matrix corresponding to each round of subdivision operation and the second initial matrix.

8. An apparatus for adaptive mesh refinement of a modeled polyhedron, comprising: It includes: At least one round of mesh division operation is performed on the polyhedron, and each round of mesh division operation is performed as follows: The division module is configured to divide the polyhedron to obtain a plurality of initial sub-polyhedra corresponding to the polyhedron and a plurality of target sub-polyhedra corresponding to each initial sub-polyhedron; The first determination module is configured to determine, for each target sub-polyhedron, a basis function coefficient conversion matrix corresponding to the target sub-polyhedron based on the target sub-polyhedron, an initial sub-polyhedron corresponding to the target sub-polyhedron, and a predetermined requirement; The second determination module is configured to determine the error of the electric field function for solving the electromagnetic problem corresponding to the target sub-polyhedron based on the basis function coefficient conversion matrix and an initial matrix of an initial sub-polyhedron corresponding to the target sub-polyhedron constructed in advance. a third determining module, configured to, in response to determining that the error of the electric field function determined by the grid partition operation of the current round is greater than or equal to a predetermined convergence error, determine a target sub-polyhedron corresponding to the error of the electric field function greater than or equal to the predetermined convergence error as a polyhedron in a next round of grid partition operation, and perform the next round of grid partition operation; the third determining module is further configured to, in response to determining that the errors of all electric field functions determined by the grid partition operation of the current round are all less than the predetermined convergence error, exit the at least one round of grid partition operation.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that, The processor implements the method in any one of claims 1 to 7 when executing the program.

10. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to make the computer execute the method in any one of claims 1 to 7.

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