An electromagnetic radiation simulation analysis method based on local mesh self-adaptive subdivision

Abstract

The application belongs to the technical field of three-dimensional electromagnetic radiation numerical solution, and relates to an electromagnetic radiation simulation analysis method based on local grid self-adaptive division. Firstly, the application carries out finite element modeling on a target antenna, introduces PML boundary and wave port excitation to establish a corresponding finite element calculation domain model, and adopts tetrahedral grid division to classify the calculation domain model; then finite element electromagnetic radiation simulation analysis is carried out to obtain finite element solution, and error estimation and encryption strategy are used to give the encryption size of the grid nodes in the non-PML region; finally, the grid is encrypted, finite element electromagnetic radiation simulation analysis is carried out again, and the process is repeated until the overall solution error is less than the set error limit, the final calculation grid is obtained, and finite element electromagnetic radiation simulation analysis is carried out. The application only encrypts the tetrahedral grid in the non-PML calculation domain, ensures the original characteristics of the tetrahedral grid in the PML calculation domain, and realizes the rapid simulation design of the antenna radiation characteristics while ensuring the calculation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional electromagnetic radiation numerical solution technology, and relates to an electromagnetic radiation simulation and analysis method based on local mesh adaptive partitioning. Background Technology

[0002] Microwave components, such as antennas, primarily transmit and receive signals by radiating or receiving electromagnetic waves. Therefore, studying the propagation characteristics of these electromagnetic waves in the air is crucial, as it determines the antenna's performance specifications. Conventional experimental testing methods, such as using microwave anechoic chambers, are difficult to implement on a large scale during the antenna design phase due to their high cost; they are typically only used for performance testing in the final testing stage. During the design phase, using commercial simulation software or self-developed programs to analyze antenna performance is a common approach. For example, commercial simulation software like HFSS or self-developed programs generally employ the finite element method (FEM). Finite element analysis generally includes several steps: modeling, mesh generation, solution calculation, and post-processing display. Among these steps, mesh generation is particularly important, determining the accuracy and efficiency of the simulation calculation; therefore, finding an efficient and high-precision mesh generation technique is key.

[0003] The widely adopted method of one-time mesh generation has many drawbacks. First, the exact size of the discrete mesh is unknown; infinite meshing will result in a huge computational burden, while an overly sparse mesh will lead to inaccurate results. Second, overall meshing of the entire computational domain will result in a waste of computational resources.

[0004] To address the aforementioned issues, an adaptive mesh refinement method has been proposed. This method automatically refines the mesh in the desired area and automatically determines whether the results converge. However, conventional adaptive mesh methods are inefficient for antenna simulation design. This is because antenna simulation analysis typically requires a truncated boundary to transform the infinite computational domain into a finite computational space; this truncated boundary is generally called an absorbing boundary. Ordinary absorbing boundaries, due to their low precision, can only be used for qualitative analysis. Another high-precision absorbing boundary, the ideal matching layer absorbing boundary condition (PML), is often favored by designers. However, PML boundaries have specific requirements for the mesh; generally, standard elements are preferred. Otherwise, the finite element matrix condition number deteriorates, resulting in poor computational convergence and impacting simulation design efficiency. Conventional adaptive mesh methods use global errors to indicate mesh refinement, which can disrupt the mesh characteristics of the PML boundary.

[0005] Therefore, it is necessary to construct an efficient mesh adaptive method to ensure the mesh characteristics of the PML boundary, improve the efficiency of finite element solution, and ultimately realize the rapid simulation design of antenna radiation characteristics. Summary of the Invention

[0006] To address the aforementioned problems and shortcomings, and to solve the issue of low efficiency in applying existing mesh adaptive methods to antenna simulation design, this invention provides an electromagnetic radiation simulation analysis method based on local mesh adaptive partitioning. This method effectively guarantees the mesh characteristics of the PML boundary, thereby enabling rapid simulation design of antenna radiation characteristics.

[0007] An electromagnetic radiation simulation and analysis method based on local mesh adaptive partitioning includes the following steps:

[0008] A. Perform finite element modeling on the target antenna structure, and introduce PML boundary and wave port excitation to establish the corresponding computational domain model.

[0009] B. Using the computational domain model established in step A of tetrahedral mesh generation, a discrete model of the computational domain composed of tetrahedral meshes is obtained.

[0010] C. Classify the discrete model of the computational domain obtained in step B into tetrahedral meshes. The tetrahedral meshes of the PML region are denoted as P-class region meshes, and their mesh count is M. P Tetrahedral meshes in non-PML regions are denoted as Q-type meshes, and their mesh count is M. Q .

[0011] D. Select vector basis functions and perform standard finite element electromagnetic radiation simulation analysis to obtain finite element solutions on each tetrahedral mesh.

[0012] E. Based on the finite element solution on each tetrahedral mesh obtained in step D, construct the recovered solution for all Q-type tetrahedral meshes to obtain the recovered solution and finite element solution on each Q-type tetrahedral mesh node.

[0013] F. Based on the recovered solution and finite element solution on the nodes of the Q-type tetrahedral mesh obtained in step E, perform error estimation on all Q-type tetrahedral meshes to obtain the solution error norm of each Q-type tetrahedral mesh and the overall solution error of the Q-type tetrahedral mesh.

[0014] G. Based on the solution error norm on each Q-type tetrahedral mesh obtained in step F, a mesh refinement strategy is used to determine the mesh refinement, distinguish the Q-type tetrahedral meshes that need to be refined, and calculate the corresponding mesh refinement size.

[0015] H. Traverse all tetrahedral mesh nodes. If a node is contained in a P-class tetrahedral mesh, the mesh node size remains unchanged; otherwise, calculate the mesh node size based on the mesh refinement size obtained in step G.

[0016] I. Based on the tetrahedral mesh node size obtained in step H, perform Q-type tetrahedral mesh refinement to obtain a new computational domain discrete model.

[0017] J. Based on the new discrete model of the computational domain obtained in step I, repeat steps C to I until the overall solution error is less than the set error limit.

[0018] K. Perform finite element electromagnetic radiation simulation analysis on the final discrete model of the computational domain obtained in step J to obtain the electromagnetic parameters of the target antenna.

[0019] This invention first performs finite element modeling on the target antenna, introducing PML boundaries and waveport excitations to establish a corresponding finite element computational domain model, and then uses tetrahedral meshing to partition the computational domain model and classify the tetrahedral mesh. Next, it obtains the finite element solution through finite element electromagnetic radiation simulation analysis, and uses error estimation and refinement strategies to give the refinement dimensions of mesh nodes in non-PML regions. Finally, it refines the mesh and performs finite element electromagnetic radiation simulation analysis again until the overall solution error is less than the set error limit, obtaining the final computational mesh. Finite element electromagnetic radiation simulation analysis is then performed, thereby achieving rapid simulation design of antenna radiation characteristics.

[0020] In summary, this invention employs a local mesh adaptive method, refining the tetrahedral mesh only within the non-PML computational domain. This preserves the original characteristics of the tetrahedral mesh within the PML computational domain, thus preventing a deterioration in the condition number of the finite element matrix and improving the efficiency of matrix solving. Therefore, this invention can achieve rapid simulation design of antenna radiation characteristics while maintaining computational accuracy. Attached Figure Description

[0021] Figure 1 This is a flowchart of the present invention;

[0022] Figure 2 This is a finite element computational domain model diagram of an embodiment;

[0023] Figure 3 This is a schematic diagram of region classification in an embodiment;

[0024] Figure 4 This is a schematic diagram of the tetrahedral nodes in an embodiment;

[0025] Figure 5 This is a diagram showing the mesh generation effect of an embodiment;

[0026] Figure 6 This is a graph showing the computational performance of an example. Detailed Implementation

[0027] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0028] Reference Figure 1 An electromagnetic radiation simulation and analysis method based on local mesh adaptive partitioning includes the following steps:

[0029] A. Perform finite element modeling on the target antenna structure, and introduce PML boundary and wave port excitation to establish the corresponding computational domain model.

[0030] This embodiment uses the electromagnetic radiation simulation analysis of a horn antenna as an example. Based on the characteristics of antenna radiation analysis, a simulation analysis is established as follows: Figure 2 The finite element computational domain model shown is represented by a patterned area in the middle region of the computational domain model, which is a horn antenna. The area outside the middle region is the PML boundary, with waveport excitation as the feed source.

[0031] B. Using the computational domain model established in step A of tetrahedral mesh generation, a discrete model of the computational domain composed of tetrahedral meshes is obtained.

[0032] Using tetrahedral meshes to partition the computational domain model is a well-known process in the finite element method, so this step will not be described in detail here. The partitioned computational domain model is artificially divided into multiple three-dimensional tetrahedral meshes, thereby transforming the continuous computational domain model space into a discrete mesh space.

[0033] C. Classify the discrete model of the computational domain obtained in step B into tetrahedral meshes. The tetrahedral meshes of the PML region are denoted as P-type region meshes, and the tetrahedral meshes of the non-PML region are denoted as Q-type region meshes.

[0034] The entire computational domain discrete model consists of many tetrahedrons, which are classified according to the different regions to which the four faces belong, such as... Figure 3 As shown, the tetrahedral mesh within the PML region is denoted as a P-type region mesh, with a mesh count of M. P The tetrahedral meshes of non-PML regions are denoted as Q-type region meshes, with a mesh count of M. Q .

[0035] D. Select vector basis functions and perform standard finite element electromagnetic radiation simulation analysis to obtain finite element solutions on each tetrahedral mesh.

[0036] Finite element electromagnetic radiation simulation analysis is a well-known process, which we will not elaborate on further. Below, we present the final finite element solution on the tetrahedral mesh. Finite element solution is a general term; here, we use electric field intensity as the reference. If it is indicated, then there is

[0037]

[0038] Where e represents the e-th tetrahedral mesh. For the finite element solution of the e-th tetrahedral mesh, Let represent vector basis functions, which are functions of x, y, and z in Cartesian coordinates. Let represent the solution of the finite element matrix on the e-th tetrahedral mesh, and n represent the number of vector basis functions.

[0039] E. Based on the finite element solution on each tetrahedral mesh obtained in step D, construct the recovered solution for all Q-type tetrahedral meshes to obtain the recovered solution and finite element solution on each Q-type tetrahedral mesh node.

[0040] Construct the reconstructed solution for all Q-type tetrahedral meshes to obtain the reconstructed solution on the e-th tetrahedral mesh. It is a function of x, y, z in the Cartesian coordinate system. The specific method for constructing the recovered solution is a well-known process, which we will not elaborate on here.

[0041] Substitute the coordinates of the four nodes of the tetrahedral mesh into the solution to restore the original solution. The recovered solution at each of the four nodes of the tetrahedral mesh can be obtained. A schematic diagram of a tetrahedral mesh node is shown below. Figure 4 As shown.

[0042] Substituting the coordinates of the four nodes of the tetrahedral mesh into formula (1) yields the finite element solution at the four nodes of the tetrahedral mesh.

[0043] F. Based on the recovered solution and finite element solution on the nodes of the Q-type tetrahedral mesh obtained in step E, perform error estimation on all Q-type tetrahedral meshes to obtain the solution error norm of each Q-type tetrahedral mesh and the overall solution error of the Q-type tetrahedral mesh.

[0044] The solution error for each Q-type tetrahedral mesh is obtained according to formula (2).

[0045]

[0046] Where η e Let |η| represent the solution error on the e-th tetrahedral mesh, and |η| represent the modulus value, the norm of the solution error in the tetrahedral mesh. e ||for

[0047]

[0048] Where V e Let the volume of the e-th tetrahedral mesh be denoted as , then the overall solution error of a Q-type tetrahedral mesh can be constructed in the following format.

[0049]

[0050] Where ζ represents the overall solution error. For the field The norm of the modulus can be represented in a tetrahedral mesh as:

[0051]

[0052] G. Based on the solution error norm on each Q-type tetrahedral mesh obtained in step F, a mesh refinement strategy is used to determine the mesh refinement, distinguish the Q-type tetrahedral meshes that need to be refined, and calculate the corresponding mesh refinement size.

[0053] The solution error norm ||η on all Q-class tetrahedral meshes e ||Sorting in ascending order yields the following sequence W

[0054]

[0055] Based on the set mesh encryption ratio θ1∈(0,1), the set of tetrahedral meshes H to which the encryption strategy needs to be executed is given.

[0056]

[0057] The Q-class tetrahedral meshes that need to be encrypted are marked in reverse order using an encryption strategy. The encryption strategy is a well-known process, so this step will not be described in detail.

[0058] For the Q-class tetrahedral meshes that need encryption, calculate the encryption size for each mesh.

[0059]

[0060] Where θ2∈(0,1) represents the set mesh refinement size. ξ represents the average of the sum of the lengths of all sides of element e. e The subscript 'r' indicates the element tolerance, 'p' indicates the order of the basis function, 'r' indicates mesh refinement, and 'o' indicates length averaging.

[0061] H. Traverse all tetrahedral mesh nodes. If a node is contained in a P-class tetrahedral mesh, the mesh node size remains unchanged; otherwise, calculate the mesh node size based on the mesh refinement size obtained in step G.

[0062] The process iterates through all tetrahedral mesh nodes within the computational domain. If a node is contained within a class P tetrahedral mesh, the mesh node size remains unchanged; otherwise, the mesh node size h is calculated. n

[0063]

[0064] in This represents the smallest element in the tetrahedral mesh that needs to be encrypted, associated with node n.

[0065] I. Based on the tetrahedral mesh node size obtained in step H, perform Q-type tetrahedral mesh refinement to obtain a new computational domain discrete model.

[0066] Mesh refinement is a well-known process, so this step will not be described in detail here. Mesh refinement can yield a new discrete model of the computational domain.

[0067] J. Repeat steps C through I until the overall solution error is less than the set error limit.

[0068] Based on the new discrete model of the computational domain obtained in step I, steps C through I are executed again, and this process is repeated until the overall solution error is less than the set error limit.

[0069] K. Perform finite element electromagnetic radiation simulation analysis on the final discrete model of the computational domain obtained in step J to obtain the electromagnetic parameters of the antenna.

[0070] After the above steps, the final encrypted mesh can be obtained. Based on this mesh, finite element electromagnetic radiation simulation analysis can be performed to obtain the electromagnetic parameters of the antenna of interest.

[0071] For the same target horn antenna, this embodiment is compared with the traditional solution in the following tests: Figure 5 The image shows a comparison of the mesh refinement results between the proposed solution and the traditional solution. The results indicate that the proposed solution can guarantee the characteristics of the PML boundary mesh. Figure 6 This is a comparison chart of computational performance, further based on... Figure 6 The comparison of computational performance between the present invention and the traditional solution shows that the present invention improves the efficiency of finite element analysis and enables rapid simulation design of antenna radiation characteristics.

[0072] As can be seen from the above embodiments and comparative examples, this invention employs a local mesh adaptive method, refining only the tetrahedral mesh outside the PML computational domain. This preserves the original characteristics of the tetrahedral mesh within the PML computational domain, thus preventing a deterioration in the condition number of the finite element matrix and improving the efficiency of matrix solving. This invention achieves rapid simulation design of antenna radiation characteristics while maintaining computational accuracy.

Claims

1. A simulation analysis method for electromagnetic radiation based on adaptive local mesh partitioning, characterized in that, Includes the following steps: A. Perform finite element modeling on the target antenna structure, and introduce PML boundary and wave port excitation to establish the corresponding computational domain model; B. Using the computational domain model established in step A of tetrahedral meshing, a discrete model of the computational domain composed of tetrahedral meshes is obtained; C. Classify the discrete model of the computational domain obtained in step B into tetrahedral meshes. The tetrahedral meshes of the PML region are denoted as P-class region meshes, and their mesh count is... Tetrahedral meshes in non-PML regions are denoted as Q-type meshes, and their mesh count is... ; D. Select vector basis functions, perform standard finite element electromagnetic radiation simulation analysis, and obtain finite element solutions on each tetrahedral mesh; E. Based on the finite element solution obtained in step D on each tetrahedral mesh, construct the recovered solution for all Q-type tetrahedral meshes to obtain the recovered solution and finite element solution on each Q-type tetrahedral mesh node; F. Based on the recovered solution and finite element solution on the nodes of the Q-type tetrahedral mesh obtained in step E, the error is estimated for all Q-type tetrahedral meshes to obtain the solution error norm of each Q-type tetrahedral mesh and the overall solution error of the Q-type tetrahedral mesh. Specifically: The solution error for each Q-type tetrahedral mesh is obtained according to formula (2). （2）； in Indicates the first Solution error on a tetrahedral mesh Indicates the modulo value. For the first Finite element solution for a tetrahedral mesh For the first The reconstructed solution of a tetrahedral mesh is obtained by solving for the norm of the error in the tetrahedral mesh. for （3）； in For the first The volume of a tetrahedral mesh can be used to construct the overall solution error of a Q-type tetrahedral mesh in the following format. （4）； in This represents the overall solution error. For the field The norm of the modulus is represented in a tetrahedral mesh as （5）； G. Based on the solution error norm on each Q-type tetrahedral mesh obtained in step F, a mesh refinement strategy is used to determine the mesh refinement, distinguish the Q-type tetrahedral meshes that need to be refined, and calculate the corresponding mesh refinement size. H. Traverse all tetrahedral mesh nodes. If a node is contained in a P-class tetrahedral mesh, the mesh node size remains unchanged; otherwise, calculate the mesh node size based on the mesh refinement size obtained in step G. I. Based on the tetrahedral mesh node size obtained in step H, perform Q-type tetrahedral mesh refinement to obtain a new computational domain discrete model; J. Based on the new discrete model of the computational domain obtained in step I, repeat steps C to I until the overall solution error is less than the set error limit. K. Perform finite element electromagnetic radiation simulation analysis on the final discrete model of the computational domain obtained in step J to obtain the electromagnetic parameters of the target antenna.

2. The electromagnetic radiation simulation and analysis method based on local mesh adaptive partitioning as described in claim 1, characterized in that, Step G shown is specifically as follows: Solution error norm for all Q-class tetrahedral meshes Sort in ascending order to obtain the following sequence （6）； Based on the set grid encryption ratio Given the tetrahedral mesh set for which the encryption strategy needs to be executed. （7）； The Q-type tetrahedral meshes that need to be encrypted are marked in reverse order using an encryption strategy. For each Q-type tetrahedral mesh that needs encryption, the encryption dimension is calculated. （8）； in This indicates the set mesh encryption size. Representation unit The average of the sum of the lengths of all sides. Indicates unit tolerance, Indicates the order of the basis functions, subscript Indicates grid encryption, subscript It indicates the average length.

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