Nested mesh generation method for fast simulation of electromagnetic-thermal-mechanical multiphysics fields

Abstract

This invention discloses a nested mesh generation method for rapid electromagnetic-thermal-mechanical multiphysics simulation, mainly addressing the problem of reduced simulation efficiency caused by using the same set of meshes for computational calculations in electromagnetic-thermal-mechanical multiphysics simulations. The method includes: 1) obtaining an initial coarse mesh element; 2) taking the midpoint of each edge in the initial coarse mesh element, connecting the midpoints to obtain a sub-tetrahedron at the vertex of the initial coarse mesh element, and then trimming it to obtain an octahedron; 3) dividing the octahedron by using the two parallelograms formed inside as tangents to obtain the sub-tetrahedrons; 4) repeating the refinement operation a preset number of times to obtain a dense mesh; 6) performing electromagnetic simulation using the dense mesh, and thermal and mechanical simulations using the initial coarse mesh and the finite element method to complete the multiphysics simulation. This invention can save computational load in thermal and mechanical simulations and effectively improve the efficiency of electromagnetic-thermal-mechanical multiphysics simulations without affecting simulation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of electrical technology, and further relates to computational electromagnetics. Specifically, it is a nested mesh generation method for rapid simulation of electromagnetic-thermal-mechanical multiphysics fields. This method can be used to improve the simulation efficiency of electromagnetic-thermal-mechanical multiphysics fields and promote the application of multiphysics simulation technology in wireless communication, integrated circuits, microwave circuits, antenna design, precision guidance and other fields. Background Technology

[0002] In fields such as wireless communication, integrated circuits, microwave circuits, antenna design, and precision guidance, the coupling problem of multiple physics fields, including electromagnetic fields, temperature fields, and stress fields, is becoming increasingly prominent, with electromagnetic fields at the core. However, experimental research on these electromagnetic-thermal-mechanical multiphysics coupling problems suffers from drawbacks such as high cost, long development cycles, and susceptibility to environmental influences. Therefore, electromagnetic-thermal-mechanical multiphysics simulation technology has become an essential tool for studying multiphysics effects. Currently, mainstream electromagnetic-thermal-mechanical multiphysics simulation methods are typically based on the finite element method (FEM), meaning that electromagnetic, thermal, and force simulations all employ the FEM. During simulation, the geometric model of the simulation object needs to be meshed first, with tetrahedral meshes being the most common. Electromagnetic, thermal, and force simulations typically use the same tetrahedral mesh.

[0003] Because the rate of change of electromagnetic fields is much faster than that of heat and force, the actual mesh element sizes required for simulations of different physical fields (electromagnetic, thermal, and mechanical) differ. Electromagnetic simulations require much smaller mesh sizes than thermal and mechanical simulations. To ensure simulation accuracy, current mainstream electromagnetic-thermal-mechanical multiphysics simulation methods uniformly adopt the dense mesh required for electromagnetic simulations. However, this meshing method introduces a large amount of unnecessary computation for thermal and mechanical simulations, affecting simulation efficiency. Therefore, there is an urgent need to research a meshing technique applicable to the different simulation requirements in multiphysics. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a nested mesh generation method for rapid electromagnetic-thermal-mechanical multiphysics simulation. This method primarily solves the problem of computational overhead caused by using the same set of meshes in electromagnetic-thermal-mechanical multiphysics simulations, which negatively impacts simulation efficiency. Based on the physical field characteristics of electromagnetic and thermal / mechanical simulations, this invention designs a novel nested mesh generation method for subdividing the geometric model of the simulation object. In electromagnetic simulations, a denser mesh is used within the nested mesh, while in thermal / mechanical simulations, a coarser mesh is used. This reduces the computational load in thermal / mechanical simulations, effectively improving the efficiency of electromagnetic-thermal-mechanical multiphysics simulations without compromising simulation accuracy.

[0005] The specific steps of this invention to achieve the above objectives are as follows:

[0006] (1) Set the initial coarse mesh size, and divide the geometric model of the simulation object according to the size to obtain the initial coarse mesh element;

[0007] (2) Take the midpoint of each edge in the initial coarse grid cell, and then connect the midpoints in the same triangular face with a straight line to obtain four sub-tetrahedrons located at the vertices of the initial coarse grid cell with similar shapes to the initial coarse grid cell, denoted as T1, T2, T3, and T4.

[0008] (3) Trim the sub-tetrahedrons T1, T2, T3 and T4 located at the vertices of the initial coarse mesh unit to obtain the octahedrons with the interior retained;

[0009] (4) Divide the octahedron into four sub-tetrahedrons by using the two parallelograms formed inside the octahedron as the cutting planes, and denot them as T5, T6, T7 and T8.

[0010] (5) Perform steps (2)-(4) on each initial coarse mesh element to obtain 8 tetrahedrons T1-T8 respectively, which realizes the first refinement of the entire initial coarse mesh. Set the number of refinement according to the actual needs of electromagnetic simulation. Perform the same operation as the initial coarse mesh element refinement on the mesh after the previous refinement until the preset number of refinement is reached to obtain a dense mesh.

[0011] (6) Electromagnetic simulation was performed using a dense grid to obtain the electric field distribution;

[0012] (7) Locate the dense grid cells containing the coarse grid nodes. After performing electromagnetic simulation, use the electric field intensity E at the vertices of the dense grid cells to calculate the conductor loss P at the vertices of the coarse grid. c and dielectric loss P d , will P c +P d The heat source at the vertex of the coarse mesh is used as the initial coarse mesh and the finite element method to perform thermal and mechanical simulations, thereby realizing electromagnetic-thermal-mechanical multiphysics simulation.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] First, considering that the actual mesh element sizes required for simulations of different physical fields such as electromagnetics, heat, and force are not the same, this invention designs nested meshes of different sizes for multiphysics simulations, taking into account the characteristics of electromagnetics and heat and force themselves. This ensures that electromagnetic simulations and heat and force simulations can each select meshes of appropriate density, i.e., electromagnetic simulations use dense meshes, while heat and force simulations use coarse meshes. This saves on the computational load of heat and force simulations and effectively improves the overall efficiency of electromagnetic-thermal-force multiphysics simulations without affecting the simulation accuracy.

[0015] Secondly, since the dense mesh for electromagnetic simulation and the coarse mesh for thermal and mechanical simulation designed in this invention are nested together, and the vertices of the coarse mesh overlap with some vertices of the dense mesh, information can be transferred between electromagnetic simulation and thermal simulation. After electromagnetic simulation, the heat source at the vertex of the coarse mesh can be obtained by calculating the electric field intensity at the vertex of the dense mesh element where the coarse mesh node is located. Thermal and mechanical simulation can be performed using the coarse mesh and the finite element method, thereby realizing electromagnetic-thermal-mechanical multiphysics simulation. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the initial coarse mesh unit;

[0017] Figure 2 This is a schematic diagram of the result obtained by taking the midpoints of each edge of the initial coarse mesh unit and connecting them in this invention;

[0018] Figure 3 This is a schematic diagram of the octahedrons retained inside the initial coarse mesh unit after removing four sub-tetrahedrons T1, T2, T3, and T4 in this invention.

[0019] Figure 4 This is a schematic diagram illustrating two different ways of dividing the internal octahedron of a parallelogram in this invention.

[0020] Figure 5 A schematic diagram of the nested mesh for electromagnetic simulation and thermal / mechanical simulation generated using the method of this invention;

[0021] Figure 6 This is a schematic diagram of the structure of the high-power microwave irradiation filter in an embodiment of the present invention;

[0022] Figure 7 The temperature distribution of the filter surface at 10 ns is shown in the embodiment of the present invention; wherein (a) is the temperature distribution of the filter surface at 10 ns obtained by using the method of the present invention, and (b) is the temperature distribution of the filter surface at 10 ns obtained without using the method of the present invention.

[0023] Figure 8 The diagram shows the displacement distribution of the filter surface in an embodiment of the present invention; wherein (a) is the displacement distribution of the filter surface obtained by using the method of the present invention, and (b) is the displacement distribution of the filter surface obtained without using the method of the present invention. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the accompanying drawings.

[0025] Example 1: Refer to Figure 1 The present invention proposes a nested mesh generation method for rapid simulation of electromagnetic-thermal-mechanical multiphysics fields, and the specific implementation steps are as follows:

[0026] Step 1. Set the initial coarse mesh size, and divide the geometric model of the simulation object according to the size to obtain the initial coarse mesh element; the initial coarse mesh size adopts 1-3 times the wavelength.

[0027] Step 2. Take the midpoint of each edge in the initial coarse mesh cell, and then connect the midpoints in the same triangular face with straight lines to obtain four sub-tetrahedrons located at the vertices of the initial coarse mesh cell with similar shapes, denoted as T1, T2, T3, and T4.

[0028] Step 3. Trim the sub-tetrahedrons T1, T2, T3 and T4 located at the vertices of the initial coarse mesh cells to obtain the octahedrons with the interior intact;

[0029] Step 4. Divide the octahedron into four sub-tetrahedrons by using the two parallelograms formed inside the octahedron as tangents. Specifically, divide the octahedron into four sub-tetrahedrons by using any two perpendicularly intersecting parallelograms formed inside the octahedron as tangents, resulting in four sub-tetrahedrons, denoted as T5, T6, T7, and T8.

[0030] Step 5. Perform steps (2)-(4) on each initial coarse mesh element to obtain 8 tetrahedrons T1-T8, thus refining the entire initial coarse mesh once. Set the number of refinements according to the actual needs of electromagnetic simulation. Repeat the same operation as refining the initial coarse mesh element on the previously refined mesh until the preset number of refinements is reached to obtain a dense mesh. Setting the number of refinements according to the actual needs of electromagnetic simulation allows the mesh size to be reduced to 0.1 times the wavelength after the preset number of refinements, which meets the requirements of electromagnetic simulation.

[0031] The dense mesh is specifically obtained by performing steps 2-4 on the initial coarse mesh cells to obtain the first fine mesh, treating the first fine mesh as the initial coarse mesh and performing steps 2-4 again to obtain the second fine mesh, then treating the second fine mesh as the initial coarse mesh and performing steps 2-4 again to obtain the third fine mesh, and so on, until a preset number of refinements are completed to obtain a dense mesh that meets the requirements of electromagnetic simulation.

[0032] Step 6. Perform electromagnetic simulation using a dense mesh to obtain the electric field distribution;

[0033] Step 7. Locate the dense grid cells containing the coarse grid nodes. After performing electromagnetic simulation, use the electric field intensity E at the vertices of the dense grid cells to calculate the conductor loss P at the vertices of the coarse grid. c and dielectric loss P d , will P c +P dThe heat source at the vertex of the coarse mesh is used as the initial coarse mesh and the finite element method to perform thermal and mechanical simulations, thereby realizing electromagnetic-thermal-mechanical multiphysics simulation.

[0034] The conductor loss P at the vertex of the coarse grid c and dielectric loss P d The result is obtained by calculation using the following formula:

[0035] P c =σ|E| 2 ,

[0036]

[0037] Where σ is the conductivity, D is the electric displacement vector, D = εE, ε represents the dielectric constant, and t is the time variable.

[0038] Example 2: The overall implementation steps of the present invention are the same as those of Example 1, and will now be described in conjunction with the appendix. Figure 1-5 The implementation process of this invention is further described in detail with specific examples:

[0039] Step 1) First, perform initial coarse mesh generation on the geometric model of the simulation object. In this embodiment, the initial coarse mesh generation size is preferably 1 wavelength. Figure 1 This shows an initial coarse mesh cell obtained from the subdivision.

[0040] Step 2) as Figure 2 As shown, first, take the midpoint of each edge of the initial coarse mesh unit, and then connect the midpoints in the same triangular face with a straight line. This will result in four similar sub-tetrahedrons at the vertex of the initial coarse mesh unit. These four sub-tetrahedrons are denoted as T1, T2, T3, and T4.

[0041] Step 3) as Figure 3 As shown, the four sub-tetrahedrons T1, T2, T3, and T4 in the initial coarse mesh unit are cut off to obtain the octahedrons that are retained inside.

[0042] Step 4) For the internal octahedron, according to Figure 4 The two parallelograms shown in the shaded area divide the internal octahedron into four additional sub-tetrahedrons: T5, T6, T7, and T8.

[0043] Step 5) Through steps 1) to 4), the initial coarse mesh element can be refined into 8 sub-tetrahedrons T1, T2, T3, T4, T5, T6, T7, and T8. Among them, T1, T2, T3, and T4 are sub-tetrahedrons located at the vertices of the initial coarse mesh element, and T5, T6, T7, and T8 are sub-tetrahedrons divided from the internal octahedron. By performing the above operation on each coarse mesh element, the entire initial coarse mesh can be refined once. The above operation can also be performed again on the refined mesh to achieve further refinement of the refined mesh. In electromagnetic-thermal-mechanical multiphysics simulation, this embodiment preferably refines the initial coarse mesh 3-4 times.

[0044] Step 6) Figure 5 As shown, taking the two-dimensional case as an example, the nested meshes for electromagnetic simulation and thermal-mechanical simulation obtained through the above mesh refinement process are displayed. In the two-dimensional case, tetrahedral mesh elements degenerate into triangular mesh elements. In the figure, circles represent vertices of coarse meshes, and solid dots represent vertices of dense meshes. In electromagnetic-thermal-mechanical multiphysics simulation, electromagnetic simulation uses dense meshes, while thermal-mechanical simulation uses coarse meshes.

[0045] Step 7) In electromagnetic-thermal-mechanical multiphysics simulation, electromagnetic losses can cause heat generation. Therefore, information needs to be transferred between electromagnetic and thermal simulations. In this invention, the dense mesh of the electromagnetic simulation and the coarse mesh of the thermal and mechanical simulations are nested together, such as... Figure 5 As shown, since the vertices of the coarse mesh used in thermal simulation inevitably overlap with some vertices of the dense mesh used in electromagnetic simulation, we can first find the dense mesh cells where the coarse mesh nodes are located. After performing the electromagnetic simulation, we can substitute the electric field intensity E at the vertex of the dense mesh cell into the following formula to calculate the conductor loss P at the position of the coarse mesh vertex. c and dielectric loss P d :

[0046] P c =σ|E| 2 ,

[0047]

[0048] Where σ is the conductivity, D is the electric displacement vector, D = εE, ε represents the dielectric constant, and t is the time variable. Then P c +P d As the heat source at the vertex of the coarse mesh, the electromagnetic-thermal-mechanical multiphysics simulation can be achieved by using the coarse mesh and the finite element method, just like traditional thermal and mechanical simulations.

[0049] The effects of the present invention will be further explained below with reference to simulation experiments.

[0050] In this experiment, the nested mesh technique for rapid simulation of electromagnetic-thermal-mechanical multiphysics fields proposed in this invention was used with and without the technique to test the results. Figure 6 The electromagnetic-thermal-mechanical multiphysics simulation of the high-power microwave irradiation filter structure shown was performed, and the computation time of the two simulations was compared to verify the effectiveness of the present invention.

[0051] In this example, the high-power microwave irradiation direction is along the -z direction, the polarization direction is the +x direction, the amplitude is 1MV / m, and the frequency is 4GHz. Figure 7 Figures (a) and (b) show the temperature distribution of the filter surface at 10 ns obtained by using and not using the method of the present invention, respectively, and the two are in perfect agreement. Figure 8 Figures (a) and (b) show the displacement distributions of the filter surface obtained using and without the method of this invention, respectively, and the two distributions are in perfect agreement. This demonstrates that the method of this invention does not affect the simulation accuracy. Furthermore, in this example, the computation time using this method is 9800 seconds, while the computation time without this method is 13523 seconds, effectively proving that this invention can effectively improve the efficiency of electromagnetic-thermal-mechanical multiphysics simulations.

[0052] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0053] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A nested mesh generation method for rapid simulation of electromagnetic-thermal-mechanical multiphysics fields, characterized in that, Includes the following steps: (1) Set the initial coarse mesh size, and divide the geometric model of the simulation object according to the size to obtain the initial coarse mesh element; (2) Take the midpoint of each edge in the initial coarse grid cell, and then connect the midpoints in the same triangular face with a straight line to obtain four sub-tetrahedrons located at the vertices of the initial coarse grid cell with similar shapes to the initial coarse grid cell, denoted as T1, T2, T3, and T4. (3) Trim the sub-tetrahedrons T1, T2, T3 and T4 located at the vertices of the initial coarse mesh cells to obtain the octahedrons with the interior retained; (4) Divide the octahedron into four sub-tetrahedrons by using the two parallelograms formed inside the octahedron as the cutting planes, and denot them as T5, T6, T7 and T8. (5) Perform steps (2)-(4) on each initial coarse mesh element to obtain 8 tetrahedrons T1-T8 respectively, which realizes the first refinement of the entire initial coarse mesh. Set the number of refinement according to the actual needs of electromagnetic simulation. Perform the same operation as the initial coarse mesh element refinement on the mesh after the previous refinement until the preset number of refinement is reached to obtain a dense mesh. (6) Electromagnetic simulation was performed using a dense grid to obtain the electric field distribution; (7) Locate the dense grid cells containing the coarse grid nodes. After performing electromagnetic simulation, use the electric field intensity E at the vertices of the dense grid cells to calculate the conductor loss P at the vertices of the coarse grid. c and dielectric loss P d , will P c +P d The heat source at the vertex of the coarse mesh is used as the initial coarse mesh and the finite element method to perform thermal and mechanical simulations, thereby realizing electromagnetic-thermal-mechanical multiphysics simulation.

2. The method according to claim 1, characterized in that: The initial coarse mesh size mentioned in step (2) is 1-3 times the wavelength.

3. The method according to claim 1, characterized in that: Step (4) refers to dividing the octahedron by using two parallelograms formed inside the octahedron as tangents. Specifically, it means dividing the octahedron by using any two perpendicularly intersecting parallelograms formed inside the octahedron as tangents.

4. The method according to claim 1, characterized in that: Step (5) describes setting the number of refinements according to the actual needs of electromagnetic simulation, so that the size of the refined mesh is reduced to 0.1 times the wavelength to meet the requirements of electromagnetic simulation.

5. The method according to claim 1, characterized in that: The dense mesh mentioned in step (5) is obtained by performing steps (2)-(4) on the initial coarse mesh unit to obtain the first fine mesh. The first fine mesh is regarded as the initial coarse mesh and steps (2)-(4) are performed again to obtain the second fine mesh. Then, the second fine mesh is regarded as the initial coarse mesh and steps (2)-(4) are performed again to obtain the third fine mesh. This process is repeated until the preset number of refinements is completed.

6. The method according to claim 1, characterized in that: The conductor loss P at the coarse grid vertex position in step (7) c and dielectric loss P d The result is obtained by calculation using the following formula: P c =σE 2 , Where σ is the conductivity, D is the electric displacement vector, D = εE, ε represents the dielectric constant, and t is the time variable.

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