SDIE-based method for solving electromagnetic field of IBC object in layered medium through moment method

Abstract

The invention provides a moment method solving method for an electromagnetic field of an IBC object in a layered medium based on SDIE. The method comprises the following steps that modeling is conducted on a scatterer to be simulated and a background layered medium of the scatterer in COMSOL; mesh generation is carried out on the surface of the scatterer, meshes cannot be distributed in a cross-layer mode, and for areas in different layers, the corresponding meshes adopt different sampling rates to guarantee the calculation accuracy of results; compared with a finite element method for solving such problems, the method has the advantages that mesh generation does not need to be performed on a background medium, and the degree of freedom and memory used for solving an integral equation are far smaller than those used by the finite element method; the method shows excellent calculation efficiency and calculation precision in actual calculation examples.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic field modeling and simulation, and in particular relates to a method for solving the electromagnetic field of an IBC object in a layered medium using a moment method based on SDIE. Background Art

[0002] With the improvement of the integration and miniaturization of integrated circuits, layered dielectric structures appear in a large number of integrated circuits, and are used in antenna design, microwave device design, and various high-frequency circuits. Accurate and fast electromagnetic field solutions for layered dielectric structures can greatly assist circuit design and reduce the cycle and cost of circuit design.

[0003] In integrated circuit design, impedance boundary condition conductors (IBC) are widely used in layered dielectric substrates. For field-path simulation of such problems, the finite element method, finite-difference time-domain method, moment method and hybrid numerical algorithms can be used to solve them. These algorithms have been widely used in EDA software, greatly assisting scientific research and industrial production.

[0004] For the finite element method and the finite difference time domain method, when solving the problem of layered media, they both need to mesh the background medium, which usually leads to the simulation process requiring more computer memory and computing time; while for the moment method, due to the introduction of Green's function, it only needs to mesh the surface of the IBC object, which greatly reduces the scale of the problem to be solved and improves the solution efficiency.

[0005] Secondly, the moment method divides the two-dimensional surface mesh, which has a lower dimension and less computational complexity than the three-dimensional mesh of other numerical algorithms. After the introduction of SDIE, the moment method can directly list the surface integral equation according to the IBC surface impedance boundary conditions, and construct the relationship between the IBC outer surface current and the surface magnetic current, without the need to construct the surface integral equation for the inner surface; and for common PEC and PMC objects, SDIE can directly solve related problems by adjusting the size of the surface impedance, which has good universality.

[0006] In view of this, it is very meaningful to propose a moment method solution for the electromagnetic field of an IBC object in a layered medium based on SDIE. Summary of the invention

[0007] The present invention provides a method for solving the electromagnetic field of an IBC object in a layered medium by the method of moment based on SDIE, which can quickly and accurately solve the current and magnetic flow on the surface of the IBC object; the algorithm can also give an accurate solution for the electromagnetic field in the solution area. Compared with the mature finite element electromagnetic simulation software COMSOL, the invention has obvious advantages in computing efficiency and computing memory consumption, and has broad application prospects.

[0008] In a first aspect, the present invention proposes a method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE, the method comprising the following steps:

[0009] Model the scatterer to be simulated and its background layered medium in COMSOL;

[0010] When meshing the scatterer surface, the mesh cannot be distributed across layers, and for areas in different layers, the corresponding meshes should use different sampling rates to ensure the calculation accuracy of the results;

[0011] The mesh is imported into the SDIE algorithm for moment method solution. Compared with the finite element method for solving such problems, since there is no need to mesh the background medium, the degrees of freedom and memory used to solve the integral equation are much smaller than the finite element method. This method shows excellent computational efficiency and accuracy in actual examples.

[0012] Preferably, the model is firstly built and meshed in COMSOL software, and then the mesh is exported, and the SDIE algorithm is used to perform moment method solution and electromagnetic parameter simulation.

[0013] Further preferably, when modeling in COMSOL, it is necessary to mark the position of the plane layering and model the shape and position of the scatterer.

[0014] Further preferably, for the model after modeling, the wavelength of each layer of area must be determined according to the electromagnetic parameters of each layer of the medium, and the sampling rate of the grid must be further determined, so as to ensure the accuracy and reliability of the final numerical simulation.

[0015] Further preferably, the scatterer surface is divided into triangular meshes, the divided meshes cannot cross layers, and the overall divided meshes are guaranteed to be conformal meshes to ensure the normal continuity of the surface current.

[0016] Further preferably, after the meshing is completed, the result of the meshing is exported, which includes the nodes of the mesh and their corresponding three-dimensional coordinates, and the node numbers of the triangular mesh.

[0017] Further preferably, the grid is imported into the SDIE algorithm. After completing the relevant settings, the algorithm can obtain the corresponding model information for the corresponding electromagnetic simulation.

[0018] The relevant settings include: setting the electromagnetic parameter information of the scatterer and the background medium, the simulation frequency, the electromagnetic excitation source and the position information of the field receiving point.

[0019] In the second aspect, the present invention adopts a method for solving the electromagnetic field of an IBC object in a layered medium using the moment method based on SDIE, mainly in that:

[0020] SDIE is a three-dimensional method-of-moment solver that can directly list the surface integral equation based on the surface impedance boundary conditions of the IBC object and construct the relationship between the outer surface current and the surface magnetic current of the IBC object. It does not need to construct the surface integral equation for the inner surface. After obtaining the corresponding surface current and surface magnetic current, the electromagnetic field in the corresponding spatial area is calculated based on the field type Green's function in the layered medium.

[0021] Compared with the prior art, the beneficial results of the present invention are:

[0022] Compared with the finite element method and the finite difference time domain method, the SDIE equation is mainly constructed based on the surface integral equation. In essence, it only needs to mesh the surface of the object, reducing the degree of freedom of the background medium in the equation, greatly reducing the scale of solution. After introducing the impedance boundary condition of the IBC object, it is only necessary to solve the equivalent current and equivalent magnetic current on the outer surface of the IBC. There is no need to list the integral equation for the inner surface of the IBC object. For PEC or PMC objects, SDIE can directly solve related problems by adjusting the size of the surface impedance, and has good universality. The present invention can be used to analyze the electromagnetic field problems of IBC objects in layered media, and can be applied to geophysics and EDA simulation design; compared with finite element simulation software, it has very obvious advantages in computing efficiency and computing resource consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present invention. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0024] Figure 1 A schematic flow chart of a method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to an embodiment of the present invention;

[0025] Figure 2 A schematic diagram of a simulation structure of a method for solving the electromagnetic field of an IBC object in a layered medium based on SDIE according to an embodiment of the present invention;

[0026] Figure 3 This is a calculation example of an IBC sphere in a layered medium according to an embodiment of the present invention. An electric dipole source is used for excitation, and the magnitude of the electromagnetic field in the layered medium is calculated and compared with COMSOL.

[0027] Figure 4 Based on Figure 2 The model uses COMSOL and SDIE simulation to obtain the three-dimensional field intensity component result diagram of the electric field at the receiving field point;

[0028] Figure 5 Based on Figure 2 The model uses COMSOL and SDIE simulation to obtain the three-dimensional field intensity component result diagram of the magnetic field at the receiving field point; DETAILED DESCRIPTION

[0029] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are shown by illustrative specific embodiments in which the present invention can be put into practice. To this end, directional terms, such as "top", "bottom", "left", "right", "up", "down", etc., are used with reference to the orientation of the figures described. Because the parts of the embodiments can be positioned in several different orientations, directional terms are used for the purpose of illustration and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present invention is defined by the appended claims. Figure 1 It is shown that the embodiment of the present invention discloses a method for solving the electromagnetic field of an IBC object in a layered medium by the method of moment based on SDIE, such as Figure 1 As shown, the method comprises the following steps:

[0030] S1. First, use COMSOL to model the IBC object to be simulated and its background layered medium, and then mesh the surface of the IBC object;

[0031] by Figure 3 Take the layered medium shown in the figure as an example, which contains three layers of medium, and the layer numbers increase from bottom to top. For the plane layered medium, each layer is infinite space in the horizontal direction and layered in the vertical direction. Therefore, in the top and bottom layers, there is infinite space in the +z direction and -z direction. Finally, the background medium and IBC object are modeled, and their electromagnetic parameters are shown in Table 1;

[0032] area Relative dielectric constant Relative magnetic permeability Conductivity First floor 1 1 0.01 Second floor 4.4 1 0.01 Third floor 1 1 0.01 IBC 1 1 58130000

[0033] Table 1

[0034] S2. Mesh the IBC object. Pay attention to the electromagnetic parameters of the layer where the IBC is located to determine the sampling rate of the mesh to ensure the calculation accuracy of the numerical results. Then export the mesh file after the mesh is finished. Take this example as an example. At 2GHz, the IBC is in the first layer, and the wavelength of the electromagnetic wave in this layer is 0.15m. In order to ensure the calculation accuracy of the numerical algorithm, the mesh sampling rate should be greater than 10PPW (Points Per Wavelength), that is, a mesh with a size less than 0.015m should be used for meshing. Finally, export the mesh file.

[0035] S3. Import the grid into the SDIE algorithm, set the parameters of electromagnetic excitation, background medium and field receiving point, and then accurately solve the surface current and surface magnetic current of the IBC object. Then introduce the Green's function in the layered medium to achieve efficient and accurate electromagnetic calculation of the field strength at any position in the background.

[0036] In this embodiment, the position of the electric dipole is (-0.05, 0, 0.01) m, and its polarization direction is (1, 1, 1), and the receiving field point is set on the plane of z = 0.05 m with distribution x, y∈[-0.02, 0.02] m. For the IBC sphere, its center position is set at (0, 0, 0.025) m, and the radius is set to 0.01 m. These model settings are the same in COMSOL and SDIE algorithms; the difference is that since two algorithms are used to calculate the models respectively, the meshes they are based on are not the same. For COMSOL, it uses a tetrahedral mesh, while for SDIE, it uses a triangular mesh. In particular, for COMSOL, it is based on the finite element method for calculation, and it needs to use a perfect matching layer for spatial truncation of the three-dimensional area of ​​the calculation. The thickness of the perfect matching layer is determined by the wavelength of each layer of the layered medium. Usually, the thickness of the perfect matching layer should be greater than 0.5 times the wavelength, but it cannot be set too large, resulting in a large calculation area and a waste of computing resources; and for the SDIE algorithm, due to the introduction of the layered medium Green's function, the radiation boundary conditions of the calculation area are automatically met, and it does not require special treatment of the calculation boundary. It can also be seen that the SDIE algorithm is simple in modeling such problems. After solving the SDIE equation using the moment method, the equivalent current and equivalent magnetic current on the outer surface of the IBC can be obtained, and then the field-type Green's function is used to calculate the electromagnetic field at any position in the space, thereby completing the solution of the entire problem.

[0037] Furthermore, in the use of COMSOL and SDIE to complete the Figure 2The solution of the IBC model shown in the figure has electric and magnetic field results. Figure 4 and Figure 5 As shown, it gives the comparison results of the real and imaginary parts of the three-dimensional components of the field intensity. From the results, the results of the two are very consistent. The calculation results of the two are further quantified. For the calculation results of the electric field, the relative error between the two is 0.70%; for the calculation results of the magnetic field, the relative error between the two is 0.81%, which verifies the calculation accuracy of the algorithm proposed by the present invention. Further comparison, the calculation resources consumed by the two are compared as shown in Table 2. The equation solved by COMSOL has a degree of freedom of one hundred thousand times that of SDIE, and correspondingly, its memory consumption is also one thousand times that of SDIE; and from the perspective of the CPU time consumed, SDIE only consumes about one tenth of the time of COMSOL to complete the solution of the problem. From the comparison of numerical results, the SDIE algorithm has obvious advantages over COMSOL in solving the electromagnetic field problem of IBC objects in the layer. It can use less computer memory and shorter CPU calculation time to obtain the calculation results with the same accuracy as COMSOL. The algorithm has great application value for multi-physics simulation and EDA circuit design.

[0038] Software / Methodology Degrees of freedom (unknown quantity) CPU Time Memory consumption COMSOL 50212950 2633s 401.41GB SDIE 456 266s 97.6MB

[0039] Table 2

[0040] The present invention proposes an algorithm pre-processing method for solving the electromagnetic field of an IBC object in a layered medium based on SDIE. The scatterer to be simulated and its background layered medium are modeled in COMSOL. The surface of the scatterer is meshed, the meshes cannot be distributed across layers, and for areas in different layers, the corresponding meshes should use different sampling rates to ensure the calculation accuracy of the results. Excellent calculation accuracy is shown in actual examples.

[0041] Secondly, the present invention introduces the SDIE algorithm into the electromagnetic field solution of IBC objects in layered media. Compared with COMSOL, a mature multi-physics field simulation software based on finite element algorithm, the algorithm proposed by the present invention has great advantages in calculation speed and computing resource consumption while obtaining results similar to COMSOL. This shows that the present invention can greatly reduce the time spent on early industrial simulation in multi-physics field calculations and EDA, shorten the R&D cycle, and is of great help in improving scientific research and R&D efficiency.

[0042] The above description is only a preferred embodiment of the present invention and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the above features are replaced with the technical features with similar functions disclosed in the present invention (but not limited to) to form a technical solution.

Claims

1. A method for solving the electromagnetic field of an IBC object in a layered medium using the moment method based on SDIE, characterized in that: The method comprises the following steps: Model the scatterer to be simulated and its background layered medium in COMSOL; When meshing the scatterer surface, the mesh cannot be distributed across layers. After determining the sampling rate, meshes of different sizes are used for meshing in different layers. The grid is imported into the SDIE algorithm for moment method solution. The SDIE algorithm constructs integral equations according to the impedance boundary conditions of the IBC object, and uses the moment method to directly solve the IBC surface current and magnetic current. In the algorithm post-processing, the Green's function in the layered medium is introduced to calculate the electric field and magnetic field of the model.

2. The method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to claim 1, characterized in that: First, the model is built and meshed in COMSOL software and its information is exported. The SDIE algorithm is used to perform moment method solution and electromagnetic parameter simulation.

3. The method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to claim 2, characterized in that: When modeling in COMSOL, the locations of the plane layers are marked, and then the shapes and locations of the scatterers are modeled.

4. The method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to claim 3, characterized in that: After the modeling is completed, the electromagnetic wave wavelength of the corresponding area is determined according to the electromagnetic parameters of each layer of the medium, and the grid size is determined by ensuring the sampling rate of the grid to complete the grid division.

5. The method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to claim 4, characterized in that: The surface of the IBC object is divided using a triangular mesh. The divided mesh cannot cross layers, and the overall divided mesh must be a conformal mesh to ensure the normal continuity of the surface current and surface magnetic current when crossing layers.

6. The method for solving the electromagnetic field of an IBC object in a layered medium using the method of moments based on SDIE according to claim 5, characterized in that: The results of the completed mesh generation are exported, including the mesh nodes and their corresponding three-dimensional coordinates, as well as the node numbers of the triangular mesh.

7. According to the method of moment method for solving the electromagnetic field of an IBC object in a layered medium based on SDIE according to claim 6, the grid is imported into the SDIE algorithm, and after the relevant settings are completed, the algorithm reads the corresponding model information to perform the corresponding electromagnetic simulation The relevant settings include: Set the electromagnetic parameter information of the scatterer and background medium, the simulation frequency, the electromagnetic excitation source, and the location information of the field receiving point.

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