An electromagnetic scattering simulation method for microstrip antennas based on multi-resolution preprocessing

Abstract

The present invention belongs to the field of electromagnetic simulation technology, and specifically provides an electromagnetic scattering simulation method for microstrip antennas based on multi-resolution preprocessing, which is used to complete the electromagnetic scattering simulation calculation of microstrip structure targets, accelerate iterative convergence while ensuring the simulation calculation accuracy, and effectively reduce the memory requirement. The present invention introduces multi-resolution (MR) preprocessing on the basis of the global coupled multiple unknown equation (global MTF). First, the global MTF is constructed and the linear equation is symmetrized; then the MR-global MTF is constructed; finally, the unknown coefficient vector is obtained by solving the equation, and then the electromagnetic scattering of the microstrip structure target is calculated. The symmetrization method proposed by the present invention can reduce the memory requirement by nearly half, and can further improve the matrix property through multi-resolution preprocessing, significantly accelerating the iterative convergence without affecting the numerical accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic simulation technology, and specifically provides a method for electromagnetic scattering simulation of a microstrip antenna based on multi-resolution preprocessing. Background Art

[0002] A microstrip patch antenna is composed of a closely contacted open metal sheet and a closed dielectric body. Its electromagnetic scattering characteristics have important research value in aspects such as antenna design and target recognition. Computational electromagnetics provides powerful electromagnetic simulation technology for this purpose. Among them, the global multitrace formulation (global MTF) divides the microstrip structure target into a metal sheet and a dielectric body by introducing an infinitesimal virtual gap, and then defines unknowns for the meshes of each part. The processing method is flexible and the calculation result is accurate. For example, in the literature “S. Lasisi, T. M. Benson, G. Gradoni, M. Greenaway and K. Cools, “A fast converging resonance-free global multi-trace method for scattering by partially coated composite structures,” IEEE Trans. Antennas Propag., vol. 70, no. 10, pp. 9534 - 9543, 2022”. However, global MTF belongs to the first-kind Fredholm integral equation, and the condition number of the impedance matrix increases rapidly with the refinement of the mesh, which hinders the convergence of iterative calculations. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for electromagnetic scattering simulation of a microstrip antenna based on multi-resolution preprocessing, which is used to complete the electromagnetic scattering simulation calculation of the microstrip structure target, accelerate iterative convergence while ensuring the simulation calculation accuracy, and effectively reduce the memory requirement.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A method for electromagnetic scattering simulation of a microstrip antenna based on multi-resolution preprocessing, characterized by including the following steps:

[0006] Step 1. Divide the microstrip structure target into an open metal sheet and a closed dielectric body with an infinitesimal virtual gap, discretize the surface of each part using conformal triangular meshes, and define RWG basis functions within the discrete triangular element pairs.

[0007] Step 2. For the metal and dielectric parts respectively, use the mesh aggregation method to generate macro-elements with irregular shapes and construct stacked meshes;

[0008] Step 3. For the metal and dielectric parts respectively, define the gRWG (generalized RWG) basis functions within the macro-element pairs. Utilize the charge conservation of the inter-layer gRWG bases to express the gRWG bases of the l-th layer as a linear combination of the gRWG bases of the (l - 1)-th layer, where l = 2, 3,..., L, and L is the number of layers of the stacked meshes (L = Y + 1, and Y is the number of mesh aggregations). The gRWG bases of the first layer degenerate to the RWG bases;

[0009] Step 4. For the metal and dielectric parts respectively, use singular value decomposition to decompose the gRWG bases of the l-th layer into curl bases and divergence-free bases, and the obtained result is the MR (multi-resolution) basis functions of the l-th layer;

[0010] Step 5. Use the recurrence relation to generate the global RWG-MR transformation matrix that converts the RWG bases of the first layer to all the MR bases of the first L layers;

[0011] Step 6. Construct the global MTF and symmetrize this linear equation;

[0012] Step 7. Based on the symmetrized global MTF, use the global RWG-MR transformation matrix to construct the MR-global MTF and calculate the electromagnetic scattering of the microstrip structure target.

[0013] Furthermore, the specific process of Step 5 is as follows:

[0014] Let the material label a ∈ {d, c}, where d represents the dielectric and c represents the metal;

[0015] For the part of material a of the microstrip structure target, represents the current gRWG-MR transformation matrix of the l-th layer, represents the current gRWG basis reconstruction matrix between the (l - 1)-th layer and the l-th layer, represents the transformation matrix between the current RWG bases of the first layer and all the current MR bases of the first l layers. Then is expressed as:

[0016]

[0017] For the dielectric part of the microstrip structure target, let the transformation matrix between the magnetic current RWG bases of the first layer and all the magnetic current MR bases of the first l layers be satisfying

[0018] Let the global RWG-MR transformation matrix be The matrix blocks on its main diagonal are successively The remaining part is a zero matrix.

[0019] Furthermore, in step 6, the symmetrization process is as follows:

[0020] In the impedance matrix, multiply the matrix block containing the integral operator by the imaginary number ±j;

[0021] In the unknown coefficient vector, multiply the magnetic current vector by the imaginary number j;

[0022] In the excitation vector, multiply the magnetic field vector by the imaginary number j;

[0023] Symmetrizing the global MTF can reduce the memory consumption of the matrix by nearly half and lower the memory requirement.

[0024] Furthermore, the specific process of step 7 is as follows:

[0025] Let the impedance matrix obtained by discretely symmetrizing the global MTF with the RWG basis be Z RWG , C be the unknown coefficient vector, and V be the excitation vector. Then the linear equation is Z RWG ·C = V;

[0026] Multiply Z by the global RWG-MR transformation matrix RWG and its transpose matrix to obtain the MR basis impedance matrix

[0027]

[0028] Select the elements on the diagonal of Z MR , take the reciprocal of the square root of the element value, and construct a diagonal matrix D -12 with the same dimension size; then use D -12 to perform diagonal preprocessing on the MR basis matrix equation to obtain the MR-global MTF as:

[0029]

[0030] where is the unknown coefficient vector after multi-resolution preprocessing;

[0031] Use the restarted generalized minimum residual method (GMRES) to iteratively solve the equation to obtain Then the original unknown coefficient vector C is: It is used to calculate the electromagnetic scattering of the microstrip structure target.

[0032] It should be noted that the core creation of the present invention lies in: introducing multi-resolution (MR) preprocessing based on the global multi-trace formulation (global MTF) of a multi-unknown equation. First, construct the global MTF and symmetrize the equation; then construct the MR-global MTF equation; finally, solve the equation to obtain the unknown coefficient vector, and further calculate the electromagnetic scattering of the microstrip structure target. Among them, the basic theory of the global multi-trace formulation (global MTF) of a multi-unknown equation is well-known prior art in the field, and the present invention will not elaborate further. References can be made to the literature “S. Lasisi, T. M. Benson, G. Gradoni, M. Greenaway and K. Cools, “A fast converging resonance-free global multi-trace method for scattering by partially coated composite structures,” IEEE Trans. Antennas Propag., vol. 70, no. 10, pp. 9534-9543, 2022”, “F. P. Andriulli, F. Vipiana, and G. Vecchi, “Hierarchical bases for nonhierarchic 3-D triangular meshes,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2288-2297, 2008”, “F. Vipiana and G. Vecchi, “A novel, symmetrical solenoidal basis for the MoM analysis of closed surfaces,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 1294-1299, 2009” and “F. Vipiana, P. Pirinoli, and G. Vecchi, “A multi-resolution method of moments for triangular meshes,” IEEE Trans. Antennas Propag., vol. 53, no. 7, pp. 2247-2258, 2005”.

[0033] Based on the above technical solutions, the beneficial effects of the present invention are as follows:

[0034] The present invention provides a method for electromagnetic scattering simulation of microstrip antennas based on multi-resolution preprocessing, which is used to calculate the electromagnetic scattering of microstrip structure targets. Compared with the traditional globally coupled multiple unknown equations, the proposed symmetrization method can reduce the memory requirement by about half, and the matrix property can be further improved through multi-resolution preprocessing, significantly accelerating the iterative convergence without affecting the numerical accuracy. Description of the Drawings

[0035] Figure 1 It is a geometric model diagram of a cylindrical microstrip structure in an embodiment of the present invention.

[0036] Figure 2 It is a polymerized grid diagram generated by MR preprocessing in an embodiment of the present invention.

[0037] Figure 3 It is a GMRES(400) iteration error diagram of a cylindrical microstrip structure in an embodiment of the present invention.

[0038] Figure 4 It is a bistatic RCS diagram of a cylindrical microstrip structure in an embodiment of the present invention. Detailed Embodiment

[0039] To make the purpose, technical solution and beneficial effects of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and embodiments.

[0040] This embodiment provides a method for electromagnetic scattering simulation of microstrip antennas based on multi-resolution preprocessing. Taking the electromagnetic scattering of a cylindrical microstrip structure as an example, the bistatic radar cross section (RCS) is calculated. The specific steps are as follows:

[0041] Step 1. The geometric model of the cylindrical microstrip structure is as Figure 1 shown. The height of the dielectric cylinder is 30 mm, the outer radius is 10 mm, the inner radius is 6 mm, the relative dielectric constant is ε r = 4.0, and the relative permeability is μ r = 1.0. The inner wall of the dielectric cylinder is exactly covered by an open metal surface, and a smaller open metal surface with a length of 20 mm and a width of 5π mm is also covered on the outer wall.

[0042] The microstrip structure is divided into open metal sheets and closed dielectric bodies by infinitesimal virtual gaps. Assume that a plane wave (E i , H i ) is incident along the -z axis, the frequency is 5 GHz, and the wavelength in the medium is λ d . The surface of each part is discretized using conformal triangular meshes, and λ d / 20 is the average dissection size; the electromagnetic current RWG basis functions are defined within the triangle element pairs, and the total number of unknowns is 11732;

[0043] Step 2. For the metal and dielectric parts respectively, use the mesh aggregation scheme, aggregate once, and aggregate the first-layer triangle elements into the second-layer irregularly shaped macro elements to obtain a set of two-layer meshes; the aggregated mesh diagram generated by MR preprocessing is as Figure 2 shown, where each gray level represents a macro element;

[0044] Step 3. For the metal and dielectric parts respectively, define the gRWG basis within the macro element pairs, and use the charge conservation of the inter-layer gRWG basis to represent the second-layer gRWG basis as a linear combination of the first-layer RWG basis;

[0045] Step 4. For the metal and dielectric parts respectively, use singular value decomposition to decompose the first-layer RWG basis and the second-layer gRWG basis into curl bases and divergence-free bases, and the obtained results are the first-layer and second-layer MR basis functions;

[0046] Step 5. Use the recurrence relation to generate the global transformation matrix that transforms the first-layer RWG basis into all the MR bases of the first two layers The matrix blocks on the main diagonal are successively The remaining part is a matrix of all zeros;

[0047] Step 6. Construct the global MTF and symmetrize the linear equation;

[0048] Step 7. Multiply both sides of the symmetrized global MTF by , and then combine diagonal preprocessing to obtain the MR-global MTF; use the restarted GMRES iteration to solve the equation, and then calculate the bistatic RCS of the target; specifically as follows:

[0049] Let the impedance matrix obtained by discretizing the symmetrized global MTF with the RWG basis be Z RWG , C is the vector of unknown coefficients, V is the excitation vector, and the linear equation is Z RWG ·C = V; use the global RWG-MR transformation matrix and its transpose matrix to multiply with Z RWG to obtain the MR basis impedance matrix Use the reciprocal of the square root of the elements on the diagonal of Z MR to construct the diagonal matrix D -1 / 2 , and then perform diagonal preprocessing on the MR basis matrix equation to obtain the MR-global MTF as follows

[0050]

[0051] Using the restarted Generalized Minimal RESidual algorithm (GMRES(400)) with m = 400, setting 0.001 as the iteration convergence threshold, and iteratively solving the equation to obtain the vector Then the unknown coefficient vector Use C to calculate the bistatic RCS of HH polarization.

[0052] In this embodiment, taking global MTF and the globally diagonal preconditioned global MTF (DP-global MTF) as comparative examples, the residual errors of global MTF, DP-global MTF, and MR-global MTF at each iteration are as Figure 3 shown; the condition number of the global MTF impedance matrix is 3404.8, and it is required to iterate 2184 times to reach the convergence threshold of 0.001; the condition number of the DP-global MTF impedance matrix is 2727.4, reduced to 1492 iterations, having a certain ability to promote iteration convergence; while the condition number of the MR-global MTF impedance matrix is 710.8, only 105 iterations are needed, which can efficiently improve the iteration convergence characteristics of the system; thus, it can be seen that the impedance matrix of global MTF is relatively ill-conditioned under relatively dense meshing conditions, however, MR preconditioning can significantly accelerate iteration convergence, with a better effect than DP. Then, using the software FEKO, for this cylindrical microstrip structure, take λ d / 50 as the meshing size, then the total number of triangular elements is 21890, and calculate the RCS; referring to the data of FEKO, the relative root-mean-square error (RMSE) of the RCS of global MTF is 0.0044, the RMSE of the RCS of DP-global MTF is 0.0036, and the RMSE of the RCS of MR-global MTF is 0.0040, and the errors are all at the same order of magnitude, indicating similar precision; the bistatic RCS curve of the cylindrical microstrip structure is as Figure 4 shown, and the RCSs of the three methods are all in good agreement with the FEKO reference results; thus, it can be seen that the use of the preconditioning method will not significantly change the numerical calculation accuracy.

[0053] The above is only the specific implementation manner of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or similar-purpose alternative features; all the features disclosed, or all the steps in any method or process, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for electromagnetic scattering simulation of a microstrip antenna based on multi-resolution preprocessing, characterized in that Including the following steps: Step 1. Divide the microstrip structure target into open metal sheets and closed dielectric bodies with infinitesimal virtual gaps, discretize the surfaces of each part using conformal triangular meshes, and define RWG basis functions within the pairs of the discretized triangular elements; Step 2. For the metal and dielectric parts respectively, use the mesh aggregation method to generate macro-elements with irregular shapes and construct hierarchical meshes; Step 3. For the metal and dielectric parts respectively, define gRWG basis functions within the macro-element pairs, and utilize the charge conservation of the inter-layer gRWG bases to express the gRWG basis of the l-th layer as a linear combination of the gRWG bases of the (l - 1)-th layer, where l = 2, 3,..., L and L is the number of layers of the hierarchical meshes; Step 4. For the metal and dielectric parts respectively, decompose the gRWG basis of the l-th layer into curl bases and irrotational bases using singular value decomposition, and the obtained result is the MR basis function of the l-th layer; Step 5. Generate the global RWG-MR transformation matrix that transforms the RWG basis of the first layer into all the MR bases of the first L layers using recurrence relations; Step 6. Construct the global MTF and symmetrize this linear equation; Step 7. Based on the symmetrized global MTF, construct the MR-global MTF using the global RWG-MR transformation matrix and calculate the electromagnetic scattering of the microstrip structure target.

2. The electromagnetic scattering simulation method of a microstrip antenna based on multi-resolution preprocessing according to claim 1, characterized in that, The specific process of Step 5 is as follows: Let the material label a ∈ {d, c}, where d represents dielectric and c represents metal; For the material a part of the microstrip structure target, Denote the current gRWG-MR conversion matrix of the l-th layer, Denote the current gRWG basis reconstruction matrix between the (l - 1)-th layer and the l-th layer, Denote the conversion matrix between the RWG basis of the current of the first layer and all the MR bases of the currents of the previous l layers, then It is expressed as: For the dielectric part, let the conversion matrix between the first-layer magnetic current RWG basis and all magnetic current MR bases of the previous l layers be Satisfy Let the global RWG-MR transformation matrix be The matrix blocks on its main diagonal are successively The remaining part is an all-zero matrix.

3. The electromagnetic scattering simulation method of a microstrip antenna based on multi-resolution preprocessing according to claim 1, characterized in that In Step 6, the symmetrization process is as follows: In the impedance matrix, multiply the matrix block containing the integral operator by the imaginary number ±j; In the unknown coefficient vector, multiply the magnetic current vector by the imaginary number j; In the excitation vector, multiply the magnetic field vector by the imaginary number j.

4. The electromagnetic scattering simulation method of a microstrip antenna based on multi-resolution preprocessing according to claim 1, characterized in that, The specific process of Step 7 is as follows: Let the impedance matrix obtained by global MTF of the RWG-based discrete symmetricization be Z RWG , C be the vector of unknown coefficients, and V be the excitation vector; Using the global RWG-MR transformation matrix Construct the MR-based impedance matrix: Select Z MR For the elements on the diagonal, take the reciprocal of the square root of the element values to construct a diagonal matrix D with the same dimension size -12 ; Then use D -12 Perform diagonal preprocessing on the MR basis matrix equation to obtain the MR-global MTF as: Among them, is the unknown coefficient vector for multi-resolution preprocessing; The equation is iteratively solved using the restarted generalized minimal residual algorithm to obtain Then the original unknown coefficient vector C is:[[]] It is used to calculate the electromagnetic scattering of the microstrip structure target.[[]]

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