Method for realizing regional decomposition of electromagnetic field problem of dielectric fully-coated metal target

Abstract

A regional decomposition implementation method of electromagnetic field problem of a medium full-coated metal target, first, the medium full-coated metal target to be calculated is divided into a plurality of sub-domains which do not overlap each other according to the geometric structure characteristics, triangular elements are used to independently mesh the surface of each sub-domain to obtain the grid information of each sub-domain; RWG basis functions are constructed on the inner edges of the sub-domain grids, and MB-RWG basis functions are constructed at the boundary lines of adjacent sub-domains; PMCHWT and EFIE equations are established on the boundary surfaces of the model, and matrix equations are obtained by testing the area integral equations by selecting appropriate test basis functions; a preconditioning matrix is constructed, and the above matrix equations are preconditioned to obtain the current and magnetic current, and then the results are obtained by performing RCS calculation. In the present application, there are no line area integral terms and line-line integral terms in the calculation of the coefficient matrix, there is no internal penalty stabilization term, and the coefficient of the internal penalty stabilization term does not need to be determined; and the total number of unknowns at the boundary surfaces is not increased.

Description

Technical Field

[0001] The present invention relates to a technology in the field of electromagnetics, in particular to a method for realizing regional decomposition of an electromagnetic field problem of a dielectric fully coated metal target. Background Art

[0002] The increasing complexity of electromagnetic systems has brought greater difficulties to electromagnetic simulation. One of the more important issues is that the total number of unknown quantities in the discretized system is large, and the grid has obvious non-uniformity. As a result, conventional electromagnetic simulation methods often encounter slow convergence or even non-convergence problems when iteratively solving equations, and the reliability of the simulation results cannot be guaranteed.

[0003] Domain decomposition methods can effectively address convergence issues. Existing domain decomposition methods for surface integral equations typically use half Rao-Wilton-Glisson (hRWG) basis functions to expand the current and magnetic fluxes at the junctions of adjacent subdomains. Transmission conditions are imposed at the dividing lines between the subdomains to ensure continuity of the current and magnetic fluxes, and internal penalty stability terms are introduced to improve convergence. This domain decomposition method ensures weak continuity of the current and magnetic fluxes between subdomains, but it involves additional surface integrals or line-line integrals in the calculation of the coefficient matrix. The coefficients preceding the internal penalty stability terms vary in different frequency bands and equations, requiring individual determination for specific application scenarios. Another domain decomposition method for calculating dielectrically fully metal-coated targets employs the multitrace method. Two grids are used at the same interface, along with two sets of current and magnetic flux unknowns. Equations for these two sets of unknowns are established based on the equivalence principle or extinction theorem, and Robin transmission conditions are applied across the interface. This domain decomposition method increases the total number of unknowns at the interface. Summary of the Invention

[0004] To address the aforementioned shortcomings of the prior art, the present invention proposes a regional decomposition method for the electromagnetic field problem of a fully coated metal target using a multibranch Rao-Wilton-Glisson (MB-RWG) basis function to expand the current density in adjacent subdomains on the metal surface, and also expand the current density and magnetic flux density in adjacent subdomains at the interface between the dielectric and the background. Because the MB-RWG basis function exhibits normal continuity, the continuity of the current density and magnetic flux density at the boundary between adjacent subdomains is strictly guaranteed. Furthermore, when calculating the coefficient matrix, there are no line-area components or line-line integrals, and no internal penalty stability terms are required, eliminating the need to determine their coefficients. Furthermore, the total number of unknown quantities at the interface is not increased.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a method for realizing regional decomposition of an electromagnetic field problem of a dielectric fully-coated metal target. The method comprises the following steps: firstly, the dielectric fully-coated metal target to be calculated is divided into a plurality of non-overlapping subdomains according to geometric structure characteristics, and the surface of each subdomain is independently meshed using triangular units to obtain mesh information of each subdomain; RWG basis functions are constructed on the inner edges of the subdomain meshes, and MB-RWG basis functions are constructed at the boundaries of adjacent subdomains; appropriate surface integral equations, such as PMCHWT and EFIE equations, are established on the interface of the model, and appropriate test basis functions are selected to test the surface integral equations to obtain matrix equations; and finally, a preconditioning matrix is ​​constructed and the matrix equations are preconditioned. After solving the obtained current and magnetic current, RCS calculation is performed to obtain the result.

[0007] The MB-RWG basis functions guarantee the normal continuity of current density at the boundaries between adjacent subdomains on the metal surface, as well as the normal continuity of current density and magnetic flux density between adjacent subdomains at the interface between the dielectric and background regions. Because the hRWG basis functions are not used, no line-line integrals or line-area integrals are introduced when calculating the coefficient matrix. There are no internal penalty stability terms, and their coefficients do not need to be determined. Furthermore, only one set of meshes and unknowns is used at the interface.

[0008] The number of branches of the MB-RWG basis function is not fixed, but is determined by the difference in mesh density between two adjacent subdomains.

[0009] The MB-RWG basis functions are obtained by the following steps:

[0010] Step 1) Merge the points with the same coordinates at the boundary between subdomains in the original grid and mark the duplicate points with duplicate marks;

[0011] Step 2) Adjust the staggered points at the boundaries between subdomains so that the points of the coarse grid at the boundary line are aligned with some of the points of the fine grid, specifically including:

[0012] i) adjusting the coordinates of the coarse grid points on the boundary line between adjacent subdomains to the coordinates of the fine grid points closest to them;

[0013] ii) Project all points in the fine grid on the dividing line that do not overlap with the coarse grid points onto the edge of the coarse grid;

[0014] Step 3) Generate an MB-RWG basis function with a corresponding number of branches at the junction of adjacent subdomains, based on the difference in mesh resolution between them. For example, if the boundary between two adjacent subdomains, A and B, is Lab, and the length of the triangle edge of subdomain A on Lab is N times the length of the triangle edge of subdomain B on Lab, then generate an MB-RWG basis function with N branches.

[0015] The present invention relates to a system for implementing the above method, comprising: a subdomain division and meshing unit, a basis function generation unit, a matrix equation generation unit, a matrix equation solving unit, and a post-processing unit, wherein: the subdomain division and meshing unit performs appropriate regional block division according to the geometric structure characteristics of the object to be solved, and selects triangle units of appropriate size to independently mesh each subdomain to obtain mesh information of each subdomain; the basis function generation unit first searches for inner edges on the subdomain mesh according to the point numbers, triangle vertex numbers, and triangle edge number information on each subdomain mesh, Construct the RWG basis function in each subdomain; then, according to the semi-RWG basis function information on the grid of each subdomain, match and adjust the grid vertices at the boundary to obtain the MB-RWG basis function at the boundary of adjacent subdomains; the matrix equation generation unit establishes PMCHWT and EFIE equations on the interface of the object to be solved according to the equivalence principle, and uses the RWG basis function to expand the current density and magnetic flux density inside the subdomain; uses the MB-RWG basis function to expand the current density and magnetic flux density in the adjacent subdomains on the interface; uses the RWG and MB-RWG basis functions to test the equations and obtain the matrix equation The matrix equation solver generates the coefficient matrix in the unit according to the matrix equation Extract the self-coupling submatrix A of each subdomain i,i (i=1,2,…,N+1), generates a block diagonal preconditioned matrix The block diagonal preconditioned matrix P -1 At the same time, the matrix equation in the left-multiplication matrix equation generation unit On both sides of the matrix equation, we get the preconditioned matrix equation An iterative method (such as the GMRES method) is used to solve the preconditioned equations; the post-processing unit calculates the scattered field in the background area based on the RWG and MB-RWG coefficients of the current density and magnetic flux density on the interface between the dielectric body and the background to obtain the RCS result.

[0016] Technical Effects

[0017] The present invention uses the matrix equation generation unit to use the surface integral equation method to solve the electromagnetic field of the dielectric fully coated metal target. It uses RWG and MB-RWG basis functions to expand the current density on the metal surface, the current density and magnetic flux density on the interface between the dielectric and the background area. Compared with the existing conventional technical means, the technical details with significant improvements are as follows: the MB-RWG basis function is used to simultaneously expand the current density between adjacent subdomains on the metal surface, the current density and magnetic flux density between adjacent subdomains on the dielectric interface, rather than the commonly used semi-RWG basis function. In this way, when the regional decomposition method is used to analyze the dielectric fully coated metal target, the normal continuity of the current density and magnetic flux density is still satisfied between adjacent subdomains. In the calculation of the coefficient matrix When the element is , there are no line area integrals or line-line integrals, no internal penalty stability terms, and no need to determine their coefficients; nor does it increase the total number of unknowns at the interface. The iterative solution of the preconditioned matrix equation converges quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Flowchart of the present invention.

[0019] Figure 2 Schematic diagram of subdomain division and mesh generation for the computational object;

[0020] Figure 3 Schematic diagram of MB-RWG basis functions and subdomains;

[0021] Figure 4 Schematic diagram of RCS results calculated by the present invention, conventional non-domain decomposition, and simulation software FEKO within the range of φ=0 plane 0≤θ≤π;

[0022] Figure 5 Schematic diagram of RCS results calculated by the present invention, conventional non-domain decomposition, and simulation software FEKO within the range of θ=π / 2 plane and 0≤φ≤π;

[0023] Figure 6 Schematic diagram of the error convergence curve of the present invention and the traditional non-domain decomposition iteration when using the GMRES method to iteratively solve the matrix equation;

[0024] In the figure: 1 to 3 represent the first to third subdomains, where the third subdomain is composed of all MB-RWG basis functions, FEKO represents the calculation results of simulation software, MB-RWG-DDM represents the calculation results of the present invention, and RWG-SD represents the traditional non-domain decomposition calculation results. DETAILED DESCRIPTION

[0025] like Figure 1 As shown, this embodiment relates to a method for implementing regional decomposition of an electromagnetic field problem of a dielectric fully coated metal target, including the following steps:

[0026] Step 1) Divide the computational object into appropriate regions and mesh the surface of each sub-region independently using triangular elements;

[0027] like Figure 2 As shown in the figure, a simplified missile model with a dielectric fully coated with metal is first divided into two subdomains, named the first subdomain and the second subdomain from the beginning to the end. Each subdomain is meshed independently using triangular elements.

[0028] Step 2) Generate RWG basis functions on the inner edge of each subdomain grid, and generate MB-RWG basis functions at the connection between two adjacent subdomains after grid adjustment, specifically including:

[0029] a) Merge the points with the same coordinates at the boundary between subdomains in the original grid and mark the duplicate points with duplicate marks;

[0030] b) adjusting the offset points at the boundary between subdomains so that the coarse grid points on the boundary line are aligned with some of the fine grid points, specifically including: adjusting the coordinates of the coarse grid points on the boundary line between adjacent subdomains to the coordinates of the fine grid points closest to them; projecting all the fine grid points on the boundary line that do not overlap with the coarse grid points onto the edge of the coarse grid;

[0031] Step c) Generate an MB-RWG basis function with a corresponding number of branches at the junction of adjacent subdomains based on the difference in mesh resolution between them. For example, if the length of the triangle edge at the boundary line between the first and second subdomains is three times the length of the triangle edge at the boundary line in the first subdomain, then generate an MB-RWG basis function with a branch number of 3.

[0032] like Figure 3 As shown, the staggered mesh nodes between adjacent subdomains are aligned, and MB-RWG basis functions with an appropriate number of branches are generated at the boundary between the first and second subdomains based on the difference in mesh density. The MB-RWG basis functions at the junction of all subdomains serve as another subdomain, the third subdomain. This divides the original simplified missile model with a fully metal-coated dielectric into three subdomains. The first two subdomains correspond to the subregions partitioned in step 1, within which RWG basis functions are defined. The final subdomain is the collection of all MB-RWG basis functions.

[0033] Step 3) Select the surface integral equation. The equivalent current density and magnetic flux density on the interface in the model can be expanded using the RWG basis function and the MB-RWG basis function: Use the RWG basis function to expand the current density and magnetic flux density within the subdomain; Use the MB-RWG basis function to expand the current density at the adjacent subdomain on the metal surface and the current density and magnetic flux density at the adjacent subdomain on the interface between the medium and the background area; In this way, the normal continuity requirements of the current density and magnetic flux density are still met at the boundary line inside the metal and dielectric surfaces. Select the appropriate test basis function to test the surface integral equation to obtain the matrix equation;

[0034] Taking the Poggio–Miller–Chan–Harrington–Wu–Tsai (PMCHWT) equation and the Electric Field Integral Equation (EFIE) equation to solve the electromagnetic scattering problem of a uniform dielectric fully coated metal assembly as an example, according to SM Rao, CC Cha, RL Cravey, and DL Wilkes, “Electromagnetic scattering from arbitrarily shaped conducting bodies coated with lossy materials of arbitrary thickness,” IEEE Trans. Antennas Propagat., vol. 39, pp. 627–631, May, 1991., the PMCHWT-EFIE equation is in: is the unit external normal vector on the interface between the uniform medium and the background area, and the unit external normal vector on the metal surface, J 1 With M 1 are the unknown current density and magnetic flux density at the interface between the uniform medium and the background coal, J 2 is the unknown current density at the interface between the metal and the coating medium. k1 and k2 are the wave numbers in the background area and the dielectric body respectively. E in With H in are the incident electric field and magnetic field, respectively, η1 and η2 are the wave impedances in the background area and the inner area of ​​the dielectric body, respectively. and The specific expressions are and Where Γ is the interface, i=1 represents the wave number in the background region, and i=2 represents the wave number in the dielectric body.

[0035] The PMCHWT-EFIE equation is established in the following way:

[0036] Step a) Assume that the entire dielectric-coated metal target assembly is divided into N subdomains according to the geometric structure. RWG is used to expand the current density and magnetic flux density at the interface between the dielectric and background regions in the first N subdomains, as well as the current density on the metal surface. MB-RWG is used to expand the current density and magnetic flux density at the inner boundary line on the interface between the dielectric and background regions, as well as the current density at the inner boundary line on the metal surface (i.e., the N+1th subdomain): Substitute into the original PMCHWT-EFIE equation;

[0037] Step b) using and The PMCHWT-EFIE equations were tested separately, and the matrix equations in the form of regional decomposition were obtained: in represents the coupling matrix between the i-th subdomain and the j-th subdomain, A represents the self-coupling matrix between the same subdomains (i=j), and C represents the mutual coupling matrix between different subdomains (i≠j); represents the current density and magnetic current density on the i-th subdomain, represents the excitation vector on the i-th subdomain, where in<a,b> =∫ Γ a·bdS', p,q=R represents the RWG basis function, p,q=MB represents the MB-RWG basis function; the matrix equation obtained above is abbreviated as From the submatrix From the element expression, it can be seen that since the present invention does not use the semi-RWG basis function, but selects the MB-RWG basis function with continuous normal components, the calculation process involves There are no area components or line-line integrals in the operator, nor are there any internal penalty stability terms. Since the entire model is directly divided into open subdomains, only one set of meshes and unknowns need to be defined at the subdomain interfaces, without adding any additional unknowns.

[0038] Step 4) Construct a preconditioning matrix and precondition the matrix equation in step 3) to obtain the current and magnetic flow. The preconditioning matrix For the matrix equation Perform preconditioning: Among them A i,i (i=1,2,…,N+1) represents the self-coupling submatrix of the ith subdomain. Solving the preconditioned equation yields the unknown current density J 1 、J 2 and magnetic flux density M 1 .

[0039] Step 5) Calculate RCS: Based on the current density J on the interface between the dielectric and the background 1 , magnetic flux density M 1 The RWG and MB-RWG coefficients are used to calculate the scattered electric field E in the background area. s , according to the formula Get the RCS result.

[0040] The effectiveness of the present invention is illustrated by calculating the RCS of a simplified coated missile model. The base radius of the metal cone of the missile head is 0.06m, the height is 0.15m, and the center of the base is located at (0.5m, 0, 0). The rest of the missile structure is a metal cylinder with a radius of 0.06m and a length of 0.8m. The entire outer surface is uniformly coated with a layer of medium with a thickness of 0.02m. According to Y.Hu, G.XiaoandS.Huang, “A generalized transition matrix model combined with discontinuous galerkin method for open cavities,” IEEE Open J.Antennas Propag., vol.1, pp.272–682, Jun, 2020., the relative permeability of the medium is μ r =1, relative dielectric constant ε r = 8, and conductivity σ = 0.0583 S / m. The assembly is divided into two parts by a plane x = 0.5 m, named the first subdomain and the second subdomain, from top to bottom. The subdivisions of these two parts are 0.01 m and 0.03 m, respectively. A uniform plane wave polarized along the +x axis and propagating along the -z axis is irradiated onto the assembly. The frequency of the electromagnetic wave is 300 MHz.

[0041] The RCS results calculated by the iterative method (GMRES) to solve the matrix equation in this embodiment are in good agreement with the results calculated by the traditional whole domain direct method (LU decomposition) to solve the matrix equation. Figure 4 and Figure 5 As shown in the figure, the results calculated by the two methods are consistent with the results of the simulation software. Since MB-RWG has normal continuity like RWG, it can be used to expand the current density in adjacent subdomains on the metal surface, the current density and magnetic flux density in adjacent subdomains on the dielectric surface. The consistency of the calculated RCS results shows the accuracy of this method.

[0042] The convergence rate of the matrix equations using MB-RWG for regional decomposition iterative solution and RWG for whole domain iterative solution (such as GMRES) is compared. Figure 6As shown in the figure, the MB-RWG domain decomposition method has very fast convergence characteristics, while the RWG full-domain iterative solution has difficulty converging to the set threshold error. Compared with existing technologies, this method has improved performance indicators in terms of rapid convergence characteristics, no additional line area component and line-line integral terms are required when calculating the coefficient matrix, no internal penalty terms are required, and their coefficients do not need to be determined. It also does not increase the number of unknowns at the interface.

[0043] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principles and purpose of the present invention. The scope of protection of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. All implementation schemes within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for realizing the regional decomposition of the electromagnetic field problem of a dielectric fully coated metal target, characterized in that: First, the dielectric fully coated metal target to be calculated is divided into multiple non-overlapping subdomains based on its geometric structure characteristics. The surface of each subdomain is independently meshed using triangular elements to obtain the mesh information of each subdomain. RWG basis functions are constructed on the inner edges of the subdomain meshes, and MB-RWG basis functions are constructed at the boundaries of adjacent subdomains. PMCHWT and EFIE equations are established on the interface of the model, and appropriate test basis functions are selected to test the surface integral equation to obtain the matrix equation. A preconditioning matrix is ​​constructed and the above matrix equation is preconditioned. After solving the current and magnetic flux, the RCS calculation is performed to obtain the result. The number of branches of the MB-RWG basis function is not fixed, but is determined by the difference in mesh density between two adjacent subdomains, and is specifically obtained by the following steps: Step 1) Merge the points with the same coordinates at the boundary between subdomains in the original grid and mark the duplicate points with duplicate marks; Step 2) Adjust the staggered points at the boundaries between subdomains so that the points of the coarse grid at the boundary line are aligned with some of the points of the fine grid, specifically including: i) adjusting the coordinates of the coarse grid points on the boundary line between adjacent subdomains to the coordinates of the fine grid points closest to them; ii) Project all points in the fine grid on the dividing line that do not overlap with the coarse grid points onto the edge of the coarse grid; Step 3) According to the difference in grid resolution between adjacent subdomains, an MB-RWG basis function with a corresponding number of branches is generated at the connection between adjacent subdomains.

2. The method for realizing the regional decomposition of the electromagnetic field problem of a dielectric fully coated metal target according to claim 1 is characterized in that: The PMCHWT and EFIE equations are: ,in: is the unit external normal vector on the interface between the uniform medium and the background area, and the unit external normal vector on the metal surface, and are the unknown current density and magnetic flux density at the interface between the uniform medium and the background coal, is the unknown current density at the interface between metal and coating medium; and are the wave numbers in the background area and the dielectric body, and are the incident electric and magnetic fields, and are the wave impedances in the background area and the inner area of ​​the dielectric body respectively; the operator and The specific expressions are and ,in As the interface, The wave number in the expression is the wave number in the background area, The wave number in the expression is the wave number in the dielectric body; The PMCHWT and EFIE equations are established as follows: Step a) Assume that the entire medium-coated metal target assembly is divided into N sub-domains according to the geometric structure, and the RWG is used to expand the The current density and magnetic flux density on the interface between the medium and the background area in each subdomain, as well as the current density on the metal surface; MB-RWG is used to expand the current density and magnetic flux density at the internal boundary line on the interface between the medium and the background area, as well as the current density at the internal boundary line on the metal surface, that is, the first Subdomains: , , , substituted into the original PMCHWT-EFIE equation; Step b) using and The PMCHWT-EFIE equations were tested separately, and the matrix equations in the form of regional decomposition were obtained: ,in represents the coupling matrix between the i-th subdomain and the j-th subdomain, Represents the self-coupling matrix between the same subdomains , Represents the mutual coupling matrix between different subdomains ; represents the current density and magnetic current density on the i-th subdomain, represents the excitation vector on the i-th subdomain, where , , , , , , , , , , ,in , represents the RWG basis function, represents the MB-RWG basis function; the matrix equation obtained above is simplified as .

3. The method for realizing the regional decomposition of the electromagnetic field problem of a dielectric fully coated metal target according to claim 1 is characterized in that: The preconditioning matrix For the matrix equation Perform preconditioning: ,in Represents the self-coupling submatrix of the i-th subdomain, and solving the preconditioned equation yields the unknown current density 、 and magnetic flux density .

4. The method for realizing the regional decomposition of the electromagnetic field problem of a dielectric fully coated metal target according to claim 1 is characterized in that: The RCS calculation is: according to the current density on the interface between the dielectric body and the background , magnetic flux density The RWG and MB-RWG coefficients are used to calculate the scattered electric field in the background area. , according to the formula Get the RCS result.

5. A system for implementing the method for realizing the regional decomposition of the electromagnetic field problem of a dielectric fully coated metal target as described in any one of claims 1 to 4, characterized in that: include: Subdomain division and its meshing unit, basis function generation unit, matrix equation generation unit, matrix equation solving unit and post-processing unit, wherein: the subdomain division and its meshing unit performs appropriate regional block division according to the geometric structure characteristics of the object to be solved, and selects triangle units of appropriate size to independently mesh each subdomain to obtain the mesh information of each subdomain; the basis function generation unit first searches for inner edges on the subdomain mesh according to the point number, vertex number and number information of the triangle edge on each subdomain mesh, and constructs the RWG basis function in each subdomain; then, according to the semi-RWG basis function information on the subdomain mesh, matches and adjusts the mesh vertices at the boundary to obtain the MB-RWG basis function at the boundary of adjacent subdomains; the matrix equation generation unit establishes PMCHWT and EFIE equations on the interface of the object to be solved according to the equivalence principle, and uses the RWG basis function to expand the current density and magnetic flux density inside the subdomain; uses the MB-RWG basis function to expand the current density and magnetic flux density at the adjacent subdomains on the interface; uses the RWG and MB-RWG basis functions to test the equations to obtain the matrix equation ; The matrix equation solving unit generates the coefficient matrix in the unit according to the matrix equation Extract the self-coupling submatrix of each subdomain , generates a block diagonal preconditioned matrix , the block diagonal preconditioned matrix At the same time, the matrix equation in the left-multiplication matrix equation generation unit On both sides of the matrix equation, we get the preconditioned matrix equation , iteratively solve the preconditioned equations; the post-processing unit calculates the scattered field in the background area according to the RWG and MB-RWG coefficients of the current density and magnetic flux density on the interface between the dielectric body and the background, and obtains the RCS result.

Images