Method for improving solution speed of non-singularity electromagnetic scattering field of rotating sphere

Abstract

The invention discloses a method for improving the solving speed of a rotating sphere non-singularity electromagnetic scattering field, and belongs to the field of electromagnetic engineering. Aiming at the electromagnetic scattering problem of a rotating structural body in the field of practical engineering, the invention provides a method for improving the non-singularity electromagnetic scattering field solving speed of a rotating body, and effective analysis of the rotating body is realized based on a moment method. A rotating structure body has important application value in electromagnetic radiation and scattering research due to geometric symmetry, but under the condition of long wavelength, a traditional surface integration method often has the problem of singularity, and numerical stability and precision are affected. Therefore, a method for effectively eliminating singular integrality and converting a dense matrix needing to be solved into a sparse matrix is designed, the calculation efficiency is remarkably improved, and the memory consumption is reduced. A non-singularity surface integral equation is obtained through derivation, simulation and numerical simulation are carried out through a specific electromagnetic rotating body device model, an efficient numerical solution is provided for the electromagnetic scattering problem, and the method has wide engineering application prospects.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic engineering, and in particular relates to a method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity. Background Art

[0002] In the numerical solution of electromagnetic scattering problems, the method of moments (MoM) has been widely used due to its advantages in solving open domain problems. Compared with the commonly used finite element method (FEM) and finite difference method (FDTD), the method of moments (MoM) has significant advantages in dealing with structures with complex geometric shapes. By sampling and densely dividing the surface of the object, the number of unknowns to be solved is reduced, and the matrix equation is finally solved. However, the disadvantage is that the memory usage is too large and the calculation time is significantly increased (Jin J. The Finite Element Method in Electromagnetics [J]. Journal of the Japanese Society of Applied Electromagnetic Sci., 2002).

[0003] The electromagnetic radiation and scattering problem of bodies of rotation (BoR) has always been an important research direction in the field of computational electromagnetics. BoR is a symmetrical geometric shape formed by rotating the busbar around the symmetry axis. In actual engineering, the analysis and research of its electromagnetic scattering and radiation characteristics has always been one of the key and difficult points in the engineering field (Chen Fangtao, Wang Weili, Liu Qi. Analysis and design of high-performance microwave transmission antenna based on the method of moments of rotating bodies [J]. Modern Electronic Technology, 2009, 32 (11): 4). In actual engineering application fields such as radar, missiles, and satellite navigation antennas, objects with rotating bodies as structures all belong to the category of electromagnetic radiation and scattering. Therefore, the BOR method can transform complex three-dimensional problems into a series of simple two-dimensional problems to solve, simplifying the electromagnetic calculation process. However, in the solution process, due to the influence of Green's function, singularities will appear. When solving the surface integral equation of the rotating body, a lot of time is spent to eliminate the influence of singularities, and the calculation time is significantly increased. Therefore, it is necessary to use a non-singular method to solve the electromagnetic scattering field to improve the analysis efficiency and reliability of radar antenna surface, missile cross section and antenna problems involving rotating bodies.

[0004] The surface integration methods widely used in current research are mostly based on the Stratton-Chu or Poggio-Miller-Chew-Harrington-Wu-Tsai (PMCHWT) formulas, and the surface current density J and magnetic flux density M are usually selected as the unknowns in the boundary problem (Y. Chang and R. Harrington, A surface formulation for characteristic modes of material bodies [J]. IEEE Transactions on Antennas and Propagation, vol. 25, no. 6, pp. 789-795, November 1977). In order to ensure that the current is conserved on each surface unit, the Rao-Wilton-Glisson (RWG) vector basis function is usually used to represent the current density (S. Rao, D. Wilton and A. Glisson. Electromagnetic scattering by surfaces of arbitrary shape [J]. IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409-418, May 1982). At the same time, in order to solve the problem of Green's function singularity, the singularity subtraction technique is usually used to decompose it into a singular part that can be processed by analytical methods and a smooth non-singular part that can be numerically integrated. However, this method is not only cumbersome and laborious, but may not produce accurate results near the scatterer, so the use of traditional MoM usually faces singularity problems when applied to PEC targets. Summary of the invention

[0005] The purpose of the present invention is to provide a method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularities. The fundamental technical problem solved by the present invention is that when calculating the scattering field of an electromagnetic device based on the BoR-MoM method, it will be restricted by the singular points of the Green's function. By introducing auxiliary equations and scalar Helmholtz equations, the singularities in the solution process are eliminated, the calculation speed is improved and the amount of calculation is reduced.

[0006] The method of the present invention makes it possible to solve the rotating spherical electromagnetic device without being affected by singular points. In the process of calculating the spherical electromagnetic device, the singularity of the matrix equation of the spherical electromagnetic rotating body device is eliminated by introducing auxiliary equations. The divergence-free condition is replaced by a scalar Helmholtz equation related to the position vector r, which together with the scalar Helmholtz equations of the three Cartesian components of the electric field constitute a set of four coupled scalar wave equations. The complex solution equations of the electromagnetic scattering field are converted into a linear equation group through formula derivation. At this time, the impedance matrix will change from a dense matrix to a sparse matrix, which greatly improves the speed of numerical simulation research of electromagnetic rotating body devices and has practical application value for related device simulation technology.

[0007] The present invention comprises the following steps:

[0008] 1) Solve the radiation and scattering problems of the PEC (Perfect Electric Conductor) rotating body of the sphere based on the moment method: derive the vector wave equation based on the frequency domain Maxwell equations and vector identities; use the vector value equation and continuity equation to obtain the homogeneous scalar wave equation (scalar Helmholtz equation); use the solution in the form of boundary integral equations to calculate using Green's function;

[0009] 2) Eliminate singular integral terms in the solution equation: introduce two auxiliary functions that satisfy the Helmholtz equation, and use these functions to remove the solid angle and singularity in the boundary integral equation; through derivation, the electromagnetic scattering solution equation without singularity is obtained;

[0010] 3) Establish a simulation device for the PEC sphere: Based on the above, specifically solve the scattering problem of the PEC sphere; set the specific form of the auxiliary function to obtain four sets of integral equations containing four scalar unknowns;

[0011] 4) Solve using the moment method: In the cylindrical coordinate system, set the basis functions and test functions along the generatrix and azimuth directions; expand the four unknowns using the basis functions, substitute them into the integral equation, and simplify them into a system of linear equations;

[0012] 5) Set up the excitation source and establish a linear equation system: the incident wave is a uniform plane wave that vertically incidents on the spherical electromagnetic device; arrange the unknown coefficients in solving the scattering field equation of the electromagnetic device to form a column vector and express it in the form of a linear equation system; solve the linear equation system to obtain the coefficient matrix and reconstruct the scattering field.

[0013] In step 1), the radiation and scattering problem of the PEC (Perfect Electric Conductor) rotating body of the sphere is solved based on the moment method. Specifically: the radiation and scattering problem of the PEC rotating body of the sphere is solved based on the moment method, and the formula is specifically derived through the scattering of the incident plane wave by the PEC; in the frequency domain with time dependence exp(-iωt), the vector wave equation can be obtained according to the frequency domain Maxwell equations and vector identities:

[0014]

[0015] In the formula and The Maxwell equations can be derived from each other. Since any one of the above equations is complete, only one of them needs to be solved. Then, according to the vector value equation and the continuity equation, express or One of the Cartesian components of Satisfies the homogeneous scalar wave equation, that is, the scalar Helmholtz equation:

[0016]

[0017] According to the above formula, we can use the vector identity And the vector wave equation can be obtained:

[0018]

[0019] From (4), we can get It also satisfies the homogeneous scalar wave equation (3), so and The eight scalars satisfy the homogeneous scalar wave equation (3), and these eight scalars are: E x ,E y ,E z , H x ,H y ,H z , The second identity gives us the solution of the scalar wave equation in the form of a boundary integral equation:

[0020]

[0021] Where c0 is The solid angle of , and the specific form of Green's function is:

[0022]

[0023] In step 2), the elimination of the singular integral term in the solution equation is specifically achieved by using two auxiliary functions that satisfy the Helmerholtz equation. and That is, formula (7), and at the same time satisfying (8):

[0024]

[0025] Using the above conditions and The solid angle and singularity in the boundary integral equation (5) can be removed, and the function (9) can be defined. At this time, the effect of singularity does not need to be considered when solving the electromagnetic scattering equation, that is:

[0026]

[0027] According to formula (7) and (8), we can deduce:

[0028]

[0029] From the above conditions, it can be deduced that The boundary integral equation (11) is satisfied, and the equations (9)-(11) are simplified to obtain (12):

[0030]

[0031] In step 3), the simulation device of the PEC sphere is established, and the scattering problem of the target body is specifically solved on the basis of the above, and the formula (12) is Substitute and We can get:

[0032]

[0033] Since the tangential dimension of the total PEC field is 0, then:

[0034]

[0035] Substituting formula (15) into (13)-(14), we can get the four unknowns that need to be solved when solving the scattered field of electromagnetic devices: In the above formula, the integral surface S is the union of the BoR target surface and S. The surface of the electromagnetic device pointed to the inside of the target body is positive; when the specific form of the auxiliary function is determined, the integral along S can be calculated according to the Sommerfeld radiation condition; the specific form of the auxiliary function is set as formula (16), at this time, the integral area of ​​formula (12) is only the surface of the BOR target body, and there will be an additional term p(r0) on the left side of the equation; at this time, four sets of integral equations containing 4 scalar unknowns can be obtained, that is, formulas (13)-(14) can be rewritten as:

[0036]

[0037] In step 4), the moment method is applied to solve the problem. The moment method is applied based on the above derivation of the electromagnetic scattering calculation of the simulation device. The position variable r is (p, phi, z) in the cylindrical coordinate system. t(r) represents the length of the busbar at r, which is abbreviated as t in the following formula, t∈(0, T), where T is the total length of the busbar. The basis functions along the busbar and the azimuth direction are set to be f u (t) and Where u, v = 1, 2, 3... Nt, m, n = -M, -(M-1), ..., (M-1), M; the basis function of the equation is Set the test function f u (t)δ(t), then the four unknown quantities required in the above derivation are Expanding with basis functions yields:

[0038]

[0039] Substituting the unknown quantity after expansion with basis functions into formula (17)-(18) and simplifying it, we can get:

[0040]

[0041] In step 5), the excitation source is set and a linear equation group is established. Specifically, the excitation source is set, and the incident wave is a uniform plane wave that is perpendicular to the spherical electromagnetic device, and a linear equation group is established at the same time; after completing the above derivation, the unknown coefficients X in the electromagnetic device scattering field equation are arranged to form a column vector, which contains N = (2M + 1) Nt elements, x mu is the (m+M)Nt+uth element of x0; similarly, Let x be the column vector formed by arranging all unknown numbers, then equations (20)-(21) can be written as a system of linear equations: Ax = b; in this case, the equation can be expressed as:

[0042]

[0043] By rewriting the complex equations into the form of a linear equation group, it can be seen that there are many zero matrices in the impedance matrix A. This is why the method of the present invention can make dense matrices sparse, greatly reducing the amount of calculation and improving the calculation speed; therefore, it is only necessary to first calculate the values ​​of the excitation matrix b and the impedance matrix A obtained by solving the calculation, and then solve the linear equation group to obtain the coefficient matrix x, and reconstruct the scattering field with the solved values ​​to obtain the scattering field of the desired electromagnetic device. The solved scattering field is compared with the MIE analytical solution, and the error is 0.042%, which is within a reasonable range; therefore, the present invention has practical application value for the calculation of electromagnetic scattering fields, and also brings about an improvement in calculation efficiency.

[0044] Compared with the prior art, the technical effects and outstanding advantages of the present invention are:

[0045] 1. The present invention successfully eliminates the Green's function singular point problem encountered when solving the electromagnetic scattering field of a rotating sphere by introducing two auxiliary functions that satisfy the Helmholtz equation, thereby improving the accuracy of the calculation and avoiding calculation errors or instability caused by singular points.

[0046] 2. The present invention combines the scalar Helmholtz equations of the three Cartesian components of the electric field with a scalar Helmholtz equation related to the position vector r to form a set of four coupled scalar wave equations, thereby simplifying the solution process of the electromagnetic scattering field while maintaining the accuracy of the calculation.

[0047] 3. The present invention transforms the complex electromagnetic scattering field solution equation into a linear equation system and finds that the impedance matrix changes from a dense matrix to a sparse matrix. The storage and computational efficiency of a sparse matrix is ​​much higher than that of a dense matrix, so this transformation significantly reduces the amount of computation and memory requirements.

[0048] 4. The method of the present invention is not only applicable to simple rotating sphere electromagnetic devices, but can also be extended to more complex structures, such as rotating spheres with coatings or defects. The present invention has broad application prospects in various electromagnetic scattering field calculations and analyses. The method of the present invention provides a new and effective method for the rapid and accurate calculation of the electromagnetic scattering field of a rotating sphere. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a schematic diagram of three-dimensional coordinates and related parameters when solving the scattered field using the method of the present invention.

[0050] Figure 2 The figure is a comparison diagram of the errors of solving the coefficient matrix using the calculation method of the present invention and the MIE solution.

[0051] Figure 3 The figure is a model diagram of an actual spherical radome used as a reference for the method of the present invention. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims.

[0053] The embodiment of the present invention includes the following steps:

[0054] Step 1: Solve the radiation and scattering problem of the PEC rotating body of the sphere based on the moment method

[0055] The method of moments is mainly used to solve the radiation and scattering problems of the PEC (ideal electric conductor) rotating body of the sphere. First, the vector wave equation is derived based on the frequency domain Maxwell equations and vector identities. Then, through the changes in the vector value equation and the continuity equation, the Cartesian components of the electric field or magnetic field that satisfy the homogeneous scalar wave equation (i.e., the scalar Helmholtz equation) can be obtained. Next, the vector identity and the vector wave equation are used to further deduce that other related components also satisfy the homogeneous scalar wave equation. The homogeneous scalar wave equation is obtained, which is satisfied by all 8 scalar components of the electric field and magnetic field. Specifically:

[0056] Based on the moment method, the radiation and scattering problems of the PEC rotating body of the sphere are solved, and the formula is specifically derived through the scattering of the incident plane wave by the PEC. In the frequency domain with time dependence exp(-iωt), the vector wave equation can be obtained according to the frequency domain Maxwell equations and vector identities:

[0057]

[0058] In the formula and The Maxwell equations can be derived from each other. Since any one of the above equations is complete, only one of them needs to be solved. Then, by changing the vector value equation and the continuity equation, we can use express or One of the Cartesian components of Satisfies the homogeneous scalar wave equation, that is, the scalar Helmholtz equation:

[0059]

[0060] According to the above formula, we can use the vector identity And the vector wave equation can be obtained:

[0061]

[0062] From (4), we can get It also satisfies the homogeneous scalar wave equation (3), so and The eight scalars satisfy the homogeneous scalar wave equation (3), and these eight scalars are: E x ,E y ,E z , H x ,H y ,H z , The second identity gives us the solution of the scalar wave equation in the form of a boundary integral equation:

[0063]

[0064] Where c0 is The solid angle of , and the specific form of Green's function is:

[0065]

[0066] Step 2: Eliminate singular integral terms in the solution equation

[0067] During the calculation process, when the observation point is close to the source point, the behavior of the Green's function becomes extremely complicated, which may lead to numerical instability or loss of accuracy. Therefore, due to the influence of the Green's function, singularities will appear, and the calculation time spent on solving the surface integral equation of the rotating body will often increase significantly. In order to solve this problem, the present invention introduces two auxiliary functions that satisfy the Helmholtz equation. These two auxiliary functions can help us remove the solid angle and singularity in the boundary integral equation, thereby simplifying the calculation process and improving the calculation accuracy. By defining a new function and substituting the auxiliary function into the boundary integral equation, a new equation that does not contain singular integral terms can be obtained. When solving the equation of electromagnetic scattering, there is no need to consider the influence of singularities. Specifically:

[0068] To address this singularity problem, the present invention uses two auxiliary functions that satisfy the Helmerholtz equation: and That is, formula (7), and at the same time satisfying (8):

[0069]

[0070] Using the above conditions and The solid angle and singularity in the boundary integral equation (5) can be removed, and the function (9) can be defined. At this time, the effect of singularity does not need to be considered when solving the electromagnetic scattering equation, that is:

[0071]

[0072] According to formula (7) and (8), we can deduce:

[0073]

[0074] From the above conditions, it can be deduced that The boundary integral equation (11) is satisfied, and the equations (9)-(11) are simplified to obtain (12):

[0075]

[0076] Step 3: Set up the PEC sphere simulation device and solve the scattering problem

[0077] On the basis of the above, a simulation device of the PEC sphere is established, and the scattering problem of the target body is specifically solved. First, the new equation obtained in step 2 is substituted into the specific solution process. Then, the formula is simplified by using the characteristic that the tangential vector of the PEC total field is 0. Through simplification, the four unknown quantities that need to be solved when solving the scattered field of the electromagnetic device can be obtained. These unknown quantities serve as the basis for the subsequent solution of the linear equation system. Specifically:

[0078] On the basis of the above, we specifically solve the scattering problem of the target body and replace the Substitute and We can get:

[0079]

[0080] Since the tangential dimension of the total PEC field is 0, then:

[0081]

[0082] Substituting formula (15) into (13)-(14), we can get the four unknowns that need to be solved when solving the scattered field of electromagnetic devices: In the above formula, the integral surface S is the union of the BoR target surface and S. The positive direction is when the surface of the electromagnetic device points to the inside of the target object. Figure 1 The figure is a schematic diagram of the three-dimensional coordinates and related parameters when solving the scattered field by the method of the present invention. After the specific form of the auxiliary function is determined, the integral along S can be calculated according to the Sommerfeldr adiation condition. In the embodiment, the specific form of the auxiliary function is set as formula (16). At this time, the integral area of ​​formula (12) is only the surface of the BOR target body, and there will be an additional term p(r0) on the left side of the equation. At this time, four sets of integral equations containing four scalar unknowns can be obtained, that is, formulas (13)-(14) can be rewritten as:

[0083]

[0084] Step 4: Apply the moment method to continue solving

[0085] Based on the above derivation of the electromagnetic scattering calculation of the simulation device, the moment method is continued to be applied for solution. The position variable r is expressed in the cylindrical coordinate system, and the basis functions and test functions along the busbar and azimuth directions are set. The four required unknown quantities are expanded with basis functions and substituted into the relevant formulas for simplification. Through simplification, a linear equation system is obtained. This linear equation system contains key information such as the impedance matrix A and the excitation matrix b. Specifically:

[0086] Based on the above derivation of the electromagnetic scattering calculation of the simulation device, the moment method is continued to be applied. The position variable r is (p, phi, z) in the cylindrical coordinate system, and t(r) represents the length of the busbar at r, which is abbreviated as t in the following formula, t∈(0, T), where T is the total length of the busbar, and the basis functions along the busbar and azimuth are set to be f u (t) and Where u, v = 1, 2, 3... Nt, m, n = -M, -(M-1), ..., (M-1), M. The basis function of the equation is Set the test function f u (t)δ(t), then the four unknown quantities required in the above derivation are Expanding with basis functions yields:

[0087]

[0088] At this time, substitute the unknown quantity after the basis function expansion into formula (17-18), and simplify it to get:

[0089]

[0090] Step 5: Set up the excitation source and establish the linear equation system

[0091] Set the incident wave to be a uniform plane wave that is perpendicular to the spherical electromagnetic device as the excitation source. Arrange the unknown coefficients in the equation for solving the scattered field of the electromagnetic device to form a column vector, and associate it with the impedance matrix A and the excitation matrix b. By solving this set of linear equations, the values ​​of the unknown coefficients can be obtained. Finally, the scattered field is reconstructed with the solved values ​​to obtain the scattered field of the desired electromagnetic device. Specifically:

[0092] Set the excitation source, the incident wave is a uniform plane wave that is perpendicular to the spherical electromagnetic device, and establish a linear equation system. After completing the above derivation, the unknown coefficients x in the electromagnetic device scattered field equation are arranged into a column vector containing N = (2M + 1) Nt elements, x mu is the (m+M)Nt+uth element of x0. Let x be the column vector of all unknown numbers, then (20)-(21) can be written as a system of linear equations: Ax = b. At this time, the equation can be expressed as:

[0093]

[0094] By rewriting the complex equations into the form of a system of linear equations, it can be seen that there are many zero matrices in the impedance matrix A. This is also why the method of the present invention can make dense matrices sparse, which can greatly reduce the amount of calculation and improve the calculation speed.

[0095] In order to verify the accuracy of the method of the present invention in solving the electromagnetic scattering field of the spherical radar antenna cover, a spherical model in cylindrical coordinates is established as a simulation object, such as Figure 3 The figure shows a simulation model of a spherical radar antenna cover. The sphere is centered on the z-axis, located in the positive half of the z-axis and tangent to the x0y plane. Its generatrix is ​​a semicircle, which is subdivided into N segments. The relevant coordinate parameters are:

[0096]

[0097] Where θ is the pitch angle (polar angle), is the azimuth. Set the radius of the sphere to 2m and the frequency of the incident wave to Fre=1*10 8 HZ, bus length T is 2π, ppw is 20, bus sampling points are obtained by Nth = T / λ*ppw / 2)*2 to be 84, azimuth sampling points Nph is set to 42, each segment length of bus segmentation is dn = 2π / Nth, and each segment length of azimuth segmentation is dp = 2π / Nph. For other parameter settings, refer to Table 1.

[0098] Table 1

[0099]

[0100] After completing the model establishment and parameter setting, the method of the present invention is used to calculate the values ​​of the excitation matrix b and the impedance matrix A. The values ​​of the excitation matrix b and the impedance matrix A obtained by calculation are used to reconstruct the scattered field, and the scattered field of the desired electromagnetic device can be obtained; in order to verify the accuracy of the results, the solved scattered field is compared with the MIE analytical solution, and the error is 0.042%, that is, within a reasonable range, such as Figure 2. It shows that the method of the present invention has high accuracy and practicality in solving electromagnetic scattering fields. Therefore, the present invention has practical application value for the calculation of electromagnetic scattering fields, and also brings about an improvement in computing efficiency. The present invention can take models such as spherical antenna covers and circular cross-sections of missiles as references, design the model shape and change the relevant parameters in the program, and perform simulation input according to the design of the invention to quickly solve the problem, and perform numerical comparison and calculation based on the output results to finally verify the effect of the design.

[0101] The present invention eliminates the singularity of the matrix equation when solving the rotating spherical electromagnetic device by introducing auxiliary equations and scalar Helmholtz equations, thereby improving the calculation speed and accuracy. The impedance matrix is ​​changed from a dense matrix to a sparse matrix, which significantly reduces the amount of calculation and memory requirements. The method of the present invention is not only suitable for the calculation of the electromagnetic scattering field of the spherical antenna cover, but can also be widely used in the electromagnetic scattering analysis of models such as the circular cross-section of a missile. By designing models of different shapes and changing the relevant parameters in the program, the electromagnetic scattering fields of various complex models can be quickly solved. It provides powerful tools and support for research in the fields of electromagnetic compatibility analysis, radar stealth technology, etc.

[0102] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity, characterized in that The following steps are involved: 1) Solve the radiation and scattering problems of the PEC rotating body of the sphere based on the moment method: According to the frequency domain Maxwell equations and vector identities, the vector wave equation is derived; using the vector value equation and the continuity equation, the homogeneous scalar wave equation, that is, the scalar Helmholtz equation, is obtained; according to the solution in the form of boundary integral equation, the Green function is used for calculation; 2) Eliminate singular integral terms in the solution equation: introduce two auxiliary functions that satisfy the Helmholtz equation, and use these functions to remove the solid angle and singularity in the boundary integral equation; through derivation, the electromagnetic scattering solution equation without singularity is obtained; 3) Establish a simulation device for the PEC sphere: Based on the above, specifically solve the scattering problem of the PEC sphere; set the specific form of the auxiliary function to obtain four sets of integral equations containing four scalar unknowns; 4) Solve using the moment method: In the cylindrical coordinate system, set the basis functions and test functions along the generatrix and azimuth directions; expand the four unknowns using the basis functions, substitute them into the integral equation, and simplify them into a system of linear equations; 5) Set up the excitation source and establish a linear equation system: the incident wave is a uniform plane wave that vertically incidents on the spherical electromagnetic device; arrange the unknown coefficients in solving the scattering field equation of the electromagnetic device to form a column vector and express it in the form of a linear equation system; solve the linear equation system to obtain the coefficient matrix and reconstruct the scattering field.

2. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity as claimed in claim 1, characterized in that In step 1), the radiation and scattering problem of the PEC rotating body of the sphere is solved based on the moment method. Specifically, the formula is derived by scattering the incident plane wave by the PEC; in the frequency domain with time dependence exp(-iωt), the vector wave equation is obtained according to the frequency domain Maxwell equations and vector identities: In the formula and The Maxwell equations are derived from each other. Since any one of the above equations is complete, only one of them needs to be solved. Then, according to the vector value equation and the continuity equation, express or One of the Cartesian components of Satisfies the homogeneous scalar wave equation, that is, the scalar Helmholtz equation: According to the above formula, we can use the vector identity And the vector wave equation: From (4), we can get It also satisfies the homogeneous scalar wave equation (3), so and The eight scalars satisfy the homogeneous scalar wave equation (3), and these eight scalars are: E x ,E y ,E z , H x ,H y ,H z , The solution of the scalar wave equation in the form of boundary integral equation is obtained from the second identity: Where c0 is The solid angle of , and the specific form of Green's function is:

3. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity as claimed in claim 1, characterized in that In step 2), the elimination of the singular integral term in the solution equation is specifically achieved by using two auxiliary functions that satisfy the Helmerholtz equation. and That is, formula (7), and at the same time satisfying (8): Using the above conditions and Remove the solid angle and singularity in the boundary integral equation (5) and define function (9). At this time, it is not necessary to consider the influence of singularity when solving the equation for electromagnetic scattering, that is: According to formula (7) and (8), we can deduce: From the above conditions, we can deduce The boundary integral equation (11) is satisfied, and the equations (9)-(11) are simplified to obtain (12):

4. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity as claimed in claim 1, characterized in that In step 3), the simulation device of the PEC sphere is established, and the scattering problem of the target body is specifically solved on the basis of the above, and the formula (12) is Substitute and have to: Since the tangential dimension of the total PEC field is 0, then: Substituting formula (15) into (13)-(14), we can get the four unknowns that need to be solved when solving the scattered field of electromagnetic devices: In the above formula, the integral surface S is the union of the BoR target surface and S. The surface of the electromagnetic device pointed to the inside of the target body is positive; when the specific form of the auxiliary function is determined, the integral along S is calculated according to the Sommerfeld radiation condition; the specific form of the auxiliary function is set as formula (16), at this time, the integral area of ​​formula (12) is only the surface of the BOR target body, and there will be an additional term p(r0) on the left side of the equation; four sets of integral equations containing 4 scalar unknowns are obtained, that is, formulas (13)-(14) are rewritten as:

5. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity as claimed in claim 1, characterized in that In step 4), the moment method is applied to solve the problem. The moment method is applied based on the above derivation of the electromagnetic scattering calculation of the simulation device. The position variable r is (p, phi, z) in the cylindrical coordinate system. t(r) represents the length of the busbar at r, which is abbreviated as t in the following formula, t∈(0, T), where T is the total length of the busbar. The basis functions along the busbar and the azimuth direction are set to be f u (t) and Where u, v = 1, 2, 3... Nt, m, n = -M, -(M-1), ..., (M-1), M; the basis function of the equation is Set the test function f u (t)δ(t), then the four unknown quantities required in the above derivation are Expanding with basis functions yields: Substitute the unknown quantity after expansion with basis functions into formula (17)-(18) and simplify it to obtain:

6. A method for improving the speed of solving the electromagnetic scattering field of a rotating sphere without singularity as claimed in claim 1, characterized in that In step 5), the excitation source is set and a linear equation group is established. Specifically, the excitation source is set, and the incident wave is a uniform plane wave that is perpendicular to the spherical electromagnetic device, and a linear equation group is established at the same time; after completing the above derivation, the unknown coefficients X in the electromagnetic device scattering field equation are arranged to form a column vector, which contains N = (2M + 1) Nt elements, x mu is the (m+M)Nt+uth element of x0; similarly, a=x, y, z, and the column vector formed by arranging all unknown numbers is denoted as x, then equations (20)-(21) can be written as a system of linear equations: Ax=b; in this case, the equation can be expressed as: By rewriting the complex equations into the form of a system of linear equations, we can see that there are many zero matrices in the impedance matrix A, which makes the dense matrix sparse, greatly reducing the amount of calculation and improving the calculation speed; we only need to calculate the values ​​of the excitation matrix b and the impedance matrix A obtained by solving the calculation first, and then solve the system of linear equations to get the coefficient matrix x, and reconstruct the scattering field with the solved values ​​to obtain the scattering field of the desired electromagnetic device.

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