An Integrated Accurate Simulation Method for Electromagnetic Scattering of Partially Rotating Targets

Abstract

This invention provides an integrated and accurate simulation method for electromagnetic scattering of partially rotating targets, comprising: modeling and setting system parameters; dividing the target into relatively stationary sub-regions, rotating sub-regions, and linked sub-regions, and establishing a rotationally symmetric equivalent surface to completely enclose the rotating sub-domains; establishing a global coordinate system and a local coordinate system; using a consistent mesh in the global coordinate system as the outer mesh, and independently meshing the local coordinate system as the inner mesh, and defining the inner and outer basis functions accordingly; calculating the self-acting operator, equivalent operator, coefficient solving operator, and interaction operator of the equation to be solved; updating the coordinate system rotation operator between the global and local coordinate systems, establishing and solving the equation to be solved for the partially rotating conductor target at the current moment, and then calculating the far-field scattering field at the current moment from the scattering electromagnetic current coefficient vector; repeating the first two steps until the calculation of the far-field scattering field at different sampling time points throughout the entire rotation cycle is completed. This method has a fast modeling speed.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic simulation technology, and in particular to an integrated and accurate simulation method for electromagnetic scattering of partially rotating targets. Background Technology

[0002] The high-speed, periodic rotation of rotors in helicopters, rotary-wing UAVs, and aircraft engines during operation periodically modulates radar echoes, a phenomenon known as rotor modulation. The rotor effect can serve as an important characteristic for radar target identification. In this invention, targets containing rotor rotation are referred to as partially rotating targets. To simplify calculations, all targets are treated as conductive targets in this method. Calculating the electromagnetic scattering of partially rotating targets at various times is fundamental to analyzing and predicting the rotor effect of partially rotating targets, and has practical engineering application value. Partially rotating targets such as helicopters are generally electrically large targets. To calculate their electromagnetic scattering, a multilevel fast multipole algorithm based on integral equations (J.Song, C.Lu, W.Chew, Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects[J].IEEE Transactions on Antennas and Propagation, 1997, 45(10):1488-1493) is generally used. However, when calculating the electromagnetic scattering of a partially rotating target, the rotation of the rotor causes the overall structure of the target to constantly change. When calculating the attitude at each moment, traditional calculation methods require reconstructing the impedance matrix for each iteration. Although the overall structure of the partially rotating target changes at different times, the individual subdomains that constitute it do not change, and reconstructing the impedance matrix does not fully utilize the characteristics of the structure. Summary of the Invention

[0003] Therefore, the purpose of this invention is to provide a simulation method that can accurately calculate the electromagnetic scattering of a target at each sampling time by modeling a partially rotating target once, so as to overcome or at least partially solve the above-mentioned problems existing in the prior art.

[0004] To achieve the above-mentioned objective, this invention provides an integrated and accurate simulation method for electromagnetic scattering of a partially rotating target. The partially rotating target includes at least one component that is periodically rotating, and the component is connected to the main body of the partially rotating target. The method includes the following steps:

[0005] S101. Establish the target model of the rotating conductor to be determined at the initial time t0, and set the system parameters;

[0006] S102. Divide the target model of a partially rotating conductor into subdomains and establish a reference coordinate system;

[0007] S103. Select the inner and outer layer basis functions and perform corresponding mesh generation on the partial rotating conductor target model;

[0008] S104. Based on the electromagnetic flow of each subdomain of the target model of a rotating conductor with discrete parts of inner and outer layer basis functions, define the unknowns to be solved.

[0009] S105. Calculate the self-acting operator, equivalent operator, coefficient solving operator, and interaction operator of the equation to be solved;

[0010] S106. Update the coordinate system rotation operator between the global coordinate system and the local coordinate system, and establish and solve the equations for the unknown quantities of the partially rotating conductor target at the current moment.

[0011] S107. Use an iterator to solve the equation and obtain the solution vector. Based on the remote calculation formula, calculate the far-field scattering field at the current moment from the scattering electromagnetic current coefficient vector.

[0012] S108. Calculate the electromagnetic scattering of the partially rotated target at the next sampling time point, update the relationship between the local coordinate system and the global coordinate system, and repeat steps S106 and S107 until the calculation of the far-field scattering field at different sampling time points in the entire rotation cycle is completed.

[0013] Compared with the prior art, the beneficial effects of the present invention are:

[0014] Existing technologies require separate modeling for each discrete time point and repeated calculation of the interaction impedance matrix when dealing with electromagnetic scattering calculations for partially rotating conductor targets. This results in low computational efficiency and cumbersome operation. The method provided by this invention can complete the calculation for each sampling time point by modeling and constructing the impedance matrix once, thereby improving computational efficiency and simplifying the simulation implementation process. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of a partially rotating target (taking a helicopter in flight as an example) provided in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the integrated precise simulation method for electromagnetic scattering of partially rotating targets provided in an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the partial rotation target model subdomain partitioning and mesh generation process provided in an embodiment of the present invention.

[0019] Figure 4 This is a schematic diagram of the rotational symmetry equivalent surface of the rotational sub-region provided in an embodiment of the present invention.

[0020] Figure 5 This is a schematic diagram of the global coordinate system external mesh provided in an embodiment of the present invention (taking planar triangular meshing as an example).

[0021] Figure 6 This is a schematic diagram of the mesh subdivision in the local coordinate system provided in an embodiment of the present invention (taking planar triangular subdivision as an example).

[0022] Figure 7 This is a schematic diagram of the mesh corresponding to the basis functions on the boundary edge between the global coordinate system and the stationary sub-region and the linked sub-region, provided in an embodiment of the present invention (taking RWG basis functions and planar triangular meshing as an example). Detailed Implementation

[0023] The principles and features of the present invention are described below with reference to the accompanying drawings. The listed embodiments are only used to explain the present invention and are not intended to limit the scope of the present invention.

[0024] Reference Figures 1-2 This embodiment provides an integrated and accurate simulation method for electromagnetic scattering of a partially rotating target. The partially rotating target includes at least one periodically rotating component, which is connected to the main body of the partially rotating target, such as a helicopter in flight whose propeller rotates relative to the fuselage. The method includes the following steps:

[0025] S101. Establish the target model of the rotating conductor to be determined at the initial time t0, and set the system parameters.

[0026] S102. Divide the target model of a partially rotating conductor into subdomains and establish a reference coordinate system.

[0027] S103. Select the inner and outer layer basis functions and perform corresponding mesh generation on the target model of the rotating conductor.

[0028] S104. Based on the electromagnetic flow of each subdomain of the target model of a rotating conductor with discrete inner and outer layer basis functions, define the unknowns to be solved.

[0029] S105. Calculate the self-acting operator, equivalent operator, coefficient solving operator, and interaction operator of the equation to be solved.

[0030] S106. Update the coordinate system rotation operator between the global and local coordinate systems, and establish and solve the equations for the unknown quantities of the partially rotating conductor target at the current moment.

[0031] S107. Use an iterator to solve the equation and obtain the solution vector. Based on the remote calculation formula, calculate the far-field scattering field at the current moment from the scattering electromagnetic current coefficient vector.

[0032] S108. Calculate the electromagnetic scattering of the partially rotated target at the next sampling time point, update the relationship between the local coordinate system and the global coordinate system, and repeat steps S106 and S107 until the calculation of the far-field scattering field at different sampling time points in the entire rotation cycle is completed.

[0033] In step S101, setting the system parameters includes setting the incident field parameters and rotation speed, and the attitude of the partially rotating target model is fixed at each sampling time point, specifically as follows: Let the rotational angular velocity of the rotating part of the desired partially rotating conductor target be ω, the incident field frequency be freq, and the incident angle be (θ). inc ,φ inc Let the polarization angle be η, and let Ω be a portion of the rotating conductor target surface. The attitude of this portion of the rotating target is uniformly sampled over one rotation cycle, and the total number of sampling positions is denoted as N. spl Let t be the sampling time point corresponding to the i-th position. i i = 0, ..., N spl -1.

[0034] Reference Figure 3 , Figure 4 In step S102, a relatively stationary sub-region, a rotating sub-region, and a connecting sub-region between the two sub-regions are divided on the partially rotated target. A global coordinate system is established, with the relatively stationary sub-region stationary relative to the global coordinate system, and the rotating sub-region and the local coordinate system rotating relative to the global coordinate system. A rotationally symmetric equivalent surface and a local coordinate system are established on the rotating sub-region with its rotation axis as the axis, and the rotating sub-region is stationary relative to the local coordinate system, as detailed below:

[0035] The partially rotating conductor target surface Ω is divided into relatively stationary sub-regions Ω. S Rotational subregion Ω R and link subregion Ω c Define a global coordinate system xyz that does not change over time, Ω S and Ω c Ω is stationary relative to the global coordinate system xyz. R Around Ω c Perform periodic rotation; in Ω R Using its rotational coordinate axes, establish a coordinate system that can completely enclose Ω. R The rotationally symmetric equivalent surface E REstablish a local coordinate system x′y′z′ with the rotational symmetry axis as the z-axis, Ω R Ω is stationary relative to the local coordinate system, Ω = Ω S ∪Ω R ∪Ω C Ω S ∩Ω C =C SC , E R ∩Ω C =C EC , Where C SC Ω S and Ω C The boundary edge, C EC For E R and Ω C The boundary line, C SC and C EC Parallel to the local coordinate system x′o′y′.

[0036] In step S103, inner and outer basis functions are selected, and the model is meshed accordingly: Basis functions required for discrete electromagnetic flow are selected for each sub-region in both the global and local coordinate systems, and meshing is performed. The basis functions in the global coordinate system are denoted as outer basis functions, and the basis functions in the local coordinate system are denoted as inner basis functions. In the global coordinate system, the relatively stationary sub-region, the linked sub-region, and the rotationally symmetric equivalent surface are meshed; this mesh is called the outer mesh, corresponding to the outer basis functions. In the local coordinate system, the rotated sub-region, the linked sub-region, and the rotationally symmetric equivalent surface are meshed; this mesh is called the inner mesh, corresponding to the inner basis functions, as detailed below:

[0037] S301. In this embodiment, different basis functions are used to describe the electromagnetic flow for different coordinate systems. In the global coordinate system, Ω is discretized using a highly flexible outer basis function based on small patch partitioning. S Ω C E R Electromagnetic currents on the surface, such as RWG basis functions, are denoted as... In the local coordinate system, the inner basis functions are selected to discretize Ω based on the structural characteristics of the rotated sub-region. R Ω C E R The electromagnetic current on the surface can be the same as or different from the global basis functions, denoted as .

[0038] S302, Ω in the global coordinate system S Ω C E R according to The requirement for mesh generation is to use a uniform surface mesh, which is called the external mesh. Figure 5 A schematic diagram of the external meshing using a planar triangular element as an example is given. The external meshing is in C SC Both sides must be continuous to ensure C SC The current is continuous on both sides.

[0039] S303, Ω in the local coordinate system R Ω C E R according to The surface mesh is required to be generated, and this mesh is called the internal mesh. Figure 6 A schematic diagram of the inner mesh is given using a planar triangular element as an example. Different meshes can be used for the inner and outer layers, determined by the basis functions of the inner and outer layers.

[0040] In step S104, the electromagnetic current to be determined is discretized using the basis functions selected in step S103. The unknowns to be determined are defined on the relatively stationary sub-region, the linked sub-region, and the rotationally symmetric equivalent surface in the global coordinate system. These are the surface scattering current coefficient of the relatively stationary sub-region, the surface scattering current coefficient of the linked sub-region, and the equivalent scattered electromagnetic current coefficient on the rotationally symmetric equivalent surface, respectively. The specific steps include:

[0041] S401, in the global coordinate system, the surface Ω of the relatively stationary sub-region S Take office Unknown scattered current at the location Expand into:

[0042]

[0043] To ensure current continuity between subdomains, edge C SC The basis functions are defined on Ω S and Ω C On the grid connected to it, Figure 7 C is given SC A schematic diagram of a planar triangular mesh based on RWG basis functions. (The last part, "C," appears to be a typo and can be left as is.) SC The unknown scattering current coefficient on is attributed to Ω S In the unknown quantity to be determined, Ω S The total number of unknown current coefficients is N S Then its unknown coefficient vector is denoted as

[0044] S402, Link the sub-region surface Ω in the global coordinate system C Take office Unknown scattered current at the location Expand into:

[0045]

[0046] Ω C The total number of unknown current coefficients is N C Then its unknown coefficient vector is denoted as

[0047]

[0048] S403. In the global coordinate system, the equivalent surface E R Take office Unknown equivalent scattered current at the location and equivalent scattered magnetic current Expand into:

[0049]

[0050]

[0051] E R The total number of unknown current coefficients is N E Then its unknown equivalent scattered electromagnetic current coefficient vector is denoted as The vector of the total undetermined electromagnetic current coefficient is denoted as I = [I S T I C T I E T ] T .

[0052] S404. In the global coordinate system, Ω will be... R Scattered current on In Ω C Take office The test vector of the secondary incident field excited at the point is defined as an unknown vector, denoted as D. CR The number of its elements is N C In summary, the unknown vector to be solved in the equation is Y = [I T D CR T ] T .

[0053] Step S105 specifically includes the following steps:

[0054] S501. Calculate the self-acting operator: Define the mapping from the incident field to the scattered current in the coordinate system as the self-acting operator. Calculate the self-acting operators in the relatively stationary sub-region and the linked sub-region in the global coordinate system, and calculate the self-acting operators on the mesh in the rotated sub-region in the local coordinate system, as follows:

[0055] Ω in the global coordinate system S The self-acting operator is denoted as L.S -1 The self-acting operator Ω will be used in the global coordinate system. C Let it be L C -1 Ω will be in the local coordinate system R The self-acting operator above is denoted as If Ω S ∪Ω C If L is a closed surface, then S -1 and L C -1 Let Ω be the inverse of the impedance matrix of the mixed-field integral equation (CFIE); if Ω S ∪Ω C If it is an open surface, then L S -1 and L C -1 This is the inverse of the impedance matrix in the electric field integral equation (EFIE). If Ω R It is a closed surface. Let Ω be the inverse of the impedance matrix of the mixed-field integral equation (CFIE); if Ω R It is an open surface. This is the inverse of the impedance matrix in the electric field integral equation (EFIE). When the number of unknowns in the subdomain is large, L needs to be constructed first using an accelerated algorithm. S and L C Or its approximate expression, and then use an iterative method to calculate the self-acting current coefficient.

[0056] S502. Calculating the equivalent operator: The equivalent operator is defined as the mapping relationship between the equivalent incident electromagnetic current and the equivalent scattered electromagnetic current on the mesh within the equivalent surface in the local coordinate system. It includes three processes: internal equivalence, self-action, and external equivalence in the rotating sub-region, as detailed below:

[0057] Based on local coordinate system E R Internal mesh and basis functions Construct equivalent operators using the Equivalent Source Domain Decomposition (EPA) algorithm.

[0058]

[0059] in This represents the vector of equivalent incident electromagnetic current coefficients on the equivalent surface. Incident field test vector excited on the rotating sub-region The internal equivalent process:

[0060]

[0061] in For the self-acting operator calculated in S501 on the rotating sub-region, represents the incident field vector on the rotating sub-region. The scattering current coefficient on it Process of action:

[0062]

[0063] Represents the scattering current coefficient on the rotating sub-region Equivalent scattered electromagnetic current test vector to the equivalent surface External equivalent process:

[0064]

[0065] S503. Calculate the coefficient solver on the rotationally symmetric equivalent surface and the linked subdomain. The coefficient solver is used to calculate the coefficients of the physical quantity by expanding the basis functions based on the test vector corresponding to the physical quantity. The physical quantity is current, magnetic current, electric field, or magnetic field. Specifically, it includes steps S5031 and S5032:

[0066] S5031. In the global coordinate system, calculate E based on the external mesh. R and Ω C The coefficient solver on is denoted as U R -1 and U C -1 If E R The physical quantity X on the surface can be expanded by the outer basis functions as follows:

[0067]

[0068] Applying the Galerkin test to both sides of the above equation, we get:

[0069]

[0070] Where V X Let A be the test vector of the physical quantity X, and let A be the expansion coefficient vector of X, i.e. but:

[0071] A = U E -1 V X

[0072] Similarly, it can be based on Ω C outer basis function calculation coefficients solution matrix U C -1 .

[0073] S5032. In the local coordinate system, calculate E based on the inner mesh and inner layer basis functions. R and Ω CThe coefficient solving operator on is denoted as and The calculation method is the same as that for the coefficient solver in the global coordinate system.

[0074] S504. Calculating Interaction Operators: The interaction operator is defined as the process by which a scattered current (electromagnetic current) in one sub-region generates a secondary incident field in another sub-region. In the global coordinate system, the interaction operators between relatively stationary sub-regions and equivalent surfaces, and between relatively stationary sub-regions and linked sub-regions, are calculated based on the external mesh. In the local coordinate system, the interaction operators between linked sub-regions and rotated sub-regions are calculated based on the internal mesh, as detailed below:

[0075] The incident field on the surface of each subdomain is composed of the secondary incident fields excited by the external field source and the scattered currents from other subregions. Therefore, the solution equations must include the subdomain-to-subdomain interaction operator. In this embodiment, Ω S and Ω C The interaction between them is calculated based on the external mesh in the global coordinate system, denoted as T. SC and T CS Ω S and Ω R The interaction between them is decomposed into two processes, one being Ω S and E R The interaction between them, and E R For Ω R The equivalent effect of Ω S and E R The interaction between them is calculated based on the mesh in the global coordinate system, denoted as T. ES and T SE Ω R and Ω C The interaction between them is calculated based on the internal mesh in the local coordinate system, denoted as and The detailed calculation formulas for the interaction operators are the same as those for the equivalent source-based domain decomposition method (EPA).

[0076] Step S106 specifically includes the following steps:

[0077] S601, Let i = 0, 1, ..., N spl -1, in t i At any given moment, update the E coordinate system between the global and local coordinate systems. R and Ω C coordinate system rotation operator and t i The positional relationship between the global coordinate system and the local coordinate system at any given time is: That is, the local coordinate system rotates the x′o′y′ plane by Δφ around z′.i After obtaining the angle, we get x″o′y″, then rotate z′o′y″ around x″ by Δθ. i After adjusting the angle, we obtain z″o′y″′, and the new coordinate system x″y″′z″ follows the vector. Directional translation After the distance is calculated, it coincides with the global coordinate system xyz. The following formula is used to calculate E in the global coordinate system. R The basis function coefficient vector on Transform to the corresponding coefficient vector in the local coordinate system

[0078]

[0079] on the contrary,

[0080]

[0081] The following formula defines Ω in the global coordinate system. C The basis function coefficient vector on Transform to the corresponding coefficient vector in the local coordinate system

[0082]

[0083] on the contrary,

[0084]

[0085] The specific calculation formula for the coordinate system rotation operator can be obtained using the current coefficient transformation method in the domain decomposition method based on rotationally symmetric equivalent sources (EPA-BoR).

[0086] S602. Based on the fact that the unknown scattered current (electromagnetic current) in each sub-region is equal to the superposition of the self-acting scattered current (electromagnetic current) and the secondary scattered current (electromagnetic current) generated by the interaction with other sub-regions, the equation to be solved is established, which specifically includes the following steps:

[0087] S6021. The incident field is a uniform plane wave. In the global coordinate system, the incident field remains constant, and the incident electric field is denoted as... The incident magnetic field is denoted as Calculate the induced electromagnetic currents on the surfaces of each subdomain in the global coordinate system without considering interactions:

[0088] (1) Calculate E R Upper self-actualized equivalent scattered electromagnetic current coefficient vector

[0089]

[0090] in, For E RThe self-actualized equivalent incident electromagnetic current coefficient vector, where the nth... E element For current coefficient:

[0091]

[0092] Nth E +n E element For magnetic flux coefficient:

[0093]

[0094] (2) Calculate Ω S Upper self-actualizing scattering current coefficient vector

[0095]

[0096] in It is the right-hand vector of the mixed-field integral equation, which can be calculated from the formula, where X = αE inc +(1-α)H inc , where 'a' is the mixing coefficient, and its value is in the interval [0,1].

[0097] (3) Calculate Ω C The self-actually scattering current coefficient vector on

[0098]

[0099] S6022. Establish the system of equations to be solved:

[0100]

[0101] Step S107 specifically includes: using the GMRES iterative solver to solve the equation established in step S602, setting the truncation precision to below 2.0e-3, and obtaining t. i The solution vector Y of the partially rotated target at time step i The scattered electromagnetic current coefficient I i =[I E i I C i I S i ] T , where I E i For E R The upper self-acting equivalent scattered electromagnetic current coefficient vector, I C i Ω C The self-actualizing scattering current coefficient vector on, IS i Ω S The scattering field of a partially rotating conductor target is obtained by calculating the scattering electromagnetic current coefficient coefficient of the self-actualizing scattering vector and the reciprocity theorem. and

[0102] In step S108, let , calculate the electromagnetic scattering of the partially rotating conductor target at the next sampling time point, update the relationship between the local coordinate system and the global coordinate system, and repeat steps S106-S107 until the calculation of the far-field scattering field at different sampling time points in the entire rotation cycle is completed.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A precise simulation method for electromagnetic scattering of partially rotating targets, characterized in that, The partially rotating target includes at least one component that is periodically rotating, the component being connected to the main body of the partially rotating target, and the method includes the following steps: S101、establish initial t0 moment to be solved part of the rotating conductor target model, set system parameters, set the rotating angle velocity of the rotating part of the part of the rotating conductor target to be solved as , the incident field frequency is , the incident angle is , the polarization angle is , the surface of the part of the rotating conductor target is recorded as , the posture of the part of the rotating target is uniformly sampled in a rotating period, the total number of positions is recorded as , the sampling time point corresponding to the ith position is recorded as , , the posture of the part of the rotating target is fixed at each sampling time point. S102. Divide the partial rotating conductor target model into subdomains and establish a reference coordinate system, and define the partial rotating conductor target surface. Divided into relatively static sub-regions Rotational subregion and link sub-regions Define a global coordinate system that does not change over time. , and Relative global coordinate system still, around Perform periodic rotation; in Using its rotational coordinate axes, establish a system that can completely enclose... rotational symmetry equivalent surface Establish a local coordinate system with the rotational symmetry axis as the z-axis. , Stationary relative to the local coordinate system , , , , , ,in for and The boundary edge, for and The boundary line and Parallel to the local coordinate system ; S103. Select the inner and outer layer basis functions and perform corresponding mesh generation on the partial rotating conductor target model, specifically including the following steps: S301. In the global coordinate system, use the highly flexible outer basis function based on small patch partitioning for discretization. , , Electromagnetic current on, denoted as In the local coordinate system, the inner basis functions are selected for discretization based on the structural characteristics of the rotated sub-region. , , Electromagnetic current on, denoted as ; S302, In the global coordinate system , , according to The mesh generation requirement is to perform a uniform surface mesh generation; this mesh is called the external mesh. The external mesh is... Both sides must be continuous to ensure The current is continuous on both sides; S303, In the local coordinate system , , according to The surface mesh is required to be generated, and this mesh is called the internal mesh. S104. Based on the electromagnetic flow of each subdomain of the discretized rotating conductor target model using inner and outer layer basis functions, define the unknowns to be solved, specifically including the following steps: S401, in the global coordinate system, the surface of the relatively stationary sub-region Take office Unknown scattered current at the location Expand into: To ensure current continuity between subdomains, the edge The upper basis function is defined in and On the grid connected to it, The unknown scattering current coefficient on is attributed to In the unknown quantities to be determined, The total number of unknown current coefficients is Then its unknown coefficient vector is denoted as ; S402, Link the sub-region surfaces in the global coordinate system Take office Unknown scattered current at the location Expand into: The total number of unknown current coefficients is Then its unknown coefficient vector is denoted as ; S403. In the global coordinate system, the equivalent surface Take office Unknown equivalent scattered current at the location and equivalent scattered magnetic current Expand into: The total number of unknown current coefficients is Then its unknown equivalent scattered electromagnetic current coefficient vector is denoted as Let the vector of the total undetermined electromagnetic current coefficients be denoted as ; S404. In the global coordinate system, it will be... Scattered current on exist Take office The test vector of the secondary incident field excited at the point is defined as an unknown vector, denoted as . The number of its elements is In summary, the unknown vector to be solved in the equation is: ; S105. Calculate the self-acting operator, equivalent operator, coefficient solving operator, and interaction operator of the equation to be solved, specifically including the following steps: S501. Calculate the self-acting operator: Define the mapping from the incident field to the scattered current in the coordinate system as the self-acting operator. Calculate the self-acting operators in the relatively stationary sub-regions and linked sub-regions in the global coordinate system. Calculate the self-acting operators on the mesh within the rotated sub-region in the local coordinate system. The calculation will be performed in the global coordinate system. The self-acting operator above is denoted as Self-acting operators will be used in the global coordinate system. Recorded as In the local coordinate system The self-acting operator above is denoted as ; S502. Calculate the equivalent operator: Define the mapping relationship between the equivalent incident electromagnetic flow and the equivalent scattered electromagnetic flow on the mesh in the equivalent surface of the local coordinate system as the equivalent operator, which includes three processes: internal equivalence, self-action, and external equivalence in the rotating sub-region. S503. Calculate the coefficient solver on the rotationally symmetric equivalent surface and the linked subdomain. The coefficient solver is used to calculate the coefficients of the physical quantity by basis function expansion based on the test vector corresponding to the physical quantity. The physical quantity is current, magnetocurrent, electric field or magnetic field. S504. Calculate the interaction operator: Define the process by which a scattered current in one sub-region generates a secondary incident field in another sub-region as the interaction operator. In the global coordinate system, calculate the interaction operators between the relatively stationary sub-region and the equivalent surface, and between the relatively stationary sub-region and the linked sub-region based on the external mesh. In the local coordinate system, calculate the interaction operators between the linked sub-region and the rotated sub-region based on the internal mesh. S106. Update the coordinate system rotation operator between the global and local coordinate systems, and establish and solve the unknown equations for the partial rotating conductor target at the current moment. S107. Use an iterator to solve the equation to be solved and obtain the solution vector. According to the remote calculation formula, calculate the far-field scattering field at the current time from the scattering electromagnetic current coefficient vector. S108. Calculate the electromagnetic scattering of the partially rotated target at the next sampling time point, update the relationship between the local coordinate system and the global coordinate system, and repeat steps S106 and S107 until the calculation of the far-field scattering field at different sampling time points in the entire rotation cycle is completed.

2. The integrated and accurate simulation method for electromagnetic scattering of a partially rotating target according to claim 1, characterized in that, Step S106 specifically includes the following steps: S601, Order ,exist At any given moment, update the coordinate system between the global and local coordinate systems. and coordinate system rotation operator , , and ; S602. Based on the fact that the unknown scattering current in each sub-region is equal to the superposition of the self-actualizing scattering current and the secondary scattering current generated by the interaction with other sub-regions, establish the equation to be solved.

3. The integrated and accurate simulation method for electromagnetic scattering of a partially rotating target according to claim 2, characterized in that, Step S107 specifically includes: using the GMRES iterative solver to solve the equation established in step S602, and obtaining... The solution vector of the partially rotated target at time step The scattered electromagnetic current coefficient = ,in for The self-actualized equivalent scattered electromagnetic current coefficient vector, for The self-actualizing scattering current coefficient vector on, for The scattering field of a partially rotating conductor target is obtained by calculating the scattering electromagnetic current coefficient coefficient of the self-actualizing scattering vector and the reciprocity theorem. and .

4. The integrated and accurate simulation method for electromagnetic scattering of a partially rotating target according to claim 3, characterized in that, In step S108, let Calculate the electromagnetic scattering of the partially rotating conductor target at the next sampling time point, update the relationship between the local coordinate system and the global coordinate system, and repeat steps S106-S107 until the calculation of the far-field scattering field at different sampling time points in the entire rotation cycle is completed.

Images