A solution method and system of characteristic basis function method

Abstract

This invention discloses a solution method and system for the characteristic basis function method. The solution method includes the following steps: dividing the target into multiple subdomains based on the number of unknowns; introducing a magnetic flux component to obtain the characteristic basis function corresponding to each subdomain based on the direct solution method of the butterfly algorithm; the characteristic basis function includes primary characteristic basis function and secondary characteristic basis function; calculating the weighting coefficients corresponding to each characteristic basis function using the direct solution method based on LU decomposition; superimposing multiple weighting coefficients corresponding to multiple subdomains to obtain the surface current distribution and surface magnetic flux distribution of the target, and calculating the scattering characteristics of the target through radiation integral.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic field numerical calculation technology, and in particular to a solution method and system for the characteristic basis function method. Background Technology

[0002] The Method of Moments (MoM) is a commonly used numerical method for electromagnetic field calculations, widely applied in fields such as electromagnetic scattering analysis. However, when analyzing electrically large targets (i.e., targets with a large ratio of actual size to operating wavelength), the computational complexity and storage requirements of the MoM increase dramatically, severely limiting its application efficiency. Therefore, to reduce the number of unknowns to meet the computational needs of electrically large target scattering problems, macro-basis functions have been introduced into the MoM, with the characteristic basis function method being a typical technique. This method divides the target into multiple subdomains, denoted as M. The total number of unknowns is the sum of the unknowns in each subdomain, and the unknowns in each subdomain are determined by the number of grid cells in that subdomain. The target current distribution can be obtained by weighting using characteristic basis functions.

[0003] However, the characteristic basis function method has a significant performance bottleneck: there is a mutually restrictive relationship between the number of subdomains and the number of unknowns in each subdomain. Increasing the number of subdomains M can reduce the number of unknowns in each subdomain, but it will reduce the matrix dimension by M%. 2 The scale of the matrix increases dramatically, and the L (Lower Triangular Matrix) U (Upper Triangular Matrix) decomposition (a commonly used method for directly solving matrix equations, which decomposes the matrix into the product of the lower triangular matrix and the upper triangular matrix) to obtain the weighting coefficients of the characteristic basis function is extremely time-consuming. If M is controlled to be low in quantity to reduce the dimension of the reduced matrix, the number of unknowns in the subdomain will increase accordingly, resulting in a serious time consumption in the generation process of the characteristic basis function. The above constraints greatly reduce the computational efficiency of the characteristic basis function method.

[0004] Existing techniques for improving the computational efficiency of the characteristic basis function method are mostly optimized for reducing the matrix, but they all have shortcomings: some techniques use specific algorithms to approximate the reduced matrix as a product of a series of block diagonal matrices to accelerate the decomposition, but they are unstable when the number of subdomains is large; other techniques use iterative solution algorithms to calculate the weighting coefficients of the characteristic basis functions, but they are more prone to numerical divergence than direct solution.

[0005] Therefore, there is an urgent need for a solution method and system for the characteristic basis function method, which can further optimize the computational efficiency of the characteristic basis function method to better adapt to the electromagnetic scattering analysis requirements of electrically large targets.

[0006] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0007] The purpose of this invention is to address the problem that the current characteristic basis function method is not efficient enough and is difficult to adapt to electrically large targets. It proposes a solution method and system for the characteristic basis function method to improve the simulation efficiency and computational efficiency of the characteristic basis function method.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solution: The first aspect of this invention provides a method for solving the characteristic basis function method, comprising: Based on the number of unknowns in the target, the target is divided into multiple subdomains; Based on the direct solution method using the butterfly algorithm, a magnetic flux component is further introduced to obtain the characteristic basis function corresponding to each subdomain; the characteristic basis function includes primary characteristic basis function and secondary characteristic basis function; The weighting coefficients corresponding to each of the characteristic basis functions are calculated using a direct solution method based on LU decomposition. The weighting coefficients corresponding to the multiple subdomains are superimposed to obtain the surface current distribution and surface magnetic flux distribution of the target, and the scattering characteristics of the target are calculated by radiation integration.

[0009] Optionally, dividing the target into multiple subdomains based on the number of unknowns of the target includes: dividing the target into M subdomains based on the number N of unknowns of the target, where M is γ. The result of rounding up, where 1.2 ≤ γ ≤ 3.0.

[0010] Optionally, the step of further introducing a magnetic flux component to obtain the characteristic basis function corresponding to each subdomain, based on the direct solution method using the butterfly algorithm, includes: A system of integral equations containing the coupling relationship between current and magnetocurrent is constructed. The system of integral equations is discretized to form matrix equations and then solved to obtain the characteristic basis function corresponding to each subdomain.

[0011] Optionally, the system of integral equations includes: in, Operators representing currents acting in free space; Indicates dielectric impedance; Operators that represent currents acting on a dielectric region; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Represents the surface normal vector; Indicates the incident electric field; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Operators representing currents acting in free space; Operators that represent currents acting on a dielectric region; J represents the incident magnetic field; J represents the electric current; M represents the magnetic current.

[0012] Optionally, the matrix equation is as follows: in, When solving for the principal characteristic basis functions This is the current self-coupling self-impedance matrix of the corresponding subdomain; This is the coupling self-impedance matrix of the current and magnetic current in the corresponding subdomain; This is the coupling self-impedance matrix of the magnetic current and current in the corresponding subdomain; This is the magnetic flux self-coupling self-impedance matrix of the corresponding subdomain; This corresponds to the voltage caused by the incident electric field; The voltage caused by the incident magnetic field; When solving for the minor characteristic basis functions This is the current self-coupling mutual impedance matrix of the corresponding subdomain; This represents the coupling mutual impedance matrix between the current and magnetic current in the corresponding subdomain. This represents the mutual impedance matrix of the magnetic current and the current in the corresponding subdomain. This is the magnetic flux self-coupling mutual impedance matrix of the corresponding subdomain; The primary current characteristic base voltage; The primary characteristic voltage of the magnetocurrent is the base voltage.

[0013] Optionally, the step of calculating the weighting coefficients corresponding to each characteristic basis function using a direct solution method based on LU decomposition includes: A reduced matrix is ​​constructed to form a reduced matrix equation containing the coefficients of the current characteristic basis function and the coefficients of the magnetocurrent characteristic basis function. The reduced matrix equation is solved using a direct solution method based on LU decomposition to obtain the weighting coefficients of the characteristic basis functions.

[0014] Optionally, the Galerkin method can be used to construct a reduced matrix.

[0015] Optionally, the reduced matrix equation is as follows: Among them, Z 11 Z represents the shrinking matrix of the current; 12 The reduced matrix representing the current and magnetic current; Z 21The reduced matrix representing magnetic current and electric current; Z 22 The self-reducing matrix representing the magnetic flux; and These are the coefficients of the current characteristic basis function and the coefficients of the magnetocurrent characteristic basis function, respectively. Here is the voltage reduction matrix caused by the incident electric field; Let be the voltage reduction matrix caused by the incident magnetic field.

[0016] Optionally, the surface current distribution of the target J This can be expressed by the following formula: in, J i Indicates the current distribution over each subdomain; when the superscript... k and subscript i When they are the same, Indicates the primary current characteristic basis functions; when the superscript is... k and subscript i At the same time, Denotes the secondary current characteristic basis functions; Representing the characteristic basis function of current Weighting coefficients; i , k All are positive integers between 1 and M, where M is the number of subfields; The surface magnetic flux distribution of the target This can be expressed by the following formula: in, This represents the magnetic current distribution over each subdomain; when the superscript k and subscript i are the same, Indicates the main magnetic current characteristic basis functions; when the superscript k and subscript i are different, Indicates the secondary magnetic current characteristic basis functions; Represents the characteristic basis functions of magnetic current The weighting coefficients.

[0017] A second aspect of the present invention provides a solution system for the characteristic basis function method, comprising: A subdomain partitioning unit is used to calculate based on the number of unknowns of the target to divide the target into multiple subdomains; The characteristic basis function calculation unit is connected to the subdomain partitioning unit. It is used to further introduce magnetic flux components on the basis of the direct solution method based on the butterfly algorithm, and obtain and output the characteristic basis function corresponding to each subdomain. The characteristic basis function includes primary characteristic basis function and secondary characteristic basis function. The weighting coefficient calculation unit is connected to the feature basis function calculation unit, and is used to receive the feature basis functions, calculate and output the weighting coefficients corresponding to each feature basis function through a direct solution method based on LU decomposition; A scattering characteristic calculation unit, connected to the weighting coefficient calculation unit, is used to superimpose multiple weighting coefficients corresponding to the multiple subdomains to obtain the surface current distribution and surface magnetic flux distribution of the target, and to calculate the scattering characteristics of the target by radiation integration.

[0018] This invention has at least the following technical effects: By balancing the number of subdomains and the unknowns in the subdomains, and by using the direct solution method twice when solving for the characteristic basis functions and their weighting coefficients, the computational speed of the characteristic basis function method can be significantly improved, and the simulation scale and applicability of the characteristic basis function method can be greatly enhanced. By employing a direct solution method based on the butterfly algorithm to obtain characteristic basis functions, the butterfly algorithm overcomes the instability and numerical divergence problems of existing technologies by leveraging its advantages of extremely low time complexity in direct solution methods, stable decomposition in large-scale computations, and no introduction of numerical divergence. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the solution method of the characteristic basis function method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the single-station radar cross section of a Cobra cavity. Figure 3 To adopt the existing subdomain basis moment method, for Figure 2 A schematic diagram of the RCS curve obtained from the calculation of the Cobra cavity is shown. Figure 4 To implement the solution method of the characteristic basis function method provided in an embodiment of the present invention, the following steps are taken: Figure 2 The RCS curve is calculated using the Cobra cavity shown. Detailed Implementation

[0020] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the solution method and system for the characteristic basis function method proposed in this invention. The advantages and features of this invention will become clearer from the following description. It should be noted that the accompanying drawings are in a very simplified form and use non-precise proportions, used only to facilitate and clearly illustrate the embodiments of this invention. Please refer to the accompanying drawings to make the objectives, features, and advantages of this invention more apparent and understandable. It should be understood that the structures, proportions, sizes, etc., depicted in the accompanying drawings are only for illustrative purposes to aid those skilled in the art and are not intended to limit the implementation conditions of this invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to the size, without affecting the effects and objectives achieved by this invention, should still fall within the scope of the technical content disclosed in this invention.

[0021] The first aspect of this embodiment provides a solution method for the characteristic basis function method, such as... Figure 1 The method includes the following steps: S1. Divide the target into multiple subdomains based on the number of unknowns in the target; S2. Based on the direct solution method using the butterfly algorithm, a magnetic flux component is further introduced to obtain the characteristic basis functions corresponding to each subdomain; the characteristic basis functions include primary characteristic basis functions and secondary characteristic basis functions. S3. The weighting coefficients corresponding to each characteristic basis function are calculated using the direct solution method based on LU decomposition. S4. Superimpose multiple weighting coefficients corresponding to multiple subdomains to obtain the surface current distribution and surface magnetofluid distribution of the target, and calculate the scattering characteristics of the target by radiation integral.

[0022] Specifically, in step S1, the target can be divided into M subdomains based on the number of unknowns N, where M is γ. The result is rounded up, where 1.2 ≤ γ ≤ 3.0. The number of unknowns N of the target depends on the number of grids in the target and can be used to characterize the scale of the problem or the electrical dimensions of the target. In this embodiment, the number of unknowns N of the target is the sum of the number of unknowns in each of the divided subdomains.

[0023] As those skilled in the art will understand, the number of subdomains is a function of the size of the problem and is closely related to the solution algorithm. In this embodiment, the direct solution method based on the butterfly algorithm used in subsequent steps has a complexity of O(N) for solving the inverse matrix. 1.5The time complexity is O(logN), where O() represents the time complexity, and the base of logN is 10. According to the characteristic basis function method, in calculating the primary characteristic basis function, secondary characteristic basis function, and reduced matrix, to optimize the number of subdomains M, the quantitative relationship between the number of unknowns N and the number of subdomains M must satisfy the following formula: By solving the above formula, we can obtain the result. .

[0024] Based on these calculations, this embodiment further adds a coefficient γ to balance the number of unknowns in each subdomain and the dimension of the reduced matrix, thus accommodating different hardware platform configurations. Therefore, the number of subdomains can be significantly reduced without affecting the efficiency of characteristic basis function generation, thereby improving the problem-solving efficiency. The aforementioned subdomain partitioning strategy reduces the computational cost of generating characteristic basis functions and compresses the number of characteristic basis functions, thereby reducing the number of main characteristic basis functions (i.e., the number of subdomains) and the time required to construct and solve the reduced matrix equations, thus improving both the scale and efficiency of the problem-solving process.

[0025] Furthermore, in step S2, a magnetic flux component can be introduced into the direct solution method of the original butterfly algorithm to construct a system of integral equations containing the coupling relationship between current and magnetic flux. After discretizing the system of integral equations to form matrix equations, these equations are solved to obtain the characteristic basis functions corresponding to each subdomain. The direct solution method of the butterfly algorithm employs multi-level LU decomposition and utilizes a randomized reconstruction method to achieve efficient matrix decomposition. Considering the universality of solving scattering problems, the system of integral equations formed by introducing a magnetic flux component into the direct solution method of the original butterfly algorithm is as follows: in, Operators representing currents acting in free space; Indicates dielectric impedance; Operators that represent currents acting on a dielectric region; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Represents the surface normal vector; Indicates the incident electric field; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Operators representing currents acting in free space; Operators that represent currents acting on a dielectric region; J represents the incident magnetic field; J represents the electric current; M represents the magnetic current.

[0026] More specifically, , , , , , , , The following formula can be used for calculation: in, i The value can be 0 or 1. i A value of 0 indicates free space. i A value of 1 indicates a medium region. u The value can be J or M. u Let J represent the current. u M represents magnetic current. G represents the wave number; G() represents the Green's function; r Indicates the field point; r’ Indicates the source point; pv The principal values ​​are represented by [value]. Discretizing the above formulas yields large matrix equations, which are then solved directly using the butterfly algorithm to obtain the principal characteristic basis functions for each subdomain. Furthermore, the secondary characteristic basis functions for each subdomain are obtained from these solutions.

[0027] The current J is calculated using the following formula: in, These are RWG basis functions (a type of basis function proposed by Rao, Wilton, and Glisson in 1982). The number of bases, The coefficients of the base.

[0028] The magnetic current M is calculated using the following formula: in, For RWG basis functions, The number of bases, The coefficients of the base.

[0029] Substituting the above calculation results into the system of integral equations, and discretizing them, we obtain the common matrix equation as follows: in, .

[0030] When solving for the principal characteristic basis functions This is the current self-coupling self-impedance matrix of the corresponding subdomain; This is the coupling self-impedance matrix of the current and magnetic current in the corresponding subdomain; This is the coupling self-impedance matrix of the magnetic current and current in the corresponding subdomain; This is the magnetic flux self-coupling self-impedance matrix of the corresponding subdomain; This corresponds to the voltage caused by the incident electric field; This is the voltage caused by the incident magnetic field.

[0031] When solving for the minor characteristic basis functions This is the current self-coupling mutual impedance matrix of the corresponding subdomain; This represents the coupling mutual impedance matrix between the current and magnetic current in the corresponding subdomain. This represents the mutual impedance matrix of the magnetic current and the current in the corresponding subdomain. This is the magnetic flux self-coupling mutual impedance matrix of the corresponding subdomain; The primary current characteristic base voltage; The primary characteristic voltage of the magnetocurrent is the base voltage.

[0032] As those skilled in the art will understand, the direct solution method based on the butterfly algorithm is commonly used in subdomain method of moments (MoM), while the iterative solution method is more commonly used in macrodomain MoM. To leverage the efficient computational power of the butterfly algorithm, this embodiment selects the characteristic basis function method, which belongs to macrodomain MoM, applying the method from the subdomain basis to the macrodomain basis. Furthermore, when the solution range is expanded from metals to media, magnetic current is introduced. Therefore, based on the advantages of the direct solution method of the butterfly algorithm, the subdomain partitioning in step S1 can result in fewer subdomains and more unknowns within each subdomain, thereby maximizing the balance between the number of unknowns and subdomains and accelerating computation.

[0033] Furthermore, in step S3, a reduced matrix equation containing the coefficients of the current characteristic basis functions and the coefficients of the magnetic current characteristic basis functions can be formed by constructing a reduced matrix. The reduced matrix equation is then solved using a direct solution method based on LU decomposition to obtain the weighting coefficients of the characteristic basis functions. By using the direct solution method twice in steps S2 and S3 to solve for different physical quantities, the entire solution process can be made more efficient.

[0034] Specifically, the Galerkin method can be used to construct the reduced matrix, and the expression for the reduced matrix equation is as follows: Among them, Z 11 Z represents the shrinking matrix of the current; 12 The reduced matrix representing the current and magnetic current; Z 21 The reduced matrix representing magnetic current and electric current; Z 22The self-reducing matrix representing the magnetic flux; and These are the coefficients of the current characteristic basis function and the coefficients of the magnetocurrent characteristic basis function, respectively. Here is the voltage reduction matrix caused by the incident electric field; Let be the voltage reduction matrix caused by the incident magnetic field.

[0035] Specifically, Z 11 The matrix expression is as follows: in, T Indicates the matrix transpose. When the superscript... k and subscript i When they are the same, Indicates the primary current characteristic basis functions. When superscript... k and subscript i At the same time, This represents the secondary current characteristic basis function. i , k The values ​​of Z are all positive integers between 1 and M, where M is the number of subdomains divided in step S1. When u and v are the same, Z uv Z represents the self-impedance matrix. When u and v are different, Z... uv This represents the mutual impedance matrix. The values ​​of u and v are both positive integers between 1 and M.

[0036] Z 12 The matrix expression of Z 11 Similar, except Z 12 The end of each element in the matrix expression Replace all with The superscript and subscript remain unchanged. When the superscript k and subscript i are the same, This represents the main magnetic current characteristic basis functions. When the superscript k and subscript i are different, ... This represents the secondary magnetic current characteristic basis function.

[0037] Z 21 The matrix expression of Z 11 Similar, except Z 21 In the matrix expression, each element begins within square brackets. Replace all with The superscript and subscript remain unchanged.

[0038] Z 22 The matrix expression of Z 11 Similar, except Z 22 In the matrix expression, each element (Whether it's within square brackets at the end or beginning of an element) should be replaced with The superscript and subscript remain unchanged.

[0039] Z 11 Z 12 Z 21 Z 22 The four matrix expressions form a large matrix equation, and the weighting coefficients of each characteristic basis function can be calculated by using the direct solution method again.

[0040] Finally, in step S4, the surface current distribution and surface magnetic flux distribution of the target can be obtained by superimposing the weighting coefficients of each characteristic basis function, and then the scattering characteristics of the target can be solved by radiation integral. This step belongs to the general solution process of the characteristic basis function method, and will not be described in detail here.

[0041] Specifically, in this embodiment, the surface current distribution of the target J can This can be expressed by the following formula: in, J i Indicates the current distribution over each subdomain; when the superscript... k and subscript i When they are the same, Indicates the primary current characteristic basis functions; when the superscript is... k and subscript i At the same time, Denotes the secondary current characteristic basis functions; Representing the characteristic basis function of current Weighting coefficients; i , k All are positive integers between 1 and M, where M is the number of subfields; Surface magnetic flux distribution of the target This can be expressed by the following formula: in, Indicates the magnetic current distribution over each subdomain; when the superscript... k and subscript i When they are the same, Indicates the main magnetic current characteristic basis functions; when the superscript is used... k and subscript i At the same time, Indicates the secondary magnetic current characteristic basis functions; Represents the characteristic basis functions of magnetic current The weighting coefficients.

[0042] The solution method of the characteristic basis function method provided in this embodiment will be further explained in more detail below. (Reference) Figure 2It shows a Cobra cavity monostatic radar cross-section (RCS) with a length of 450 mm. Plane waves are incident on the XOZ plane, vertically polarized, and scan from -X through +Z, +X, -Z back to -X.

[0043] refer to Figure 3 It demonstrates the use of existing subdomain basis moment methods for... Figure 2 The RCS curves obtained from the Cobra cavity are shown. The target surface was partitioned at 1 / 10 wavelength, resulting in 188,556 RWG basis functions at an operating frequency of 10 GHz. The RWG basis functions are subdomain bases used in the traditional method of moments. The simulation calculation employed an adaptive cross-polarization method, taking a total of 96 minutes.

[0044] refer to Figure 4 It illustrates the solution method using the characteristic basis function method provided in this embodiment, for... Figure 2 The RCS curves obtained from the Cobra cavity are shown. The target was divided into 27 subdomains, and a direct solution method based on the butterfly algorithm was used in each subdomain, while also decomposing and reducing the matrix. The total time taken was 57 minutes.

[0045] Compare Figure 3 , Figure 4 It can be seen that the calculation results of the characteristic basis function method provided in this embodiment are in good agreement with the calculation results of the existing subdomain basis moment method, but the calculation efficiency is improved by about 40%.

[0046] In other aspects, this embodiment also provides a solution system for the characteristic basis function method, including a subdomain partitioning unit, a characteristic basis function calculation unit, a weighting coefficient calculation unit, and a scattering characteristic calculation unit.

[0047] Specifically, the subdomain partitioning unit is used to divide the target into multiple subdomains based on the number of unknowns. The characteristic basis function calculation unit, connected to the subdomain partitioning unit, further introduces a magnetic flux component to obtain and output the characteristic basis function corresponding to each subdomain, building upon the direct solution method based on the butterfly algorithm. The weighting coefficient calculation unit, connected to the characteristic basis function calculation unit, receives the characteristic basis functions, calculates and outputs the weighting coefficients corresponding to each characteristic basis function using a direct solution method based on LU decomposition, and then calculates the scattering characteristics of the target by superimposing multiple weighting coefficients corresponding to multiple subdomains.

[0048] In summary, the solution method and system of the characteristic basis function method provided by this invention, by balancing the number of subdomains and the unknowns in the subdomains, and by using the direct solution method twice when solving the characteristic basis function and its weighting coefficients, can significantly improve the calculation speed of the characteristic basis function method, greatly improve the simulation scale and applicability of the characteristic basis function method, and has made significant progress compared with the prior art.

[0049] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0050] It should be noted that the apparatus and methods disclosed in the embodiments herein can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments herein. In this regard, each block in a flowchart or block diagram may represent a module, program, or part of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system to perform the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0051] In addition, the functional modules in the various embodiments of this article can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0052] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A solution method based on the characteristic basis function method, characterized in that, include: Based on the number of unknowns in the target, the target is divided into multiple subdomains; Based on the direct solution method using the butterfly algorithm, a magnetic flux component is further introduced to obtain the characteristic basis function corresponding to each subdomain; the characteristic basis function includes primary characteristic basis function and secondary characteristic basis function; The weighting coefficients corresponding to each of the characteristic basis functions are calculated using a direct solution method based on LU decomposition. The weighting coefficients corresponding to the multiple subdomains are superimposed to obtain the surface current distribution and surface magnetic flux distribution of the target, and the scattering characteristics of the target are calculated by radiation integration.

2. The solution method of the characteristic basis function method according to claim 1, characterized in that, The step of dividing the target into multiple subdomains based on the number of unknowns of the target includes: dividing the target into M subdomains based on the number N of unknowns of the target, where M is γ. The result of rounding up, where 1.2 ≤ γ ≤ 3.

0.

3. The solution method of the characteristic basis function method according to claim 1, characterized in that, The method of directly solving the problem based on the butterfly algorithm further introduces a magnetic flux component to obtain the characteristic basis function corresponding to each subdomain, including: A system of integral equations containing the coupling relationship between current and magnetocurrent is constructed. The system of integral equations is discretized to form matrix equations and then solved to obtain the characteristic basis function corresponding to each subdomain.

4. The solution method of the characteristic basis function method according to claim 3, characterized in that, The system of integral equations includes: in, Operators representing currents acting in free space; Indicates dielectric impedance; Operators that represent currents acting on a dielectric region; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Represents the surface normal vector; Indicates the incident electric field; Operators that represent magnetic currents acting on free space; Operators that represent magnetic currents acting on a medium region; Operators representing currents acting in free space; Operators that represent currents acting on a dielectric region; J represents the incident magnetic field; J represents the electric current; M represents the magnetic current.

5. The solution method of the characteristic basis function method according to claim 3, characterized in that, The matrix equation is as follows: in, For current coefficient, is the magnetic flux coefficient; When solving for the principal characteristic basis functions This is the current self-coupling self-impedance matrix of the corresponding subdomain; This is the coupling self-impedance matrix of the current and magnetic current in the corresponding subdomain; This is the coupling self-impedance matrix of the magnetic current and current in the corresponding subdomain; This is the magnetic flux self-coupling self-impedance matrix of the corresponding subdomain; This corresponds to the voltage caused by the incident electric field; The voltage caused by the incident magnetic field; When solving for the minor characteristic basis functions This is the current self-coupling mutual impedance matrix of the corresponding subdomain; This represents the coupling mutual impedance matrix between the current and magnetic current in the corresponding subdomain. This represents the mutual impedance matrix of the magnetic current and the current in the corresponding subdomain. This is the magnetic flux self-coupling mutual impedance matrix of the corresponding subdomain; The primary current characteristic base voltage; The primary characteristic voltage of the magnetocurrent is denoted by .

6. The solution method of the characteristic basis function method according to claim 1, characterized in that, The calculation of the weighting coefficients corresponding to each characteristic basis function using the direct solution method based on LU decomposition includes: A reduced matrix is ​​constructed to form a reduced matrix equation containing the coefficients of the current characteristic basis function and the coefficients of the magnetocurrent characteristic basis function. The reduced matrix equation is solved using a direct solution method based on LU decomposition to obtain the weighting coefficients of the characteristic basis functions.

7. The solution method of the characteristic basis function method according to claim 6, characterized in that, The Galerkin method is used to construct the reduced matrix.

8. The solution method of the characteristic basis function method according to claim 6, characterized in that, The equation for the reduced matrix is ​​as follows: Among them, Z 11 Z represents the shrinking matrix of the current; 12 The reduced matrix representing the current and magnetic current; Z 21 The reduced matrix representing magnetic current and electric current; Z 22 The self-reducing matrix representing the magnetic flux; and These are the coefficients of the current characteristic basis function and the coefficients of the magnetocurrent characteristic basis function, respectively. Here is the voltage reduction matrix caused by the incident electric field; Let be the voltage reduction matrix caused by the incident magnetic field.

9. The solution method of the characteristic basis function method according to claim 1, characterized in that, The surface current distribution of the target J This can be expressed by the following formula: in, J i Indicates the current distribution over each subdomain; when the superscript... k and subscript i When they are the same, Indicates the primary current characteristic basis functions; when the superscript is... k and subscript i At the same time, Denotes the secondary current characteristic basis functions; Representing the characteristic basis function of current Weighting coefficients; i , k All are positive integers between 1 and M, where M is the number of subfields; The surface magnetic flux distribution of the target This can be expressed by the following formula: in, This represents the magnetic current distribution over each subdomain; when the superscript k and subscript i are the same, Indicates the main magnetic current characteristic basis functions; when the superscript k and subscript i are different, Indicates the secondary magnetic current characteristic basis functions; Represents the characteristic basis functions of magnetic current The weighting coefficients.

10. A solution system for the characteristic basis function method, characterized in that, include: A subdomain partitioning unit is used to calculate based on the number of unknowns of the target to divide the target into multiple subdomains; The characteristic basis function calculation unit is connected to the subdomain partitioning unit. It is used to further introduce magnetic flux components on the basis of the direct solution method based on the butterfly algorithm, and obtain and output the characteristic basis function corresponding to each subdomain. The characteristic basis function includes primary characteristic basis function and secondary characteristic basis function. The weighting coefficient calculation unit is connected to the feature basis function calculation unit, and is used to receive the feature basis functions, calculate and output the weighting coefficients corresponding to each feature basis function through a direct solution method based on LU decomposition; The scattering characteristic calculation unit is used to superimpose multiple weighting coefficients corresponding to the multiple subdomains to obtain the surface current distribution and surface magnetofluid distribution of the target, and to calculate the scattering characteristics of the target by radiation integration.

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