Electromagnetic modeling method and device based on rotation basis function discrete total current

Abstract

The invention discloses an electromagnetic modeling method and device based on rotation primary function discrete total current, and the method comprises the steps: constructing a rotation primary function based on the generated unit pair information of a non-uniform medium target, the unit pair information is splitting unit data corresponding to a body splitting unit generated after geometric splitting is carried out on the inhomogeneous medium target; removing the redundant degree of freedom of the rotation primary function to obtain a target rotation primary function set; performing numerical discretization on the electric field integral equation of the total current of the inhomogeneous medium target through the target rotation basis function set to obtain a target electric field integral equation, and testing the target electric field integral equation through the test function set to obtain a global coupling matrix equation; and carrying out iterative solution on the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

Description

Technical Field

[0001] The present application relates to the field of computational electromagnetics, and more specifically, to an electromagnetic modeling method and device based on rotating basis function discretized full current. Background Art

[0002] The electromagnetic characteristics of inhomogeneous medium targets are studied in many fields, for example, in the parameter extraction of on-chip circuit devices and on-chip integrated circuit systems, biomedical electromagnetic modeling, stealth and anti-stealth of radar targets, etc., which have very important engineering application value. The integral equation method of computational electromagnetics is an equation system based on the field source relationship. It has unique advantages in analyzing the electromagnetic response of inhomogeneous medium targets: the unknown quantities of the system only exist on the surface of the analyzed target, corresponding to the surface integral equation (SIE), or in the body corresponding to the volume integral equation (VIE), without discretizing the background where the target is located. The contribution of the background is included in the Green's function of the system, so that the number of unknown quantities to be solved is small and no additional boundary conditions are required.

[0003] The volume integral equation method has the ability to handle dielectric targets with arbitrary non-uniform electrical parameters and arbitrary external structures, and is therefore an important means of analyzing the electromagnetic characteristics of non-uniform dielectric targets. Moreover, the volume integral method belongs to the second type of integral equation method, and its discrete matrix equation has good properties, which facilitates the rapid convergence of iterative solutions.

[0004] In the implementation of the volume integral equation method, the numerical matrix equation is often obtained by discretizing the equivalent body current, displacement current, or even the total electric field using the traditional roof-top basis function. However, such a discretization method usually makes the calculation of matrix elements complicated. For example, the coupling contribution of the equivalent body charge will inevitably appear in the coupling matrix elements, which will affect the solution efficiency of the matrix elements and seriously affect the final solution accuracy in engineering applications with high dielectric contrast. Summary of the invention

[0005] In response to at least one defect or improvement need in the prior art, the present invention provides an electromagnetic modeling method and device based on discretizing the full current based on a rotation basis function, which solves the problem that the calculation of volume charge in the matrix elements of the volume integral equation in the traditional method is relatively complex and the matrix elements are asymmetric, thereby achieving the purpose of improving the calculation accuracy.

[0006] To achieve the above-mentioned purpose, according to the first aspect of the present invention, there is provided an electromagnetic modeling method of discretizing the full current based on a rotation basis function, the method comprising: constructing a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target; removing the redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set; numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain a target electric field integral equation, and testing the target electric field integral equation through a test function set to obtain a global coupling matrix equation; iteratively solving the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0007] In an exemplary embodiment, before constructing the rotation basis function based on the unit pair information of the generated inhomogeneous medium target, the method further includes: geometrically segmenting the inhomogeneous medium target to generate a series of the volume segmentation units; constructing volume unit pairs corresponding to the volume segmentation units, and obtaining the unit pair information of the volume unit pairs, wherein the volume unit pairs have the same common surfaces.

[0008] In an exemplary embodiment, after constructing the volume unit pair corresponding to the volume unit and obtaining the unit pair information of the volume unit pair, the method further includes: determining a plurality of volume unit pairs having common edges in the volume unit pair according to the unit pair information, wherein the plurality of volume unit pairs include hexahedral units, triangular prism units, and tetrahedral units; and establishing the rotation basis functions corresponding to the plurality of volume unit pairs having shared common edges.

[0009] In an exemplary embodiment, removing the redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set includes: constructing a Gram matrix corresponding to the rotation basis function, and decomposing the Gram matrix into a series of subdomain Gram matrices; spatially grouping the multiple volume dissection units according to their relative spatial positions to obtain multiple groups, wherein each of the multiple groups matches a corresponding number according to its relative position in space; obtaining the number of the maximum linearly independent group of each subdomain Gram matrix in the series of subdomain Gram matrices, retaining the rotation basis function corresponding to the number, and obtaining the target rotation basis function set.

[0010] In an exemplary embodiment, the target electric field integral equation is obtained by numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set, including: expanding the electric field integral equation of the full current of the inhomogeneous medium target according to the expansion coefficient through the target rotation basis function set to obtain the target electric field integral equation.

[0011] In an exemplary embodiment, the testing of the target electric field integral equation through a test function set to obtain a global coupling matrix equation includes: testing the target electric field integral equation through the test function set to obtain a matrix equation; determining the global coupling matrix equation based on matrix elements and the matrix equation, wherein the matrix elements include resistance matrix elements, inductance matrix elements, and capacitance matrix elements.

[0012] In an exemplary embodiment, the iterative solution of the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target includes: iteratively solving the global coupling matrix equation, and when the iteration converges, extracting the full current information in the solution vector of the full current; and calculating the electromagnetic characteristics of the inhomogeneous medium target based on the full current information, wherein the electromagnetic characteristics include electromagnetic wave scattering and magnetic field strength.

[0013] According to the second aspect of the present invention, there is also provided an electromagnetic modeling device for discretizing the full current based on a rotation basis function, which comprises: a construction unit for constructing a rotation basis function based on unit pair information of a generated inhomogeneous medium target, wherein the unit pair information is the divided volume unit data corresponding to the volume divided unit generated after geometrically dividing the inhomogeneous medium target; an acquisition unit for removing redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set; a discretization unit for numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain a target electric field integral equation, and testing the target electric field integral equation through a test function set to obtain a global coupling matrix equation; and a solution unit for iteratively solving the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0014] According to a third aspect of the present invention, a computer-readable storage medium is provided, in which a computer program is stored, wherein the computer program is configured to execute the above-mentioned electromagnetic modeling method based on the rotation basis function discretization of the full current when running.

[0015] According to a fourth aspect of the present invention, there is also provided an electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the electromagnetic modeling method based on the rotation basis function discrete full current through the computer program.

[0016] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0017] (1) The present invention provides an electromagnetic modeling method based on the discretization of the total current using a rotation basis function. The method uses volume unit geometry to discretize medium targets and generate volume unit pair information, constructs a rotation basis function based on the volume unit pair information, removes the redundant degrees of freedom of the rotation basis function based on the subdomain Gram matrix method of the parallel computing strategy, uses the rotation basis function to discretize and test the total current in the electromagnetic model to construct a coupling matrix, iteratively solves the system equations to obtain the total current to be solved, and then calculates the electromagnetic characteristics of the system. The method solves the problems of complex calculation of volume charge and asymmetric matrix elements in the matrix elements of the volume integral equation in the traditional method, thereby improving the calculation accuracy of electromagnetic modeling.

[0018] (2) The present invention provides an electromagnetic modeling method based on the discretization of the full current with a rotating basis function, which uses a pure algebraic method based on the Gram matrix method to remove redundant degrees of freedom. It is applicable to geometric models of arbitrary topological shapes, arbitrary subdivision unit forms, and arbitrary basis function definition forms, and has good universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 A schematic flow chart of an optional electromagnetic modeling method based on rotating basis function discretization of full current provided in an embodiment of the present application;

[0021] Figure 2 A schematic diagram of an optional rotation basis function in a planarized triangular unit i provided in an embodiment of the present application;

[0022] Figure 3 A schematic diagram of an optional rotation basis function in a planarized hexahedral unit i provided in an embodiment of the present application;

[0023] Figure 4A schematic diagram of an optional roof-top basis function with positive and negative units provided in an embodiment of the present application;

[0024] Figure 5 A schematic diagram of an optional half roof-top basis function provided in an embodiment of the present application;

[0025] Figure 6 A schematic diagram of an optional hexahedron-based rotation basis function provided in an embodiment of the present application;

[0026] Figure 7 A schematic diagram of an optional rotation basis function based on a triangular prism provided in an embodiment of the present application;

[0027] Figure 8 A schematic diagram of an optional tetrahedron-based rotation basis function provided in an embodiment of the present application;

[0028] Fig. 9 A schematic diagram of an optional grouping of simple plane type targets provided in an embodiment of the present application;

[0029] Fig.10 A schematic diagram of an optional simple plane type target subdomain Gram matrix parallel calculation provided in an embodiment of the present application;

[0030] Fig.11 A schematic diagram of an optional simple plane type target subdomain Gram matrix parallel calculation provided in an embodiment of the present application;

[0031] Fig.12 A schematic diagram of an optional simple plane-type target sub-domain Gram matrix parallel calculation provided in an embodiment of the present application;

[0032] Fig.13 A schematic diagram of an optional simple plane type target subdomain Gram matrix parallel calculation provided in an embodiment of the present application;

[0033] Fig.14 A schematic diagram of an optional inhomogeneous medium target model provided in an embodiment of the present application;

[0034] Fig.15 A schematic structural diagram of an optional electromagnetic modeling device based on a rotation basis function discretized full current provided in an embodiment of the present application;

[0035] Fig.16 A schematic diagram of the structure of an optional electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. 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. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0037] The terms "first", "second", "third", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0038] According to one aspect of the embodiments of the present application, a method for electromagnetic modeling based on a rotation basis function discretized full current is provided. Figure 1 The electromagnetic modeling method based on the rotation basis function discretization of the full current provided in the embodiment of the present application is described.

[0039] Figure 1 is a flow chart of an optional electromagnetic modeling method based on rotating basis function discretization of full current provided in an embodiment of the present application, such as Figure 1 As shown, the process of the method may include the following steps:

[0040] S102, constructing a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target;

[0041] S104, removing redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set;

[0042] S106, numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target by using a target rotation basis function set to obtain a target electric field integral equation, and testing the target electric field integral equation by using a test function set to obtain a global coupling matrix equation;

[0043] S108, iteratively solving the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0044] The present application provides an optional electromagnetic modeling method based on rotating basis function discretized full current, which can be used in efficient electromagnetic modeling calculations of volume integral equations of dielectric targets. It should be noted that the dielectric target here is a non-uniform dielectric target.

[0045] In the electromagnetic modeling calculation of the embodiment of the present application, according to the classical Maxwell electromagnetic field theory, the "field-source" in the frequency domain satisfies the following equation:

[0046]

[0047] Where H is the magnetic field strength (A / m); E is the electric field strength (V / m); σ is the loss conductivity of the medium (S / m); J V =[σ+jω(∈-∈ b )]E is the equivalent current density (A / m2); J T is the total current density (A / m2); ∈ is the dielectric constant of the dielectric body (F / m); ∈ b is the dielectric constant of the background in which the dielectric body is located (F / m); μ is the magnetic permeability of the dielectric body (H / m); ω is the angular frequency of the system operation (rad / s).

[0048] Alternatively, according to the basic theory of integral equations, based on the total current J T The electric field integral equation can be expressed as: Among them, E inc is the excitation electric field strength of the system; χ is the electric parameter contrast of the medium relative to the background medium; is the electric field volume integral operator.

[0049] Furthermore, the above electric parameter contrast and electric field volume integral operator can be expressed by the definition formula:

[0050]

[0051] in, is the vector potential dyadic Green's function, K V are scalar Green's functions, which are all related to the background in which the non-uniform target is located.

[0052] In the embodiment of the present application, the basis function t can be used to calculate the total current J T Expand it and use the test function s to test the expanded volume integral equation, and we can get the matrix equation: Zα=b, where the element ts in the Z matrix can be expressed as:

[0053]

[0054] in, They are called resistance matrix elements, inductance matrix elements, and capacitance matrix elements respectively, and have the following expressions respectively

[0055]

[0056]

[0057] Full current J T The divergence of is always equal to 0, that is, J T ≡0, the embodiment of the present application can establish the rotation basis function on a group of volume division units with a common edge AB, and the division units include but are not limited to hexahedral units, triangular prism units and tetrahedral units. Assuming that there are N units sharing a common edge, the definition of the rotation basis function in these N units can be expressed as: in, The expression representing the positive unit of the roof-top basis function in unit i with the outflow surface of the rotation vector as the common surface; The expression of the positive unit of the Roof-top basis function in unit i with the rotation vector inflow surface as the common surface. The rotation basis function is a combination of the traditional Roof-top basis function, and the rotation basis function has the property that the divergence is always equal to 0. Optionally, the rotation basis function can be used to calculate the total current J T Discretize, the basis function s can be expressed as: The test function can be further defined as:

[0058] Furthermore, the resistance matrix element can be obtained Inductor Matrix Elements With the capacitor matrix element The expression is:

[0059]

[0060] like Figure 2 and Figure 3 As shown, δχ k1 , (k = i, j) represents the contrast difference between the two units of the roof-top basis function corresponding to the common surface of the unit k vector flow in the rotation basis function; δ(S k1 ) means that the vector outflow common surface of unit k in the rotation basis function takes the value 1 only, and the rest of the spatial domain takes the value 0; Represents the unit normal vector of the common face that only the vector of unit k in the rotation basis function flows out of.

[0061] Figure 4 A schematic diagram of an optional roof-top basis function with positive and negative units provided in an embodiment of the present application, such as Figure 4 As shown, the contrast difference expression is:

[0062] δχ=χ 2 -x 1

[0063] Figure 5 A schematic diagram of an optional half roof-top basis function provided in an embodiment of the present application, such as Figure 5 As shown in the figure, when the volume unit is on the boundary of the medium target, a half roof-top basis function is introduced, and the contrast difference expression is:

[0064] δχ=-χ 1

[0065] The calculation of capacitance matrix elements only occurs on interfaces with contrast mutations, avoiding the integral process of solving volume charge by traditional roof-top basis functions, thereby achieving simplified calculation of matrix elements. At the same time, there is no net charge inside the piecewise uniform medium, while the traditional roof-top basis function has volume charge. This difference often causes the traditional roof-top basis function to calculate capacitance matrix elements inaccurately, which deteriorates the solution accuracy. This degree of deterioration worsens with the increase of medium contrast. For the segmented volume unit data of the medium target, all rotation basis functions with common edges are constructed. The degrees of freedom of these basis functions are redundant and need to be removed. The set of rotation basis functions after removing redundancy can be used as a complete set of basis functions for the full current J T Discretization. The discretized equation (target electric field integral equation) is tested using a set of test functions to obtain a matrix equation (i.e., a global coupling matrix equation). By iteratively solving the matrix equation, the full current of the system can be obtained, and then the electromagnetic characteristics of the system can be calculated.

[0066] Through the above steps S102 to S108, a rotation basis function is constructed based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the divided volume unit data corresponding to the volume divided unit generated after the inhomogeneous medium target is geometrically divided; the redundant degrees of freedom of the rotation basis function are removed to obtain a target rotation basis function set; the electric field integral equation of the full current of the inhomogeneous medium target is numerically discretized through the target rotation basis function set to obtain the target electric field integral equation, and the target electric field integral equation is tested through a test function set to obtain a global coupling matrix equation; the global coupling matrix equation is iteratively solved to obtain the electromagnetic characteristics of the inhomogeneous medium target, which solves the problem of complex calculation of volume charge and asymmetric matrix elements in the matrix elements of the volume integral equation in the traditional method, thereby improving the calculation accuracy of electromagnetic modeling.

[0067] In an exemplary embodiment, before constructing the rotation basis function based on the generated unit pair information of the inhomogeneous medium target, the method further includes:

[0068] S11, geometrically divide the inhomogeneous medium target to generate a series of volume division units;

[0069] S12, constructing a volume unit pair corresponding to the volume segmentation unit, and obtaining unit pair information of the volume unit pair, wherein the volume unit pairs have the same common surface.

[0070] In this embodiment, the non-uniform medium target can be geometrically divided to generate a series of basic volume division units, which can include basic volume units such as tetrahedron, triangular prism and hexahedron or their combination units. Here, the basic volume unit can better discretize the medium target area, and the electrical parameters in the unit are constant.

[0071] Furthermore, after a series of volume decomposition units are obtained, volume unit pairs corresponding to the volume decomposition units can be constructed. The volume unit pairs have the same common surfaces, and the volume unit pairs constitute the basic roof-top basis functions.

[0072] In an exemplary embodiment, after constructing the body unit pairs corresponding to the body segmentation units and obtaining the unit pair information of the body unit pairs, the method further includes:

[0073] S21, determining a plurality of volume decomposition units having common edges in the volume unit pair according to the unit pair information, wherein the plurality of volume decomposition units include hexahedral units, triangular prism units, and tetrahedral units;

[0074] S22, establishing a rotation basis function corresponding to a plurality of volume decomposition units having a shared common edge.

[0075] In this embodiment, combined with Figure 6 , Figure 7 , Figure 8 As shown, when establishing the rotation basis function, multiple volume decomposition units with common edges in the volume unit pair can be first determined according to the unit pair information. The decomposition units here include but are not limited to hexahedral units, triangular prism units and tetrahedral units. For example, the rotation basis function can be established on several volume decomposition units with a shared common edge AB. Assuming that N units share the common edge AB, the rotation basis function associated with the common edge AB can be established, and its expression is:

[0076]

[0077] in, The expression representing the positive unit of the roof-top basis function in unit i with the rotating current outflow surface as the common surface; Represents the expression of the positive unit of the roof-top basis function in unit i with the rotating current inflow surface as the common surface.

[0078] In an exemplary embodiment, removing redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set includes:

[0079] S31, constructing a Gram matrix corresponding to the rotation basis function, and decomposing the Gram matrix into a series of sub-domain Gram matrices;

[0080] S32, spatially grouping the multiple volume dissection units according to their relative spatial position relationship to obtain multiple groups, wherein each of the multiple groups is matched with a corresponding number according to its relative position in space;

[0081] S33, obtaining the number of the maximum linearly independent group of each subdomain Gram matrix in a series of subdomain Gram matrices, retaining the rotation basis function corresponding to the number, and obtaining a target rotation basis function set.

[0082] In this embodiment, the Gram matrix method can be used to remove redundancy. By performing inner products between all subdomain basis functions (here, rotation basis functions) to construct a Gram matrix, that is,

[0083]

[0084] By solving the number of the linearly independent group of the largest row or column of the Gram matrix, the number corresponds to the set of linearly independent rotation basis functions. The rotation basis function that is not in the number is the basis function that needs to remove redundancy. If the global Gram matrix is ​​solved for the largest linearly independent group, it is usually inefficient. From the definition of the basis function, it can be known that the inner product between only two basis functions of the co-defined unit is not 0. Optionally, based on the basis function grouping strategy in this embodiment, it can be made to perform redundancy removal operations only in the basis function set with co-defined units each time. This grouping strategy decomposes the global Gram matrix into a series of subdomain Gram matrices, and there is no basis function overlap between the subdomain Gram matrices, which is suitable for parallel computing and can greatly improve the efficiency of basis function redundancy removal.

[0085] The subdomain Gram matrix method first spatially groups the target model's subdivision unit data into cubic boxes with a side length of L, and numbers the groups according to their relative position in the x, y, and z directions: {0,0,0}, {1,0,0}, ..., {2Nx+1,2Ny+1,2Nz+1}. To ensure efficiency, the side length L of the grouping cube is generally selected to be 1 to 2 times the maximum side length of the largest subdivision unit.

[0086] Specifically, taking a simple plane type target as an example, the subdomain Gram matrix method is used to remove the redundancy of the rotation basis function. Fig. 9 A schematic diagram of an optional grouping of simple plane type targets provided in an embodiment of the present application, such as Fig. 9 As shown in the figure, the subdivision units of simple plane type targets can be divided into 6×6 groups in the figure according to the spatial grouping method, numbered {0,0}, {0,1},…, {5,5} respectively. The grouping scale L is approximately 1.5 times the maximum side length of the maximum size subdivision unit.

[0087] Optionally, the symbol G can be defined {i,j,k} It represents the Gram matrix composed of all the current rotation basis functions of the subdivision unit that has an intersection with the group numbered {i,j,k}. It is a submatrix of the matrix G in the Gram matrix, that is, the subdomain Gram matrix. Definition symbol Indicates that the matrix X inside the calculation number is executed in parallel n .

[0088] The subdomain Gram matrix method can be expressed in pseudo code as:

[0089]

[0090] Exemplarily, the redundancy removal operation may be performed by parallel computing, including the following steps:

[0091] S301, perform parallel computing

[0092] Specifically, for each subfield Gram matrix G {2i,2j} Perform redundancy removal, that is, find the number of the largest linearly independent group, retain the basis function corresponding to the number, and discard the basis functions of the remaining numbers as they are redundant. Fig.10 A schematic diagram of an optional simple plane type target sub-domain Gram matrix parallel calculation provided in an embodiment of the present application, the selected grouping result is as follows Fig.10 shown.

[0093] S302, perform parallel computing

[0094] Specifically, for each subfield Gram matrix G {2i,2j+1} A redundancy removal operation is performed, and redundant basis functions are discarded on the basis of retaining the basis functions removed from redundancy in S301. Fig.11 A schematic diagram of an optional simple plane type target sub-domain Gram matrix parallel calculation provided in an embodiment of the present application. In S302 of one of the parallel calculations, the selected grouping result is as follows: Fig.11 shown.

[0095] S303, executing parallel computing

[0096] Specifically, for each subdomain Gram matrix G {2i+1,2j}A redundancy removal operation is performed, and redundant basis functions are discarded on the basis of retaining the basis functions removed from S301 and S302. Fig.12 A schematic diagram of an optional simple plane type target sub-domain Gram matrix parallel calculation provided in an embodiment of the present application. In S303 of one of the parallel calculations, the selected grouping result is as follows: Fig.12 shown.

[0097] S304, executing parallel computing

[0098] Specifically, for each subdomain Gram matrix G {2i+1,2j+1} A redundancy removal operation is performed, and redundant basis functions are discarded on the basis of retaining the basis functions in S301, S302 and S303. Fig.13 A schematic diagram of an optional simple plane type target sub-domain Gram matrix parallel calculation provided in an embodiment of the present application. In S304 of one of the parallel calculations, the selected grouping result is as follows: Fig.13 At this point, all redundant basis functions are removed, and a complete rotation basis function set (target rotation basis function set) is obtained.

[0099] Through this embodiment, the Gram matrix-based method is applicable to geometric models of arbitrary topological shapes, arbitrary subdivision unit forms, and arbitrary basis function definition forms, and thus has good universality.

[0100] In an exemplary embodiment, numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target by the target rotation basis function set to obtain the target electric field integral equation includes:

[0101] S41, expanding the electric field integral equation of the full current of the inhomogeneous medium target according to the expansion coefficient through the target rotation basis function set to obtain the target electric field integral equation.

[0102] In this embodiment, in the process of numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through a target rotation basis function set to obtain the target electric field integral equation, the electric field integral equation of the full current of the inhomogeneous medium target can be expanded according to the expansion coefficient through the target rotation basis function set to obtain the target electric field integral equation.

[0103] Optionally, J T Expand as follows:

[0104]

[0105] Among them, the unknown quantity α p Represents the expansion coefficient to be determined, and the total number of unknown quantities is N.

[0106] In an exemplary embodiment, testing the target electric field integral equation by a test function set to obtain a global coupling matrix equation includes:

[0107] S51, testing the target electric field integral equation by a test function set to obtain a matrix equation;

[0108] S52, determining a global coupling matrix equation based on matrix elements and matrix equations, wherein the matrix elements include resistance matrix elements, inductance matrix elements, and capacitance matrix elements.

[0109] In this embodiment, in the process of testing the target electric field integral equation by the test function set to obtain the global coupling matrix equation, the target electric field integral equation can be first tested by the test function set to obtain the matrix equation. Exemplarily, the test function in the test function set can be expressed as:

[0110]

[0111] After obtaining the matrix equation (ie, Zα=b), the matrix elements in the Z matrix can be determined. For example, the matrix elements include resistance matrix elements, inductance matrix elements, and capacitance matrix elements. Inductor Matrix Elements With the capacitor matrix element The expression is:

[0112]

[0113] Among them, δχ k1 , (k = i, j) represents the contrast difference between the two units of the roof-top basis function corresponding to the common surface of the unit k vector flow in the rotation basis function; δ(S k1 ) means that the vector outflow common surface of unit k in the rotation basis function takes the value 1 only, and the rest of the spatial domain takes the value 0; It represents the unit normal vector of the common surface only when the vector of unit k in the rotation basis function flows out. By filling the above matrix elements into the global Z matrix, the global coupling matrix equation is obtained, which is expressed as:

[0114]

[0115] In an exemplary embodiment, iteratively solving the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target includes:

[0116] S61, iteratively solving the global coupling matrix equation, and extracting full current information from a solution vector of the full current when the iteration converges;

[0117] S62, calculating the electromagnetic characteristics of the inhomogeneous medium target based on the full current information, wherein the electromagnetic characteristics include electromagnetic wave scattering and magnetic field strength.

[0118] In this embodiment, in order to obtain the electromagnetic characteristics of the inhomogeneous medium target, the matrix equation can be iteratively solved, and when the iteration converges, the total current J in the system can be obtained. T The solution of the total current is obtained by extracting the total current information in the solution vector of the total current, and then the electromagnetic characteristics of the inhomogeneous medium target can be obtained based on the total current information. For example, the radar cross section (RCS) of the target can be obtained in the scattering problem; the circuit S parameters (scattering parameters) of the board diagram can be obtained in the circuit problem; the electromagnetic field distribution in the target biological tissue can be obtained in the biomedical problem, etc.

[0119] Fig.14 A schematic diagram of an optional non-uniform medium target model provided in an embodiment of the present application is shown in FIG. Fig.14 As shown, the non-uniform medium target model calculated by the electromagnetic modeling method based on the rotation basis function discrete full current provided by the present application is used to calculate the dual-station radar cross-sectional area of ​​the target model. The calculation of the dual-station radar cross-sectional area under different observation angles obtained by this method is relatively high. Specifically, in the non-uniform medium target, the dielectric constant of the dielectric body can be 2F / m, 6F / m, 2F / m, respectively, and it can also be a non-uniform medium target with other dielectric constant values, E inc is the excitation electric field strength of the system, and its frequency f can be 300MHZ. The thickness of the inhomogeneous medium target along the far-field radar scattering cross-sectional area scanning direction can be 0.5m. The above values ​​are only examples and can also be other values ​​without limitation.

[0120] Through this embodiment, while meeting the requirements of efficient redundancy removal and avoiding the problem of volume charge occurring in the traditional roof-top basis function solution, very high solution accuracy is achieved.

[0121] According to another aspect of an embodiment of the present application, an electromagnetic modeling device for implementing the above-mentioned electromagnetic modeling method based on rotating basis function discretizing full current is also provided. Fig.15 is a schematic structural diagram of an optional electromagnetic modeling device based on a rotation basis function discretized full current according to an embodiment of the present application, such as Fig.15 As shown, the device may include:

[0122] A construction unit 1502 is used to construct a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target;

[0123] An acquisition unit 1504 is used to remove redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set;

[0124] The discrete unit 1506 is used to numerically discretize the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain the target electric field integral equation, and to test the target electric field integral equation through the test function set to obtain the global coupling matrix equation;

[0125] The solving unit 1508 is used to iteratively solve the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0126] It should be noted that the construction unit 1502 in this embodiment can be used to execute the above step S102, the acquisition unit 1504 in this embodiment can be used to execute the above step S104, the discrete unit 1506 in this embodiment can be used to execute the above step S106, and the solution unit 1508 in this embodiment can be used to execute the above step S108.

[0127] Through the above module, a rotation basis function is constructed based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the decomposed volume unit data corresponding to the volume decomposed unit generated after the inhomogeneous medium target is geometrically decomposed; the redundant degrees of freedom of the rotation basis function are removed to obtain a target rotation basis function set; the electric field integral equation of the full current of the inhomogeneous medium target is numerically discretized through the target rotation basis function set to obtain the target electric field integral equation, and the target electric field integral equation is tested through a test function set to obtain a global coupling matrix equation; the global coupling matrix equation is iteratively solved to obtain the electromagnetic characteristics of the inhomogeneous medium target, which solves the problem of complex calculation of volume charge and asymmetric matrix elements in the matrix elements of the volume integral equation in the traditional method, thereby improving the calculation accuracy of electromagnetic modeling.

[0128] In an exemplary embodiment, the above device further comprises:

[0129] A generating unit is used to geometrically divide the inhomogeneous medium target and generate a series of volume dividing units;

[0130] A volume unit pair corresponding to the volume decomposition unit is constructed, and unit pair information of the volume unit pair is obtained, wherein the volume unit pair has the same common surface.

[0131] In an exemplary embodiment, the above device further comprises:

[0132] A determination unit is used to determine a plurality of volume decomposition units having common edges in the volume unit pair according to the unit pair information, wherein the plurality of volume decomposition units include hexahedral units, triangular prism units, and tetrahedral units;

[0133] A unit is established for establishing a rotation basis function corresponding to a plurality of volume subdivision units having a shared common edge.

[0134] In an exemplary embodiment, the acquiring unit includes:

[0135] A building module is used to construct a Gram matrix corresponding to the rotation basis function and decompose the Gram matrix into a series of subdomain Gram matrices;

[0136] A grouping module is used to spatially group the multiple volume dissection units according to their relative spatial position relationship to obtain multiple groups, wherein each of the multiple groups is matched with a corresponding number according to its relative position in space;

[0137] The obtaining module is used to obtain the number of the maximum linearly independent group of each subdomain Gram matrix in a series of subdomain Gram matrices, retain the rotation basis function corresponding to the number, and obtain the target rotation basis function set.

[0138] In one exemplary embodiment, the discrete unit includes:

[0139] The expansion module is used to expand the electric field integral equation of the full current of the inhomogeneous medium target according to the expansion coefficient through the target rotation basis function set to obtain the target electric field integral equation.

[0140] In one exemplary embodiment, the discrete unit includes:

[0141] A testing module, used for testing the target electric field integral equation through a test function set to obtain a matrix equation;

[0142] A determination module is used to determine a global coupling matrix equation based on matrix elements and matrix equations, wherein the matrix elements include resistance matrix elements, inductance matrix elements, and capacitance matrix elements.

[0143] In an exemplary embodiment, the solving unit includes:

[0144] A solution module, used for iteratively solving the global coupling matrix equation, and extracting the full current information in the solution vector of the full current when the iteration converges;

[0145] The calculation module is used to calculate the electromagnetic characteristics of the inhomogeneous medium target based on the full current information, wherein the electromagnetic characteristics include electromagnetic wave scattering and magnetic field strength.

[0146] It should be noted here that the examples and scenarios implemented by the above-mentioned modules and corresponding steps are the same, but are not limited to the contents disclosed in the above-mentioned embodiments. It should be noted that the above-mentioned modules as part of the device can run in a hardware environment and can be implemented by software or hardware, wherein the hardware environment includes a network environment.

[0147] According to another aspect of the embodiments of the present application, a storage medium is further provided. Optionally, in this embodiment, the storage medium can be used to execute the program code of any of the electromagnetic modeling methods based on the rotation basis function discretization of the full current in the embodiments of the present application.

[0148] Optionally, in this embodiment, the storage medium is configured to store program codes for executing the following steps:

[0149] S1, constructing a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target.

[0150] S2, remove the redundant degrees of freedom of the rotation basis function and obtain the target rotation basis function set.

[0151] S3, numerically discretize the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain the target electric field integral equation, and test the target electric field integral equation through the test function set to obtain the global coupling matrix equation.

[0152] S4, iteratively solve the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0153] Optionally, the specific examples in this embodiment may refer to the examples described in the above embodiments, which will not be described in detail in this embodiment.

[0154] Among them, computer-readable storage media may include, but are not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives and magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0155] According to another aspect of the embodiment of the present application, an electronic device for implementing the above-mentioned electromagnetic modeling method based on the rotation basis function discretized full current is also provided. The electronic device can be a server, a terminal, or a combination thereof.

[0156] Fig.16 is a schematic diagram of the structure of an optional electronic device according to an embodiment of the present application, such as Fig.16 As shown, it includes a processor 1602, a communication interface 1604, a memory 1606 and a communication bus 1608, wherein the processor 1602, the communication interface 1604, and the memory 1606 communicate with each other through the communication bus 1608, wherein:

[0157] Memory 1606, used for storing computer programs;

[0158] The processor 1602 is used to execute the computer program stored in the memory 1606 to implement the following steps:

[0159] S1, constructing a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target.

[0160] S2, remove the redundant degrees of freedom of the rotation basis function and obtain the target rotation basis function set.

[0161] S3, numerically discretize the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain the target electric field integral equation, and test the target electric field integral equation through the test function set to obtain the global coupling matrix equation.

[0162] S4, iteratively solve the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

[0163] Optionally, the communication bus may be a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The communication bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.16 The communication interface is used for communication between the electronic device and other devices.

[0164] The memory may include RAM, or may include nonvolatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0165] As an example, the memory 1606 may include, but is not limited to, the construction unit 1502, the acquisition unit 1504, the discrete unit 1506, and the solution unit 1508 in the electromagnetic modeling device based on the rotation basis function discretization of the full current. In addition, other module units in the electromagnetic modeling device based on the rotation basis function discretization of the full current may also be included but are not limited to, which will not be repeated in this example.

[0166] The above-mentioned processor can be a general-purpose processor, which can include but not be limited to: CPU (Central Processing Unit), NP (Network Processor), etc.; it can also be DSP (Digital Signal Processing), ASIC (Application Specific Integrated Circuit), FPGA (Field-Programmable Gate Array) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0167] Optionally, the specific examples in this embodiment may refer to the examples described in the above embodiments, and this embodiment will not be described in detail here.

[0168] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0169] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0170] In the several embodiments provided in the present application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are only schematic, such as the division of the units, which is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some service interfaces, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0171] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0172] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0173] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a memory, including a number of instructions to enable a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned memory includes: U disk, read-only memory (ROM), random access memory (RAM), mobile hard disk, disk or optical disk and other media that can store program code.

[0174] A person of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable memory, which can include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0175] The above is only an exemplary embodiment of the present disclosure, and the scope of the present disclosure cannot be limited thereto. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the technical field not recorded in the present disclosure. The description and examples are regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0176] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0177] It will be easily understood by those skilled in the art that 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 and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An electromagnetic modeling method based on rotating basis function discretization of full current, characterized in that: include: Constructing a rotation basis function based on the unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is the segmented volume unit data corresponding to the volume segmented unit generated after geometric segmentation of the inhomogeneous medium target; Removing redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set; The electric field integral equation of the full current of the inhomogeneous medium target is numerically discretized by the target rotation basis function set to obtain a target electric field integral equation, and the target electric field integral equation is tested by a test function set to obtain a global coupling matrix equation; The global coupling matrix equation is iteratively solved to obtain the electromagnetic characteristics of the inhomogeneous medium target.

2. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 1 is characterized in that: Before constructing the rotation basis function based on the unit pair information of the generated inhomogeneous medium target, the method further includes: Geometrically dividing the inhomogeneous medium target to generate a series of volume dividing units; A volume unit pair corresponding to the volume dissection unit is constructed, and the unit pair information of the volume unit pair is obtained, wherein the volume unit pair has the same common surface.

3. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 2 is characterized in that: After constructing the volume unit pair corresponding to the volume dissection unit and obtaining the unit pair information of the volume unit pair, the method further includes: Determine a plurality of volume decomposition units having common edges in the volume unit pair according to the unit pair information, wherein the plurality of volume decomposition units include hexahedral units, triangular prism units, and tetrahedral units; The rotation basis functions corresponding to the plurality of volume decomposition cells having shared common edges are established.

4. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 1 is characterized in that: The step of removing the redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set comprises: Constructing a Gram matrix corresponding to the rotation basis function, and decomposing the Gram matrix into a series of sub-domain Gram matrices; The plurality of volume dissection units are spatially grouped according to their relative spatial positions to obtain a plurality of groups, wherein each of the plurality of groups is matched with a corresponding number according to its relative position in space; The number of the maximum linearly independent group of each sub-domain Gram matrix in the series of sub-domain Gram matrices is obtained, and the rotation basis function corresponding to the number is retained to obtain the target rotation basis function set.

5. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 1, characterized in that: The target electric field integral equation is obtained by numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set, including: The electric field integral equation of the full current of the inhomogeneous medium target is expanded according to the expansion coefficient through the target rotation basis function set to obtain the target electric field integral equation.

6. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 1, characterized in that: The global coupling matrix equation obtained by testing the target electric field integral equation through a test function set includes: Testing the target electric field integral equation by using the test function set to obtain a matrix equation; The global coupling matrix equation is determined based on matrix elements and the matrix equation, wherein the matrix elements include resistance matrix elements, inductance matrix elements, and capacitance matrix elements.

7. The electromagnetic modeling method based on the rotation basis function discretization of the full current according to claim 1 is characterized in that: The iteratively solving the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target includes: Iteratively solving the global coupling matrix equation, and extracting full current information from a solution vector of the full current when the iteration converges; The electromagnetic characteristics of the inhomogeneous medium target are calculated based on the full current information, wherein the electromagnetic characteristics include electromagnetic wave scattering and magnetic field strength.

8. An electromagnetic modeling device based on rotating basis function discretization of full current, characterized in that: include: A construction unit, configured to construct a rotation basis function based on unit pair information of the generated inhomogeneous medium target, wherein the unit pair information is segmented volume unit data corresponding to a volume segmentation unit generated after geometric segmentation of the inhomogeneous medium target; An acquisition unit, used to remove redundant degrees of freedom of the rotation basis function to obtain a target rotation basis function set; A discrete unit is used for numerically discretizing the electric field integral equation of the full current of the inhomogeneous medium target through the target rotation basis function set to obtain a target electric field integral equation, and testing the target electric field integral equation through a test function set to obtain a global coupling matrix equation; A solving unit is used to iteratively solve the global coupling matrix equation to obtain the electromagnetic characteristics of the inhomogeneous medium target.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein the program executes the method according to any one of claims 1 to 7 when executed.

10. An electronic device comprising a memory and a processor, characterized in that: A computer program is stored in the memory, and the processor is configured to execute the method according to any one of claims 1 to 7 through the computer program.

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