Electrically large target electromagnetic calculation method based on Fourier transform fast multipole

Abstract

The invention relates to an electromagnetic calculation technology, and discloses an electrically large target electromagnetic calculation method based on a Fourier transform fast multipole, which comprises the following steps of: performing triangular mesh generation on an electrically large target body, and linearly representing a split triangular mesh by using an RWG primary function; and calculating an integral value of each plane wave corresponding to each RWG primary function by utilizing multiple cycles according to the triangular grid, and calculating electromagnetic distribution of the electrically large target body according to the integral value of each plane wave. The invention further provides an electrically large target electromagnetic calculation device based on the Fourier transform fast multipole, electronic equipment and a storage medium. The method can reduce the number of calculation times of electrically large target electromagnetic calculation, improve the calculation efficiency and save calculation resources.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic computing technology, and in particular to an electromagnetic computing method for electrically large targets based on Fourier transform fast multipole. Background Art

[0002] Electromagnetic calculations for electrically large targets involve numerically simulating the electromagnetic properties of complex, electrically large electromagnetic targets, such as vehicles, aircraft, and ships. These calculations are commonly used in fields such as electromagnetic engineering, communications, radar, and stealth design. They can solve difficult, large-scale, and highly complex electromagnetic problems.

[0003] Traditional computational methods typically use the method of moments for electromagnetic calculations. This is achieved by discretizing integral equations into matrix equations and solving a system of linear equations to obtain the electromagnetic field distribution. Alternatively, the finite element method is used for electromagnetic calculations. This involves dividing the solution region into small units and solving differential equations based on the variational principle to obtain the electromagnetic field distribution. Furthermore, when using the fast multipole algorithm for electromagnetic distribution calculations, the traditional linear Fourier integral transform formula, dominated by the RWG basis function, is typically used for integral calculations. This results in a strong coupling relationship between the edges, faces, and wave numbers of the fast multipoles corresponding to the RWG basis functions, leading to numerous computational steps and, in turn, low computational efficiency. Furthermore, existing computational methods require numerous meshes for electromagnetic calculations of electrically large targets, leading to the curse of dimensionality. Furthermore, a large number of integral operations are generated during numerical electromagnetic field calculations, resulting in low computational efficiency and the consumption of significant computational resources. Summary of the Invention

[0004] The present invention provides an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole, which can reduce the number of electromagnetic calculations for electrically large targets, improve calculation efficiency and save calculation resources.

[0005] To achieve the above objectives, the present invention provides an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole, comprising:

[0006] Divide the electrically large target body into triangular meshes, and linearly represent the decomposed triangular meshes using RWG basis functions, wherein the RWG basis functions include a common edge of the electrically large target body and positive triangle surface elements and negative triangle surface elements connected to the common edge;

[0007] The integral value of each plane wave corresponding to each RWG basis function is calculated using multiple cycles according to the triangular grid, and the electromagnetic distribution of the electrically large target is calculated based on the integral value of each plane wave;

[0008] The first loop in the multi-loop calculation is as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge;

[0009] The second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the triangle normal unit vector based on the vertex coordinates of the triangle; traverse the three edges of the triangle and calculate the perpendicular direction vector between the edge vector and the triangle normal unit vector in the plane;

[0010] The third loop in the multi-loop calculation is as follows: traverse the directions of all plane waves, calculate the horizontal and vertical components of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element to calculate the edge vector, edge center point and vector transformation value.

[0011] Optionally, dividing the electrically large target into triangular meshes and linearly representing the divided triangular meshes using RWG basis functions includes:

[0012] Constructing a three-dimensional model of the electrically large target according to its geometric shape;

[0013] Discretize the three-dimensional model of the electrical target into triangular units according to the preset grid size;

[0014] Generate a triangular mesh based on the triangular cells and assign RWG basis functions to the triangular mesh.

[0015] Optionally, assigning RWG basis functions to the triangular mesh includes:

[0016] Traverse all edges of the triangle mesh and assign RWG basis functions to the shared edges;

[0017] The area, side length and vertex coordinates of adjacent triangles associated with shared edges are calculated as the basis function attributes of the RWG basis function.

[0018] Optionally, traversing the common edges of the split triangular mesh and calculating the edge vector and edge center position of each edge includes:

[0019] Calculate the edge vector l for each edge n and edge center position r nc Use the following formula:

[0020]

[0021] Among them, r n is the first vertex of the triangle face, r n+1 The second vertex of the triangle face.

[0022] Optionally, all triangles in the split triangle mesh are traversed, and the normal unit vectors of the triangles are calculated according to the vertex coordinates of the triangles, including

[0023] Calculate the normal unit vector of the triangle element according to the vertex coordinates of the triangle element Use the following formula:

[0024]

[0025] Among them, r n is the first vertex of the triangle face, r n+1 is the second vertex of the triangle face, r n+2 is the third vertex of the triangle face, and |·| is the modulus calculation.

[0026] Optionally, calculating the integral value of each plane wave corresponding to each RWG basis function includes:

[0027] The following formula is used to calculate the integral value of each plane wave corresponding to each RWG basis function:

[0028]

[0029] in, is the integral value, k is the wave number vector of the plane wave expanded by the fast multipole, k l is the horizontal component of k horizontal to the surface element, k l =kk v , k v is the vertical component of k perpendicular to the surface element, l n is the edge vector of the nth edge, is the normal unit vector of the triangle surface element, r nc is the center point of the nth edge, j0(·) is the zero-order Bessel function, j1(·) is the first-order Bessel function, A is the area of the triangle element, r c is the surface centroid, is the vertex of the triangle element, and j is the imaginary unit.

[0030] Optionally, the step of calculating the integral value of each plane wave corresponding to each RWG basis function further includes performing a vector identity transformation on the updated linear Fourier transform formula, where the identity transformation formula is:

[0031]

[0032] The updated linear Fourier integral transform formula uses the special relationship between the vertical and horizontal components of the wave number vector in the panel and the midpoint of the edge and the vertex of the triangle panel to perform an identity transformation. The transformation formula is:

[0033]

[0034] In order to solve the above problems, the present invention also provides an electrically large target electromagnetic calculation device based on Fourier transform fast multipole, the device comprising:

[0035] The electrical target body segmentation module is used to divide the electrical target body into triangular meshes and use the RWG basis function to linearly represent the split triangular meshes;

[0036] The electromagnetic distribution calculation module is used to calculate the integral value of each plane wave corresponding to each RWG basis function using multiple cycles according to the triangular grid, and calculate the electromagnetic distribution of the electrically large target body according to the integral value of each plane wave;

[0037] The multi-layer loop calculation module is used for the first loop in the multi-loop calculation as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and index value of each edge; the second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the normal vector of the triangle according to the vertex coordinates of the triangle. Position vector; traverse the three sides of the triangle surface element, and calculate the perpendicular direction vector between the edge vector and the normal unit vector of the triangle surface element in the plane; the third loop in the multiple loop calculation is as follows: traverse the directions of all plane waves, and calculate the horizontal component and vertical component of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component according to the vertex coordinates of the triangle surface element; when the horizontal component is not zero, traverse the three sides of the triangle surface element, and calculate the edge vector, edge center point and vector transformation value.

[0038] In order to solve the above problem, the present invention further provides an electronic device, comprising:

[0039] at least one processor; and,

[0040] a memory communicatively connected to the at least one processor; wherein,

[0041] The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can perform the above-mentioned electrically large target electromagnetic calculation method based on Fourier transform fast multipole.

[0042] In order to solve the above problems, the present invention also provides a computer-readable storage medium, which stores at least one computer program. The at least one computer program is executed by a processor in an electronic device to implement the above-mentioned electromagnetic calculation method for electrically large targets based on Fourier transform fast multipoles.

[0043] The present invention reduces the number of unknowns in the electromagnetic distribution calculation process by dividing the electrically large target into a triangular mesh and linearly representing the split triangular mesh using RWG basis functions. In addition, in the first loop, the cyclic calculation of edges and plane waves is carried out, and the plane waves are expanded based on the fast multipole algorithm, converting the global integral into a local interaction calculation, which can reduce the computational complexity. Furthermore, in the second loop, the calculation of triangular facets and plane waves can ensure that the local coordinate system of each triangular facet is aligned with the global electromagnetic field direction, reducing the influence of the complex geometric shape of the electrically large target on the calculation error. In addition, in the third loop, the plane wave component judgment and optimization calculation based on triangular facets can avoid invalid calculations and accelerate the integration process by pre-calculating Bessel functions and exponential values. The present invention uses the above-mentioned triangular mesh division and multiple loops to calculate the integral value of each plane wave corresponding to each RWG basis function to obtain the electromagnetic distribution of the electrically large target. The integral calculation based on facets can reduce the number of repeated calculations, improve computational efficiency and save computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart of an electromagnetic calculation method for an electrically large target based on Fourier transform fast multipole according to an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of a multi-loop calculation process of an electrically large target electromagnetic calculation method based on Fourier transform fast multipole according to an embodiment of the present invention;

[0046] Figure 3 A schematic diagram of the RWG basis functions of the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to one embodiment of the present invention;

[0047] Figure 4 An example diagram of an electrically large target body according to an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole provided in one embodiment of the present invention;

[0048] Figure 5 An electromagnetic distribution diagram of an electrically large target body according to an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole provided in one embodiment of the present invention;

[0049] Figure 6 A functional module diagram of an electrically large target electromagnetic calculation device based on Fourier transform fast multipole provided by one embodiment of the present invention;

[0050] Figure 7 A schematic structural diagram of an electronic device for implementing the Fourier transform fast multipole-based electromagnetic calculation method for electrically large targets provided in one embodiment of the present invention.

[0051] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0052] 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.

[0053] The embodiment of the present application provides an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipoles. The execution subject of the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipoles includes but is not limited to at least one of the electronic devices such as a server, a terminal, etc. that can be configured to execute the method provided by the embodiment of the present application. In other words, the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipoles can be executed by software or hardware installed on a terminal device or a server device, and the software can be a blockchain platform. The server includes but is not limited to: a single server, a server cluster, a cloud server or a cloud server cluster, etc. The server can be an independent server, or it can be a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content delivery networks (CDNs), and big data and artificial intelligence platforms.

[0054] Reference Figure 1 FIG. 1 is a flow chart of an electrically large target electromagnetic calculation method based on Fourier transform fast multipole according to an embodiment of the present invention. In this embodiment, the electrically large target electromagnetic calculation method based on Fourier transform fast multipole includes:

[0055] S1. Divide the electrically large target into triangular meshes and use the RWG basis function to linearly represent the split triangular meshes.

[0056] In the embodiment of the present invention, the electrically large target refers to a structure whose geometric size is larger than the wavelength of the electromagnetic wave.

[0057] In an embodiment of the present invention, the RWG basis function refers to a function that discretizes the continuous surface current into a linear combination, wherein the RWG basis function includes a common edge of the electrically large target body and positive triangular surface elements and negative triangular surface elements connected to the common edge.

[0058] As an embodiment of the present invention, the electrically large target body is divided into triangular meshes, and the split triangular meshes are linearly represented using RWG basis functions, including:

[0059] Constructing a three-dimensional model of the electrically large target according to its geometric shape;

[0060] Discretize the three-dimensional model of the electrical target into triangular units according to the preset grid size;

[0061] Generate a triangular mesh based on the triangular cells and assign RWG basis functions to the triangular mesh.

[0062] Furthermore, allocating RWG basis functions to the triangular mesh includes:

[0063] Traverse all edges of the triangle mesh and assign RWG basis functions to the shared edges;

[0064] The area, side length and vertex coordinates of adjacent triangles associated with shared edges are calculated as the basis function attributes of the RWG basis function.

[0065] S2. Calculate the integral value of each plane wave corresponding to each RWG basis function using multiple loops according to the triangular grid, and calculate the electromagnetic distribution of the electrically large target body according to the integral value of each plane wave.

[0066] In the embodiment of the present invention, the plane wave refers to a basic model in electromagnetic theory and can be used to simplify modeling.

[0067] In the embodiment of the present invention, a linear Fourier transform formula is generally used to calculate the electromagnetic distribution of an electrically large target according to the integral value of each plane wave.

[0068] Furthermore, the integral value of each plane wave corresponding to each RWG basis function is calculated, including:

[0069] The following formula is used to calculate the integral value of each plane wave corresponding to each RWG basis function:

[0070]

[0071] in, is the integral value, k is the wave number vector of the plane wave expanded by the fast multipole, k l is the horizontal component of k horizontal to the surface element, k l =kkv , k v is the vertical component of k perpendicular to the surface element, l n is the edge vector of the nth edge, is the normal unit vector of the triangle surface element, r nc is the center point of the nth edge, j0(·) is the zero-order Bessel function, j1(·) is the first-order Bessel function, A is the area of the triangle element, r c is the surface centroid, is the vertex of the triangle element, and j is the imaginary unit.

[0072] Furthermore, in the calculation of the integral value of each plane wave corresponding to each RWG basis function, the updated linear Fourier transform formula is subjected to a vector identity transformation, and the identity transformation formula is:

[0073]

[0074] The updated linear Fourier integral transform formula uses the special relationship between the vertical and horizontal components of the wave number vector in the panel and the midpoint of the edge and the vertex of the triangle panel to perform an identity transformation. The transformation formula is:

[0075]

[0076] The present invention performs identity transformation on some parameters in the linear Fourier integral transform formula, so as to achieve a certain decoupling between the wave numbers of edges, surfaces and fast multipoles corresponding to the RWG basis functions, thereby reducing the number of circulation layers.

[0077] Among them, S201, the first layer of loop in the multiple loop calculation is as follows: traverse the common edges of the split triangular mesh, and calculate the edge vector and edge center point position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, and traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge.

[0078] In an embodiment of the present invention, the Fast Multipole Method (FMM) refers to a numerical acceleration algorithm for efficiently calculating large-scale physical interactions. Through hierarchical grouping and multipole expansion approximation, the interactions between all particles or grids that originally need to be calculated directly are converted into hierarchical local and global approximations, thereby reducing the computational complexity.

[0079] In the embodiment of the present invention, the Bessel function is a special function used in the present invention to describe the radial distribution of high-order electromagnetic modes.

[0080] As an embodiment of the present invention, traversing the common edges of the split triangular mesh and calculating the edge vector and edge center position of each edge includes:

[0081] Calculate the edge vector l for each edge n and edge center position r nc Use the following formula:

[0082]

[0083] Among them, r n is the first vertex of the triangle face, r n+1 The second vertex of the triangle face.

[0084] The present invention traverses the common edges of the split triangular mesh and calculates the edge vector and edge center point position of each edge, which can convert discrete geometric information into structured data that can be used for numerical calculations and reduce the complexity of subsequent algorithms.

[0085] S202. The second loop in the multi-loop calculation is as follows: traverse all the triangles in the split triangular mesh, and calculate the normal unit vector of the triangle based on the vertex coordinates of the triangle; traverse the three sides of the triangle, and calculate the perpendicular direction vector between the edge vector and the normal unit vector of the triangle in the plane.

[0086] In the embodiment of the present invention, a facet refers to a basic geometric unit in a triangular mesh that is linearly represented by an RWG basis function after being split.

[0087] As an embodiment of the present invention, all triangles in the split triangular mesh are traversed, and the normal unit vectors of the triangles are calculated according to the vertex coordinates of the triangles, including

[0088] Calculate the normal unit vector of the triangle element according to the vertex coordinates of the triangle element Use the following formula:

[0089]

[0090] Among them, r n is the first vertex of the triangle face, r n+1 is the second vertex of the triangle face, r n+2 is the third vertex of the triangle face, and |·| is the modulus calculation.

[0091] S203, the third loop in the multiple loop calculation is as follows: traverse the directions of all plane waves, and calculate the horizontal component and vertical component of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element, calculate the edge vector, edge center point and vector transformation value.

[0092] The embodiment of the present invention calculates the horizontal component k of the wave number vector of each plane wave on the corresponding bin l and the vertical component k v , using the following formula: k l =kk v ;

[0093] The present invention reduces the number of unknowns in the electromagnetic distribution calculation process by dividing the electrically large target into a triangular mesh and linearly representing the split triangular mesh using RWG basis functions. In addition, in the first loop, the cyclic calculation of edges and plane waves is carried out, and the plane waves are expanded based on the fast multipole algorithm, converting the global integral into a local interaction calculation, which can reduce the computational complexity. Furthermore, in the second loop, the calculation of triangular facets and plane waves can ensure that the local coordinate system of each triangular facet is aligned with the global electromagnetic field direction, reducing the influence of the complex geometric shape of the electrically large target on the calculation error. In addition, in the third loop, the plane wave component judgment and optimization calculation based on triangular facets can avoid invalid calculations and accelerate the integration process by pre-calculating Bessel functions and exponential values. The present invention uses the above-mentioned triangular mesh division and multiple loops to calculate the integral value of each plane wave corresponding to each RWG basis function to obtain the electromagnetic distribution of the electrically large target. The integral calculation based on facets can reduce the number of repeated calculations, improve computational efficiency and save computing resources.

[0094] like Figure 2 FIG. 1 is a schematic diagram of a multi-loop calculation process of an electrically large target electromagnetic calculation method based on Fourier transform fast multipole according to an embodiment of the present invention.

[0095] like Figure 3 , which is a schematic diagram of the RWG basis functions of the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to an embodiment of the present invention.

[0096] like Figure 4 , which is an example diagram of an electrically large target body according to an electromagnetic calculation method for an electrically large target based on Fourier transform fast multipole provided by an embodiment of the present invention.

[0097] like Figure 5, which is an electromagnetic distribution diagram of an electrically large target body according to an electromagnetic calculation method of an electrically large target based on Fourier transform fast multipole provided by an embodiment of the present invention.

[0098] like Figure 6 , which is a functional module diagram of an electrically large target electromagnetic calculation device based on Fourier transform fast multipole provided by one embodiment of the present invention.

[0099] The present invention discloses an electrically large target electromagnetic calculation device 100 based on Fast Fourier Transform Multipole (FTMF) technology, which can be installed in an electronic device. Depending on the functionality implemented, the device 100 can include an electrically large target volume segmentation module 101, an electromagnetic distribution calculation module 102, and a multi-layer loop calculation module 103.

[0100] The module described in the present invention may also be referred to as a unit, which refers to a series of computer program segments that can be executed by a processor of an electronic device and can complete fixed functions, and is stored in a memory of the electronic device.

[0101] In this embodiment, the functions of each module / unit are as follows:

[0102] The electrically large target body segmentation module 101 is used to segment the electrically large target body into triangular meshes and linearly represent the segmented triangular meshes using RWG basis functions.

[0103] In the embodiment of the present invention, the electrically large target refers to a structure whose geometric size is larger than the wavelength of the electromagnetic wave.

[0104] In an embodiment of the present invention, the RWG basis function refers to a function that discretizes the continuous surface current into a linear combination, wherein the RWG basis function includes a common edge of the electrically large target body and positive triangular surface elements and negative triangular surface elements connected to the common edge.

[0105] As an embodiment of the present invention, the electrically large target body is divided into triangular meshes, and the split triangular meshes are linearly represented using RWG basis functions, including:

[0106] Constructing a three-dimensional model of the electrically large target according to its geometric shape;

[0107] Discretize the three-dimensional model of the electrical target into triangular units according to the preset grid size;

[0108] Generate a triangular mesh based on the triangular cells and assign RWG basis functions to the triangular mesh.

[0109] Furthermore, allocating RWG basis functions to the triangular mesh includes:

[0110] Traverse all edges of the triangle mesh and assign RWG basis functions to the shared edges;

[0111] The area, side length and vertex coordinates of adjacent triangles associated with shared edges are calculated as the basis function attributes of the RWG basis function.

[0112] The electromagnetic distribution calculation module 102 is used to calculate the integral value of each plane wave corresponding to each RWG basis function using multiple cycles according to the triangular grid, and calculate the electromagnetic distribution of the electrically large target according to the integral value of each plane wave.

[0113] In the embodiment of the present invention, the plane wave refers to a basic model in electromagnetic theory and can be used to simplify modeling.

[0114] In the embodiment of the present invention, a linear Fourier transform formula is generally used to calculate the electromagnetic distribution of an electrically large target according to the integral value of each plane wave.

[0115] Furthermore, the integral value of each plane wave corresponding to each RWG basis function is calculated, including:

[0116] The following formula is used to calculate the integral value of each plane wave corresponding to each RWG basis function:

[0117]

[0118] in, is the integral value, k is the wave number vector of the plane wave expanded by the fast multipole, k l is the horizontal component of k horizontal to the surface element, k l =kk v , k v is the vertical component of k perpendicular to the surface element, l n is the edge vector of the nth edge, is the normal unit vector of the triangle surface element, r nc is the center point of the nth edge, j0(·) is the zero-order Bessel function, j1(·) is the first-order Bessel function, A is the area of the triangle element, r c is the surface centroid, are the vertices of the triangle.

[0119] Furthermore, in the calculation of the integral value of each plane wave corresponding to each RWG basis function, the updated linear Fourier transform formula is subjected to a vector identity transformation, and the identity transformation formula is:

[0120]

[0121] The updated linear Fourier integral transform formula uses the special relationship between the vertical and horizontal components of the wave number vector in the panel and the midpoint of the edge and the vertex of the triangle panel to perform an identity transformation. The transformation formula is:

[0122]

[0123] The present invention performs identity transformation on some parameters in the linear Fourier integral transform formula, so as to achieve a certain decoupling between the wave numbers of edges, surfaces and fast multipoles corresponding to the RWG basis functions, thereby reducing the number of circulation layers.

[0124] The multi-layer loop calculation module 103 is used for the first loop in the multiple loop calculation as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center point position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge; the second loop in the multiple loop calculation is as follows: traverse all triangle face elements in the split triangular mesh and calculate the triangle face element according to the vertex coordinates of the triangle face element Normal unit vector; traverse the three sides of the triangle surface element, and calculate the perpendicular direction vector between the edge vector and the normal unit vector of the triangle surface element in the plane; the third loop in the multiple loop calculation is as follows: traverse the directions of all plane waves, and calculate the horizontal component and vertical component of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component according to the vertex coordinates of the triangle surface element; when the horizontal component is not zero, traverse the three sides of the triangle surface element, calculate the edge vector, edge center point and vector transformation value.

[0125] In an embodiment of the present invention, the Fast Multipole Method (FMM) refers to a numerical acceleration algorithm for efficiently calculating large-scale physical interactions. Through hierarchical grouping and multipole expansion approximation, the interactions between all particles or grids that originally need to be calculated directly are converted into hierarchical local and global approximations, thereby reducing the computational complexity.

[0126] In the embodiment of the present invention, the Bessel function is a special function used in the present invention to describe the radial distribution of high-order electromagnetic modes.

[0127] As an embodiment of the present invention, traversing the common edges of the split triangular mesh and calculating the edge vector and edge center position of each edge includes:

[0128] Calculate the edge vector l for each edge n and edge center position r nc Use the following formula:

[0129]

[0130] Among them, r n is the first vertex of the triangle face, r n+1 The second vertex of the triangle face.

[0131] The present invention traverses the common edges of the split triangular mesh and calculates the edge vector and edge center point position of each edge, which can convert discrete geometric information into structured data that can be used for numerical calculations and reduce the complexity of subsequent algorithms.

[0132] The second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the normal unit vector of the triangle based on the vertex coordinates of the triangle; traverse the three edges of the triangle and calculate the perpendicular direction vector between the edge vector and the normal unit vector of the triangle in the plane.

[0133] In the embodiment of the present invention, a facet refers to a basic geometric unit in a triangular mesh that is linearly represented by an RWG basis function after being split.

[0134] As an embodiment of the present invention, all triangles in the split triangular mesh are traversed, and the normal unit vectors of the triangles are calculated according to the vertex coordinates of the triangles, including

[0135] Calculate the normal unit vector of the triangle element according to the vertex coordinates of the triangle element Use the following formula:

[0136]

[0137] Among them, r n is the first vertex of the triangle face, r n+1 is the second vertex of the triangle face, r n+2 is the third vertex of the triangle face, and |·| is the modulus calculation.

[0138] The third loop in the multi-loop calculation is as follows: traverse the directions of all plane waves, calculate the horizontal and vertical components of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element to calculate the edge vector, edge center point and vector transformation value.

[0139] The embodiment of the present invention calculates the horizontal component k of the wave number vector of each plane wave on the corresponding bin l and the vertical component k v , using the following formula: kl =kk v ;

[0140] Reference Figure 7 FIG. 1 is a schematic diagram of the structure of an electronic device for implementing the electromagnetic calculation method of an electrically large target based on Fourier transform fast multipole according to an embodiment of the present invention.

[0141] The electronic device may include a processor 10, a memory 11, a communication bus 12 and a communication interface 13, and may also include a computer program stored in the memory 11 and executable on the processor 10, such as a program for an electromagnetic calculation method for electrically large targets based on Fourier transform fast multipoles.

[0142] In some embodiments, the processor 10 may be composed of an integrated circuit, for example, a single packaged integrated circuit, or a plurality of packaged integrated circuits with the same or different functions, including one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and a combination of various control chips. The processor 10 is the control core (Control Unit) of the electronic device, connecting the various components of the entire electronic device using various interfaces and lines, and executing or executing programs or modules stored in the memory 11 (for example, executing a program for an electromagnetic calculation method for an electrically large target based on Fourier transform fast multipole, etc.), as well as calling data stored in the memory 11, to execute various functions of the electronic device and process data.

[0143] The memory 11 includes at least one type of readable storage medium, and the readable storage medium includes a flash memory, a mobile hard disk, a multimedia card, a card-type memory (for example, an SD or DX memory, etc.), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the memory 11 can be an internal storage unit of an electronic device, such as a mobile hard disk of the electronic device. In other embodiments, the memory 11 can also be an external storage device of an electronic device, such as a plug-in mobile hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the electronic device. Furthermore, the memory 11 can also include both an internal storage unit of the electronic device and an external storage device. The memory 11 can not only be used to store application software and various types of data installed in the electronic device, such as the code of a program for an electrically large target electromagnetic calculation method based on Fourier transform fast multipoles, but can also be used to temporarily store data that has been output or is to be output.

[0144] The communication bus 12 may be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. The bus is configured to enable communication between the memory 11 and at least one processor 10, etc.

[0145] The communication interface 13 is used for communication between the above-mentioned electronic device and other devices, including a network interface and a user interface. Optionally, the network interface may include a wired interface and / or a wireless interface (such as a WI-FI interface, a Bluetooth interface, etc.), which is generally used to establish a communication connection between the electronic device and other electronic devices. The user interface may be a display (Display), an input unit (such as a keyboard (Keyboard)), optionally, the user interface may also be a standard wired interface, a wireless interface. Optionally, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, and an OLED (Organic Light-Emitting Diode, organic light-emitting diode) touch device, etc. Among them, the display may also be appropriately referred to as a display screen or a display unit, which is used to display information processed in the electronic device and to display a visual user interface.

[0146] Figure 7 Only the electronic device with components is shown, and it can be understood by those skilled in the art that Figure 7 The structure shown does not limit the electronic device, and may include fewer or more components than shown in the figure, or combine certain components, or arrange the components differently.

[0147] For example, although not shown, the electronic device may further include a power source (such as a battery) for powering various components. Preferably, the power source may be logically connected to the at least one processor 10 via a power management device, thereby implementing functions such as charge management, discharge management, and power consumption management through the power management device. The power source may further include any components such as one or more DC or AC power sources, a recharging device, a power failure detection circuit, a power converter or inverter, a power status indicator, etc. The electronic device may further include various sensors, Bluetooth modules, Wi-Fi modules, etc., which will not be described in detail here.

[0148] It should be understood that the embodiment is for illustration only and the scope of the patent application is not limited to this structure.

[0149] The program of the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole stored in the memory 11 of the electronic device is a combination of multiple instructions. When running in the processor 10, it can achieve:

[0150] The electrical target body is divided into triangular meshes, and the split triangular meshes are linearly represented using RWG basis functions;

[0151] The integral value of each plane wave corresponding to each RWG basis function is calculated using multiple cycles according to the triangular grid, and the electromagnetic distribution of the electrically large target is calculated based on the integral value of each plane wave;

[0152] The first loop in the multi-loop calculation is as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge;

[0153] The second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the triangle normal unit vector based on the vertex coordinates of the triangle; traverse the three edges of the triangle and calculate the perpendicular direction vector between the edge vector and the triangle normal unit vector in the plane;

[0154] The third loop in the multi-loop calculation is as follows: traverse the directions of all plane waves, calculate the horizontal and vertical components of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element to calculate the edge vector, edge center point and vector transformation value.

[0155] Specifically, the specific implementation method of the processor 10 for the above instructions can refer to the description of the relevant steps in the corresponding embodiment of the accompanying drawings, which will not be repeated here.

[0156] Furthermore, if the modules / units integrated into the electronic device 1 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. The computer-readable storage medium can be volatile or non-volatile. For example, the computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a mobile hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0157] The present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. When the computer program is executed by a processor of an electronic device, the computer program can implement:

[0158] The electrical target body is divided into triangular meshes, and the split triangular meshes are linearly represented using RWG basis functions;

[0159] The integral value of each plane wave corresponding to each RWG basis function is calculated using multiple cycles according to the triangular grid, and the electromagnetic distribution of the electrically large target is calculated based on the integral value of each plane wave;

[0160] The first loop in the multi-loop calculation is as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge;

[0161] The second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the triangle normal unit vector based on the vertex coordinates of the triangle; traverse the three edges of the triangle and calculate the perpendicular direction vector between the edge vector and the triangle normal unit vector in the plane;

[0162] The third loop in the multi-loop calculation is as follows: traverse the directions of all plane waves, calculate the horizontal and vertical components of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element to calculate the edge vector, edge center point and vector transformation value.

[0163] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the module division is merely a logical function division, and other division methods may be used in actual implementation.

[0164] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical units, that is, they may be located in one place or distributed across multiple network elements. Some or all of the modules may be selected to achieve the purpose of the solution of this embodiment according to actual needs.

[0165] In addition, the functional modules in various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or hardware plus software functional modules.

[0166] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0167] Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and all changes that come within the meaning and range of equivalents of the claims are intended to be embraced therein. Any reference to a figure in a claim should not be construed as limiting the claim to which it relates.

[0168] Blockchain, as used in this article, refers to a novel application model for computer technologies such as distributed data storage, peer-to-peer transmission, consensus mechanisms, and encryption algorithms. Blockchain is essentially a decentralized database, a series of data blocks generated using cryptographic methods. Each block contains information about a batch of online transactions, used to verify the validity of this information (to prevent counterfeiting) and generate the next block. Blockchain can include the underlying blockchain platform, the platform product service layer, and the application service layer.

[0169] The embodiments of the present application can acquire and process relevant data based on artificial intelligence technology. Artificial Intelligence (AI) is the theory, method, technology, and application system that uses digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use knowledge to achieve optimal results.

[0170] Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices recited in a system claim may also be implemented by a single unit or device through software or hardware. Terms such as "first" and "second" are used to indicate names and do not imply any particular order.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for electromagnetic calculation of electrically large targets based on Fourier transform fast multipole, characterized in that: The method comprises: The electrical target body is divided into triangular meshes, and the split triangular meshes are linearly represented using RWG basis functions; The integral value of each plane wave corresponding to each RWG basis function is calculated using multiple cycles according to the triangular grid, and the electromagnetic distribution of the electrically large target is calculated based on the integral value of each plane wave; The first loop in the multi-loop calculation is as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and exponential value of each edge; The second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the triangle normal unit vector based on the vertex coordinates of the triangle; traverse the three edges of the triangle and calculate the perpendicular direction vector between the edge vector and the triangle normal unit vector in the plane; The third loop in the multi-loop calculation is as follows: traverse the directions of all plane waves, calculate the horizontal and vertical components of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component based on the vertex coordinates of the triangular surface element; when the horizontal component is not zero, traverse the three edges of the triangular surface element to calculate the edge vector, edge center point and vector transformation value.

2. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 1, characterized in that: The method of dividing the electrically large target into triangular meshes and linearly representing the divided triangular meshes using RWG basis functions includes: Constructing a three-dimensional model of the electrically large target according to its geometric shape; Discretize the three-dimensional model of the electrical target into triangular units according to the preset grid size; Generate a triangular mesh based on the triangular cells and assign RWG basis functions to the triangular mesh.

3. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 2, characterized in that: The assigning of RWG basis functions to the triangular mesh includes: Traverse all edges of the triangle mesh and assign RWG basis functions to the shared edges; The area, side length and vertex coordinates of adjacent triangles associated with shared edges are calculated as the basis function attributes of the RWG basis function.

4. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 1, characterized in that: The traversal of the common edges of the split triangle mesh and calculation of the edge vector and edge center position of each edge includes: Calculate the edge vector l for each edge n and edge center position r nc Use the following formula: Among them, r n is the first vertex of the triangle face, r n+1 The second vertex of the triangle face.

5. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 1, characterized in that: Traverse all triangles in the split triangle mesh and calculate the normal unit vector of the triangle according to the vertex coordinates of the triangle, including Calculate the normal unit vector of the triangle element according to the vertex coordinates of the triangle element Use the following formula: Among them, r n is the first vertex of the triangle face, r n+1 is the second vertex of the triangle face, r n+2 is the third vertex of the triangle face, and |·| is the modulus calculation.

6. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 1, characterized in that: Calculating the integral value of each plane wave corresponding to each RWG basis function includes: The following formula is used to calculate the integral value of each plane wave corresponding to each RWG basis function: in, is the integral value, k is the wave number vector of the plane wave expanded by the fast multipole, k l is the horizontal component of k horizontal to the surface element, k l =kk v , k v is the vertical component of k perpendicular to the surface element, l n is the edge vector of the nth edge, is the normal unit vector of the triangle surface element, r nc is the center point of the nth edge, j0(·) is the zero-order Bessel function, j1(·) is the first-order Bessel function, A is the area of the triangle element, r c is the surface centroid, is the vertex of the triangle element, and j is the imaginary unit.

7. The electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to claim 6, characterized in that: The calculation of the integral value of each plane wave corresponding to each RWG basis function further includes: performing a vector identity transformation on the updated linear Fourier transform formula, where the identity transformation formula is: The updated linear Fourier integral transform formula uses the special relationship between the vertical and horizontal components of the wave number vector in the panel and the midpoint of the edge and the vertex of the triangle panel to perform an identity transformation. The transformation formula is:

8. An electromagnetic calculation device for electrically large targets based on Fourier transform fast multipole, characterized in that: The device implements the electromagnetic calculation method for electrically large targets based on Fourier transform fast multipole according to any one of claims 1 to 7, and the device includes: The electrical target body segmentation module is used to divide the electrical target body into triangular meshes and use the RWG basis function to linearly represent the split triangular meshes; The electromagnetic distribution calculation module is used to calculate the integral value of each plane wave corresponding to each RWG basis function using multiple cycles according to the triangular grid, and calculate the electromagnetic distribution of the electrically large target body according to the integral value of each plane wave; The multi-layer loop calculation module is used for the first loop in the multi-loop calculation as follows: traverse the common edges of the split triangular mesh and calculate the edge vector and edge center position of each edge; use the fast multipole algorithm to perform plane wave expansion on the split triangular mesh, traverse all plane wave numbers expanded by the fast multipole algorithm, and calculate the wave number vector of each plane wave number and the Bessel function and index value of each edge; the second loop in the multi-loop calculation is as follows: traverse all triangles in the split triangular mesh and calculate the normal vector of the triangle according to the vertex coordinates of the triangle. Position vector; traverse the three sides of the triangle surface element, and calculate the perpendicular direction vector between the edge vector and the normal unit vector of the triangle surface element in the plane; the third loop in the multiple loop calculation is as follows: traverse the directions of all plane waves, and calculate the horizontal component and vertical component of the wave number vector of each plane wave on the corresponding surface element, and determine whether the horizontal component is zero; when the horizontal component is zero, calculate the coordinates of the center of mass point and the exponential value of the vertical component according to the vertex coordinates of the triangle surface element; when the horizontal component is not zero, traverse the three sides of the triangle surface element, and calculate the edge vector, edge center point and vector transformation value.

9. An electronic device, characterized in that: The electronic device comprises: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can execute the electrically large target electromagnetic calculation method based on Fourier transform fast multipole according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the electrically large target electromagnetic calculation method based on Fourier transform fast multipole is implemented according to any one of claims 1 to 7.

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