TDFIT fast far field analysis method based on fast multipole

Abstract

The application discloses a TDFIT fast far-field analysis method based on a fast multipole, which is based on a region interaction acceleration scheme of a fast multipole, and complexity and storage capacity of TDFIT calculation of an electrically large size target scattering problem are greatly reduced based on an MLFMA interlayer interpolation principle, so as to provide a technical basis and an acceleration scheme for evaluation of scattering and radiation characteristics of a target coexisting with an electrically large metal carrier and an electrically small fine structure. The application obtains full-space far-field with sufficient sampling rate through multiple interlayer interpolations, accelerates interaction between regions, and reduces time consumption of electrically large target calculation. Meanwhile, the application saves memory and reduces memory allocation times under the premise of ensuring correctness through observation driving mode.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic communication, and particularly relates to a TDFIT fast far-field analysis method based on a fast multipole. BACKGROUND

[0002] The radome is used to protect the internal radar or antenna, to ensure that the internal radar or antenna can still work normally when encountering external harsh environment such as storm, rain and snow, sand and dust, hail and high temperature, and will not affect the transmission of electromagnetic waves. The wave transmission performance of the radome has a very important influence on important technical indicators of the antenna. When the radome is designed, whether the electromagnetic modeling and simulation method used is efficient and accurate is crucial to the simulation result. To ensure the calculation accuracy, using the correct electromagnetic modeling and simulation calculation method can greatly help to improve the calculation efficiency and calculation capacity.

[0003] At present, the high-frequency approximation method and the full-wave numerical method are the main methods used in the simulation calculation of the radome. However, the high-frequency method cannot accurately analyze the non-smooth structure and complex medium, which will bring great error. The full-wave numerical method has high calculation complexity and low calculation efficiency, and can only be used for analyzing small-size radomes.

[0004] In addition, the commonly used equivalent principle algorithm (CrossFlux theory) in the prior art is to independently calculate each region, and update the scattering surface flow on the equivalent surface of the region through the scattering near field of each region, so as to obtain a high-precision approximate solution. However, the efficiency of independent solution of each component region depends on the efficiency of the algorithm itself. In the CrossFlux theory, the interaction between each region to obtain the spatial scattering field distribution is essentially the interaction between the scattering equivalent surface and the incident equivalent surface of different regions, which will grow linearly with N obs ×N rad , resulting in that the interaction between regions consumes an unacceptable amount of time for the calculation of large-size targets.

[0005] Therefore, the fast and accurate calculation of the far field becomes an important link in analyzing the radome problem. SUMMARY

[0006] Invention aims / technical problems : In view of the technical problems existing in the prior art, the application provides a TDFIT fast far-field analysis method based on a fast multipole. The application conducts in-depth research on the far-field calculation efficiency problem in the time-domain finite integral (TDFIT) method, accelerates the post-processing process of the TDFIT algorithm through a multi-layer fast multipole layer interpolation technology, and realizes the fast implementation of the far-field calculation.

[0007] Technical Solution: To achieve the above-mentioned technical objectives, the present invention provides the following technical solution: a fast far-field analysis method based on fast multipole TDFIT, comprising the following steps:

[0008] S1 divides the analysis space of the antenna, which is located in an isotropic, infinitely large, and uniform background, into several regions. , ,area The equivalent surface is ,area The incident equivalent surface is The scattering equivalent surface is , Represents the p-th region The native surface or virtual equivalent surface;

[0009] S2, Area Equivalent surface The surface flow is formed by the equivalent surface of the remaining region. The scattering surface jointly influences the modification, and the region is calculated based on the Gauss-Seidel external iteration scheme. Equivalent surface Equivalent scattered current and equivalent scattered magnetic current Thus characterizing the region Scattered field contribution Surface flow data for each region were obtained. The surface flow data of the region is a one-dimensional array.

[0010] ,

[0011] In the formula, express Upper The scattering surface current obtained by the second solution and magnetic current ; Indicates the region The solution process of the internal algorithm can be compared with the solution of matrix equations in the method of moments; Represents the incident plane wave and right The contribution of the flow at the upper incident surface; For the transition operator, satisfying , indicating that Upward scattering surface flow conversion Operation of the flow on the upper incident surface; express Upper The scattering surface current obtained by the second solution and magnetic current ; express Upper The scattering surface current obtained by the second solution and magnetic current ;

[0012] S3, the analysis space includes at least one region, which is formed by the interaction of the scattering equivalent surface and the incident equivalent surface of other regions. The surface flow data of each region is divided into layers according to the octree grouping principle, and each region is labeled according to different layers to complete the rapid search of electromagnetic data radiated and received in each region.

[0013] S4 refers to the electromagnetic field of a region in the analysis space, which is formed by the interaction between regions, including the combined effect of adjacent and non-adjacent regions on the target region, wherein:

[0014] (1) The effect of adjacent regions on the target region is obtained by directly calculating the field value.

[0015] (2) The effect of non-adjacent regions on the target region is calculated using the multipole form according to the following formula:

[0016] ,

[0017] In the formula, Indicates field point electric field, Indicates field point magnetic field, Indicates the relationship with the current region Numbering of non-adjacent regions that interact with each other. Represents the free-space wavenumber of electromagnetic waves. The wave impedance in free space is... , This indicates the total number of regions in the analysis space. Indicates the region The corresponding number of non-adjacent regions, Denotes the unit dummy tensor. A unit vector representing the direction of propagation. Indicates the first Equivalent surface current in each region The phase factor representing electromagnetic waves, Denotes an integral infinitesimal element. Indicates the first Equivalent surface magnetic current in each region Represents the transition operator, ;

[0018] (3) The electromagnetic field of the target region is obtained by vector summation of the effects of adjacent and non-adjacent regions on the target region;

[0019] (4) Obtain the electromagnetic field of other regions in the analysis space according to steps (1)-(3).

[0020] Further, in step S2, the equivalent scattering current Equivalent surface , and the equivalent scattering magnetic current of the equivalent surface are calculated based on the Gauss-Seidel outer iteration format, and the attenuation threshold T is taken as the convergence judgment condition, T=-30dB.

[0021] Advantages: Compared with the prior art, the present application has the following advantages:

[0022] (1) The scheme for representing and determining the interaction of any two regions is designed, the "observation driven mode" is adopted, the problem of non-reciprocity between regions caused by different TDFIT scattering and incident equivalent surfaces is solved, the part of directly calculating the field value and the part of calculating by using the multipole form are determined, and the TDFIT far field calculation based on the fast multipole is accelerated.

[0023] (2) The multipole tree established for each region can realize fast far field calculation, the far field calculation involved in the TDFIT algorithm is applied to the MLFMA interlayer interpolation technology, the scale of the far field calculation is independent of the number of radiating elements, the number of memory allocation is reduced, the correct memory allocation mode is ensured, and the shared memory does not conflict. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The figure is a flowchart of the TDFIT fast far field analysis method based on the fast multipole of the present application.

[0025] Figure 2 The figure is a schematic diagram of the octree structure of the present application.

[0026] Figure 3 The figure is a schematic diagram of three PEC spheres as scattering targets in the embodiment of the present application.

[0027] Figure 4 The figure is a comparison of bistatic RCS under different outer iteration numbers (HH polarization) in the embodiment of the present application.

[0028] Figure 5 The figure is a comparison of bistatic RCS under different outer iteration numbers (VV polarization) in the embodiment of the present application.

[0029] Figure 6 The figure is a waveguide phased array antenna radome simulation model in the embodiment of the present application.

[0030] Figure 7The simulation results of the waveguide phased array antenna radome in the embodiments of the present application. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. The following description of at least one exemplary embodiment is merely illustrative in nature and not intended to limit the present application and its applications or uses in any way. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work under the premise that the scope of the present application. Unless otherwise specified, the relative arrangement, expressions and values of the components and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for the convenience of description, the size of each part shown in the drawings is not drawn in proportion. The technology, method and equipment known to those skilled in the relevant art can not be discussed in detail, but under appropriate circumstances, the technology, method and equipment should be regarded as part of the authorized description. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments can have different values.

[0032] For the convenience of description, spatial relative terms such as "over", "above", "upper surface", "upper" and the like can be used herein to describe the spatial positional relationship of one device or feature with other devices or features as shown in the drawings. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation of the device described in the drawings. For example, if the device in the drawing is inverted, the device described as "above" or "above" other devices or structures will be positioned "below" or "below" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations).

[0033] The overall technical solution of the present application:

[0034] For a plurality of adjacent objects in space that do not contact each other, P objects that do not contact each other are assumed, i.e. the region , is placed in an isotropic infinite homogeneous background D0, and the permittivity and permeability of the background are and , the time-harmonic field and The electromagnetic scattering problem of the scenario under the incidence. Assume that the time-harmonic factor of the incident wave is , where , is the frequency of the electromagnetic wave. Denote the surface (the target original surface or the virtual equivalent surface) of under the incidence of the plane wave and the interaction of the target as . The contribution of the scattering field can be characterized by the equivalent scattering electric current and the magnetic current on . The equivalent scattering electric current and the magnetic current characterize the radiation field at any point outside . The radiation field is calculated by the following formula (all the following examples are taken as i = p):

[0035] ,

[0036] wherein and are integral operators representing the scattering electromagnetic current on the surface, is the wave impedance of the background D0. Two integral operators and are defined as follows:

[0037] ,

[0038] wherein is the wave number in the background D0, is the Green function in the background D0.

[0039] Therefore, as long as the equivalent scattering electric current and the magnetic current are solved, the scattering problem can be solved. In theory, there is interaction between two objects with limited distance. From the perspective of accuracy, it is the best choice to use the full-wave algorithm to model the above problem integrally. However, in the processing of some problems in reality, it is often not feasible to use the full-wave method to model integrally due to the limitation of problem size, computing resources and computing efficiency requirements. Therefore, the present application provides an idea for the approximate solution of the multi-region scattering problem based on the CrossFlux theory.

[0040] A single target in the background D0 constitutes a system, which gives a unique scattering surface flow output for the determined incident surface flow input on the equivalent surface (according to the equivalent principle, the incident field and the scattering field are equivalent to the surface flow on the equivalent surface). The electromagnetic algorithm for the scattering problem simulates this system. The CrossFlux theory gives an approximate solution method for the scattering field of two targets: it is assumed that there is only one target in the background​ , solve the scattering electromagnetic current and on the incident time and (the superscript (1) represents the current iteration number, and the subscript represents the region number). Then, assuming that only in the background, the field and radiation and plus the original incident field and as the incident field of , solve the scattering electromagnetic current and on (for the convenience of the following description, the process of obtaining and is called one correction of the scattering surface current of ), the approximate scattering field can be calculated using the sum of the radiation fields of the scattering current , and , . Further, if and are continuously corrected by the scattering surface current of the other, the approximate solution can eventually converge to the exact solution. The number of corrections required to achieve a certain desired accuracy is related to the distance between the two regions. The farther the interaction, the less the number of corrections required.

[0041] When the target to be solved exceeds two, the surface current is corrected by the scattering surface current of the remaining regions , and the multi-region iteration process can be referred to Figure 1 .

[0042] As shown in Figure 1 , the specific process of the method of the present application comprises:

[0043] S1, divide the calculation and analysis space into P regions (P≥2) in an isotropic infinite uniform background D0, and denote the incident equivalent surface of the i-th (1≤i≤P) region as , the scattering equivalent surface as , the outward normal direction thereof as and . Use to represent the surface of the p-th region , is the target original surface or a virtual equivalent surface.

[0044] ​S2, using the Gauss-Seidel external iteration scheme of CrossFlux theory, S i The surface flow on (1≤i≤P) is generated by the rest of the region. The scattering surface flow correction is obtained. This invention solves for the following equation: Equivalent scattered current on and equivalent scattered magnetic current Thus characterizing the region Contribution to the scattered field,

[0045] ,

[0046] In the formula, express Upper The scattering surface current obtained by the second solution and magnetic current ; Indicates the area The solution process of the internal algorithm can be compared with the solution of matrix equations in the method of moments; Represents the incident plane wave and right The contribution of the flow at the upper incident surface; For the transition operator, satisfying , indicating that Upward scattering surface flow conversion Operation of the flow on the upper incident surface; express Upper The scattering surface current obtained by the second solution and magnetic current ; express Upper The scattering surface current obtained by the second solution and magnetic current .

[0047] After acquiring the surface of each region After determining the equivalent surface current, it is necessary to solve for the interaction between different regions to obtain the spatial scattering field distribution. The interaction between regions is essentially the interaction between the scattering equivalent surfaces of different regions and the incident equivalent surface, which will... The linear growth of the incident equivalent surface area × scattering equivalent surface area means that the computation time for inter-region interactions without a fast algorithm is unacceptable for electrically large targets. Therefore, this invention introduces fast multipole technology to accelerate the process of inter-region interactions, with the specific steps as follows:

[0048] S3, each region is octree grouped according to fast multipole technique, and each region is labeled with different layers. The radiated and received electromagnetic data of each region can be quickly found. The octree grouping is a data structure for spatial grouping of basis functions by MLFMA.

[0049] S4, the transfer of region interaction adopts an "observation-driven mode", that is, in each outer iteration process, the outermost loop object is the incident equivalent surface of each region, and the inner loop is the scattering equivalent surface of other regions. Correspondingly, when storing the effect of a scattering equivalent surface on an incident equivalent surface, the outermost layer is each non-empty data bit of the receiving region, and the corresponding data bit of the radiating region is stored under each box. The interaction between regions can also be found in the global tree. According to the interaction information, the part of directly calculating the field value and the part of using the multipole form calculation can be clearly divided.

[0050] (1) The influence of adjacent regions (groups) on the study region is calculated by directly calculating the field value.

[0051] (2) The influence of non-adjacent regions on the study region is calculated by calculating the electric field and magnetic field in the multipole form, wherein the multipole form of L and K operators is as follows:

[0052]

[0053] The multipole form of the electric field and the magnetic field is arranged as follows:

[0054]

[0055] It is found from the above formula that the radiation patterns contributed by the current and the magnetic current can be superimposed and transferred at one time, and the transferred patterns can be used to calculate the electric field and the magnetic field.

[0056] Implementation case verification:

[0057] In order to verify the effectiveness of the multipole acceleration between regions, the following case is used for verification.

[0058] As shown in Figure 3 , the scattering target is three PEC spheres with a radius of 1m, and the distance between each other is very close. The incident direction is , the frequency is 300MHz, the observation bistatic angle is , the interval is , the three spheres correspond to three solving regions, and two plane waves of horizontal and vertical polarization are solved in turn to obtain the HH and VV polarization results.

[0059] Figure 4 and Figure 5 ​​The bistatic RCS of VV and HH polarization after 1, 3, 6, 8 outer iterations of Gauss-Seidel format is compared with the result of the method of moments.

[0060] From Figure 4 and 5 it can be seen that the result of one outer iteration has a large difference with the result of the method of moments, because there is strong interaction between the regions. With the increase of the number of outer iterations, the approximate solution is closer and closer to the solution of the method of moments, and after 8 outer iterations, the approximate solution is basically consistent with the solution of the method of moments, because the Gauss-Seidel format always uses the latest scattering surface flow and therefore has good convergence performance.

[0061] The above case needs 295.7s for 6 outer iterations if the multi-pole acceleration is not started, and only needs 5.5s if the multi-pole acceleration is started.

[0062] A certain type of waveguide phased array antenna radome model is simulated and calculated, as shown in Figure 6 and 7 The excitation waveform is a modulated Gaussian signal of 15GHz-17GHz, the difference beam is excited, the directional diagram gain at 15GHz is observed, the fast far field calculation method based on fast multi-pole described in the application is applied, and the simulation time is compared when the method is not applied, the reliability and effectiveness of the method are verified through the comparison of the simulation results and the simulation time. Without using the method of the application, the simulation time is 2827.56s, after starting the fast far field calculation method based on fast multi-pole described in the application, the simulation time is 18.6085s, the acceleration effect is obvious, and the simulation results can remain consistent.

[0063] The region interaction acceleration scheme based on fast multi-pole of the application starts from the idea of MLFMA layer interpolation, realizes the large reduction of complexity and storage of TDFIT calculation of large-size target scattering problem, and thus provides a technical basis and acceleration scheme for the scattering and radiation characteristic evaluation of the coexistence of large-size target metal carrier and electrically small fine structure. This scheme obtains full-space far field with sufficient sampling rate through multiple layer interpolation, accelerates the interaction between regions, and reduces the time consumption of large-size target calculation; meanwhile, the application saves memory and reduces the number of memory allocation times under the premise of ensuring correctness.

[0064] The above only describes some embodiments of the application, and it should be noted that for ordinary skilled persons in the technical field, some improvements and refinements can be made without departing from the principle of the application, and these improvements and refinements should also be regarded as the protection scope of the application.

Claims

1. A fast far-field analysis method based on fast multipole TDFIT, characterized in that The method comprises the following steps: S1, divide the analysis space where the antenna is located in an isotropic infinite and uniform background into several regions , , the equivalent surface of region , the incident equivalent surface of region , the scattering equivalent surface of region , represents the original surface or virtual equivalent surface of the pth region ​​​ S2, Area Equivalent surface The surface flow is formed by the equivalent surface of the remaining region. The scattering surface jointly influences the modification, and the region is calculated based on the Gauss-Seidel external iteration scheme. Equivalent surface Equivalent scattered current and equivalent scattered magnetic current Thus characterizing the region Scattered field contribution Surface flow data for each region were obtained. The surface flow data of the region is a one-dimensional array. In the formula, express Upper The scattering surface current obtained by the second solution and magnetic current ; Indicates the region Equivalent surface The solution process of the internal algorithm is achieved by solving matrix equations in the method of moments; Represents the incident plane wave and right The contribution of the flow at the upper incident surface; For the transition operator, satisfying , indicating that Upward scattering surface flow conversion Operation of the flow on the upper incident surface; express Upper The scattering surface current obtained by the second solution and magnetic current ; express Upper The scattering surface current obtained by the second solution and magnetic current ; S3, the analysis space comprises at least one region, which is interacted by other region scattering equivalent surface and incident equivalent surface, and the surface flow data of each region is layered according to the octree grouping principle, and each region is labeled according to different layers, so that the fast search of electromagnetic data radiated and received by each region is completed; S4, the electromagnetic field of the region in the analysis space is formed by the interaction between the regions, including the common action of adjacent regions and non-adjacent regions on the target region, wherein: (1) the action of the adjacent region on the target region is obtained by directly calculating the field value, (2) the action of the non-adjacent region on the target region is obtained by calculating the multipole form according to the following formula, ， wherein E represents the electric field at the field point , H represents the magnetic field at the field point , the subscript represents the number of non-adjacent regions that interact with the equivalent surface of the current region , k represents the free space wave number of the electromagnetic wave, Z0 represents the wave impedance of free space , N represents the number of all regions in the analysis space, M represents the number of non-adjacent regions corresponding to the region , I represents the unit dyadic tensor, e represents the unit vector in the direction of propagation, J represents the equivalent surface current of the mth region, , k represents the phase factor of the electromagnetic wave, d represents the integration infinitesimal, M represents the equivalent surface magnetic current of the mth region, , T represents the transfer operator, ; (3) the actions of the adjacent region and the non-adjacent region on the target region are vector added to obtain the electromagnetic field of the target region; (4) the electromagnetic field of other regions in the analysis space is obtained according to steps (1)-(3).

2. The fast far-field analysis method of the TDFIT based on fast multipoles according to claim 1, characterized in that: In step S2, the region Equivalent surface Equivalent scattering current and equivalent scattering magnetic current is calculated based on the Gauss-Seidel outer iteration format. When the convergence is judged by the attenuation threshold T, T = -30 dB.

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