TDFIT rapid far-field analysis method based on rapid multipole

Abstract

The invention discloses a TDFIT fast far field analysis method based on a fast multipole, which is based on a fast multipole regional interaction acceleration scheme, starts from an MLFMA interlayer interpolation principle, and realizes the purpose that the complexity and memory space of calculating an electrically large-size target scattering problem by TDFIT are greatly reduced. Therefore, a technical basis and an acceleration scheme are provided for target scattering and radiation characteristic evaluation in which an electrically large metal carrier and an electrically small fine structure coexist. According to the method, a full-space far field with enough sampling rate is obtained through multiple interlayer interpolations, interaction between regions is accelerated, and time consumption of electrically large target calculation is reduced; meanwhile, by observing the driving mode, the memory is saved and the memory allocation frequency is reduced on the premise of ensuring the correctness.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic communication technology, specifically relating to the TDFIT fast far-field analysis method based on fast multipole. Background Technology

[0002] A radome is used to protect the internal radar or antenna, ensuring its normal operation even in harsh external environments such as storms, rain, snow, sandstorms, hail, and high temperatures, without affecting electromagnetic wave transmission; it is also known as an "electromagnetic window." The wave transmission performance of the radome has a significant impact on the antenna's key technical specifications. When designing a radome, the efficiency and accuracy of the electromagnetic modeling and simulation methods used are crucial to the simulation results. To ensure computational accuracy, employing correct electromagnetic modeling and simulation methods can greatly improve computational efficiency and power.

[0003] Currently, the high-frequency approximation method and the full-wave numerical method are the two main methods used for radome simulation calculations. However, the high-frequency method cannot accurately analyze uneven structures and complex media, which will introduce large errors. The full-wave numerical method has high computational complexity and low computational efficiency, and can only be used when analyzing small-sized radomes.

[0004] Furthermore, the commonly used equivalence principle algorithm (CrossFlux theory) in existing technologies obtains a relatively accurate approximate solution by independently calculating each region and updating the scattering surface flow on the equivalent surface of the region using the scattering near-field of each region. However, the efficiency of solving each component region independently depends on the efficiency of the algorithm itself. In CrossFlux theory, the interaction between regions is used 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 have an efficiency of N. obs ×N rad Linear growth makes the time consumption for computation of electrically large targets in inter-region interactions unacceptable.

[0005] Therefore, rapid and accurate calculation of the far field has become an important part of analyzing radome problems. Summary of the Invention

[0006] Purpose of the invention / Technical problem This invention addresses the technical problems existing in the prior art by proposing a fast far-field analysis method based on the TDFIT (Time-Domain Finite Integral) method. This invention conducts in-depth research on the efficiency problem of far-field calculation in the TDFIT method and accelerates the post-processing of the TDFIT algorithm through multilayer fast multipole inter-layer interpolation technology, thereby realizing the rapid implementation of 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: 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; 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 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 ; 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 layered 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. S4, for analyzing the electromagnetic field of a region in the space, is formed by the interaction between regions, including the combined effect of adjacent and non-adjacent regions on the target region, wherein: (1) The effect of adjacent regions on the target region is obtained by directly calculating the field value. (2) The effect of non-adjacent regions on the target region is calculated using the multipole form according to the following formula: , 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 vector tensor. A unit vector representing the direction of propagation. Indicates the first Equivalent surface current of 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, ; (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; (4) Obtain the electromagnetic fields of other regions in the analysis space according to steps (1)-(3).

[0008] Furthermore, in step S2, the region is calculated based on the Gauss-Seidel external iteration format. Equivalent surface Equivalent scattered current and equivalent scattered magnetic current When the attenuation threshold T is used as the convergence criterion, T = -30dB.

[0009] Beneficial effects: Compared with the prior art, the present invention has the following advantages: (1) A scheme for characterizing and determining the interaction between any two regions was designed. The “observation-driven mode” was adopted to solve the problem of non-reciprocity of interaction between regions caused by different TDFIT scattering and incident equivalent surfaces. The direct calculation of field values ​​and the calculation using multipole form were clarified to achieve TDFIT far-field calculation acceleration based on fast multipole.

[0010] (2) The multipole subtree established for each region can be used to achieve fast far-field calculation. The far-field calculation involved in the TDFIT algorithm is all applied with MLFMA inter-layer interpolation technology, so that the scale of far-field calculation is independent of the number of radiating units, reducing the number of memory allocations, ensuring the correct memory allocation method, and preventing conflicts in shared memory. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the TDFIT fast far-field analysis method based on fast multipoles described in this invention.

[0012] Figure 2 This is a schematic diagram of the octree structure described in this invention.

[0013] Figure 3 This is a schematic diagram of three PEC spheres as the scattering targets in an embodiment of the present invention.

[0014] Figure 4 This is a comparison of bistation RCS (HH polarization) under different external iteration numbers in the embodiments of the present invention.

[0015] Figure 5 This is a comparison of bi-station RCS (VV polarization) under different external iteration numbers in the embodiments of the present invention.

[0016] Figure 6 This is a simulation model of the waveguide phased array antenna radome in an embodiment of the present invention.

[0017] Figure 7 The image shows the simulation results of the waveguide phased array antenna radome in the embodiment of this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. Unless otherwise specifically stated, the relative arrangement, expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0019] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used here to describe the spatial positional relationship of a device or feature as shown in the figure with other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figure. For example, if the device in the figure is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations).

[0020] The overall technical solution of this invention: Considering several non-contact neighboring objects in space, let's assume P non-contact objects, i.e., a region. , Placed in an isotropic, infinitely large, uniform background D0, the background has a permittivity and a permeability of and Considering harmonic fields and Electromagnetic scattering problem in this scene under incident conditions. Assume the time harmonic factor of the incident wave is... ,in , The frequency of electromagnetic waves. express The surface (target's native surface or virtual equivalent surface), under the influence of plane wave incidence and the interaction with the target, The contribution to the scattered field can be derived from Equivalent scattered current on and magnetic current Characterization. Equivalent scattered current and magnetic current right any point outside The radiation field is calculated using the following formula (all examples assume i=p): , in, and It represents the integral operator on the surface where the scattered electromagnetic current is located. This is the background impedance D0. Two integral operators. and The definition is as follows: , in, The wave number in background D0, The Green's function in background D0.

[0021] Therefore, as long as the solution can be found and magnetic current Thus, the aforementioned scattering problem can be solved. Theoretically, there is interaction between any two objects at a finite distance. From an accuracy perspective, using the full-wave algorithm for integrated modeling of the above problem is the best choice. However, in dealing with some real-world problems, limitations in problem size, computational resources, and computational efficiency requirements often make integrated modeling using the full-wave method infeasible. Therefore, this invention provides an approach based on CrossFlux theory to approximate solutions to multi-region scattering problems.

[0022] The single target in background D0 constitutes a system that, for a given incident surface flow input on the equivalent surface, produces a unique scattered surface flow output (according to the equivalence principle, the incident field and the scattered field are equivalent to the surface flow on the equivalent surface). The electromagnetic algorithm used for the scattering problem simulates this system. CrossFlux theory provides an approximate solution for the scattered field of two targets: assuming that only one target is present in the background... Solve for the incident electromagnetic wave and At incidence Scattered electromagnetic current and (The superscript (1) indicates the current iteration number, and the subscript indicates the region number). Then assume that there are only [the following text is missing from the original text] in the background. ,Bundle and Radiated field and In addition to the original incident field and As The incident field is solved. Scattered electromagnetic current and (For the convenience of the following description, the following is obtained) and The process is called the process of (First correction of the scattering surface flow), utilizing the scattering current. , as well as , The approximate scattered field can be calculated by summing the radiation fields. Furthermore, if... and By continuously using the scattering surface flow of the other region to correct its own scattering surface flow, 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 greater the distance, the weaker the interaction, and the fewer corrections are required.

[0023] When there are more than two objectives to be solved The surface flow on the surface is due to the remaining areas The scattering surface flow correction is obtained; the multi-region iterative process can be found in [reference needed]. Figure 1 .

[0024] like Figure 1 As shown, the specific process of the method of the present invention includes: S1, the computational analysis space is divided into P regions (P≥2), situated within an isotropic, infinitely large, uniform background D0. Let the incident equivalent surface of the i-th region (1≤i≤P) be denoted as . The scattering equivalent surface is The directions of their outward normal vectors are respectively and .use Represents the p-th region The surface, The target is the native surface or virtual equivalent surface.

[0025] 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, , 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 .

[0026] 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:

[0027] S3 groups the regions into octrees using the Fast Multipole technique, labeling each region with different layers. Both radiated and received electromagnetic data for each region can be quickly retrieved. The octree grouping is a data structure that spatially groups basis functions using MLFMA.

[0028] In S4, the transfer of region interactions adopts an "observation-driven mode," meaning that in each outer iteration, 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 interaction between a scattering equivalent surface and an incident equivalent surface, the outermost layer stores each non-empty data bit of the receiving region, and each box stores the corresponding data bits of the radiating region. The interactions between regions can also be found in the global tree. Based on the interaction information, the part directly calculating the field value and the part calculated using the multipole form can be clearly distinguished.

[0029] (1) The influence of adjacent regions (groups) on the study area is calculated by directly calculating the field value;

[0030] (2) The influence of non-adjacent regions on the study area is calculated using the multipole form for the electric and magnetic fields. The multipole forms for the L and K operators are as follows: , After adjusting the electric and magnetic fields, the multipole form is: , Observing the above formula, we find that the radiation patterns contributed by current and magnetic current can be superimposed and transferred at once. The electric field and magnetic field can be calculated simultaneously from the transferred pattern.

[0031] Implementation case verification: To verify the effectiveness of interregional multipole acceleration, the following case study is used.

[0032] like Figure 3 As shown, the scattering target is three PEC spheres with a radius of 1m, and the distance between each pair of spheres is very close. The incident direction is... The frequency is 300MHz, and the observed bistatic angle is... ,interval The three spheres correspond to three solution regions. The two plane waves with horizontal and vertical polarizations are solved sequentially to obtain the HH and VV polarization results.

[0033] Figure 4 as well as Figure 5 A comparison of the bistationary RCS of VV and HH polarizations after 1, 3, 6, and 8 external iterations in the Gauss-Seidel scheme with the results of the method of moments is presented.

[0034] from Figure 4 and 5It can be seen that the result of a single outer iteration differs significantly from that of the method of moments (MoM), because there are strong interactions between each pair of regions. As the number of outer iterations increases, the approximate solution becomes closer and closer to the MoM solution. After 8 outer iterations, the approximate solution and the MoM solution basically coincide. This is because the Gauss-Seidel scheme always uses the latest scattering surface flow and therefore has good convergence performance.

[0035] The above case requires 295.7 seconds for 6 external iterations without multipole acceleration, but only 5.5 seconds with it.

[0036] Simulation calculations were performed on a radome model of a certain type of waveguide phased array antenna, such as... Figure 6 and 7 As shown, a modulated Gaussian signal with an excitation waveform of 15GHz~17GHz was used for differential beam excitation. The radiation pattern gain at 15GHz was observed. The fast far-field calculation method based on fast multipole described in this invention was compared with that without the method. The reliability and effectiveness of the method were verified by comparing the simulation results and simulation time. Without the method of this invention, the simulation time was 2827.56s. After enabling the fast far-field calculation method based on fast multipole described in this invention, the simulation time was 18.6085s, showing a significant acceleration effect, and the simulation results remained consistent.

[0037] This invention, based on a fast multipole (MFFMA) regional interaction acceleration scheme, utilizes the MLFMA interlayer interpolation concept to significantly reduce the complexity and storage requirements of TDFIT computation for electrically large target scattering problems. This provides a technical foundation and acceleration solution for evaluating the scattering and radiation characteristics of electrically large targets coexisting with metallic carriers and electrically small fine structures. This scheme obtains a sufficiently high sampling rate for the full-space far field through multiple interlayer interpolations, accelerating inter-regional interactions and reducing the computation time for electrically large targets. Simultaneously, this invention employs an "observation-driven mode" to save memory and reduce memory allocation frequency while ensuring correctness.

[0038] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A fast far-field analysis method based on the TDFIT fast multipole method, characterized in that... Includes the following steps: 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; 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 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 ; 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 layered 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. S4, for analyzing the electromagnetic field of a region in the space, is formed by the interaction between regions, including the combined effect of adjacent and non-adjacent regions on the target region, wherein: (1) The effect of adjacent regions on the target region is obtained by directly calculating the field value. (2) The effect of non-adjacent regions on the target region is calculated using the multipole form according to the following formula: ， 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 vector tensor. A unit vector representing the direction of propagation. Indicates the first Equivalent surface current of 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, ; (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; (4) Obtain the electromagnetic fields of other regions in the analysis space according to steps (1)-(3).

2. The TDFIT fast far-field analysis method based on fast multipole as described in claim 1, characterized in that: In step S2, the region is calculated based on the Gauss-Seidel external iteration scheme. Equivalent surface Equivalent scattered current and equivalent scattered magnetic current When the attenuation threshold T is used as the convergence criterion, T = -30dB.

Images