CN111046603A - Electromagnetic scattering characteristic analysis method based on GPU parallel acceleration characteristic basis function algorithm - Google Patents
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Abstract
The invention discloses an electromagnetic scattering characteristic analysis method based on a GPU parallel acceleration characteristic basis function algorithm, which comprises the following steps: carrying out three-dimensional modeling on a target to be detected; mesh generation is carried out on a model of a target to be detected based on the RWG basis function; optimizing a characteristic basis function algorithm by using a discrete Galois algorithm based on mesh generation information; performing parallel acceleration on the characteristic basis function algorithm by using the GPU; and taking the mesh generation information as the input of the feature basis function algorithm after parallel acceleration, thereby outputting the electromagnetic scattering property of the target to be detected. The method optimizes the characteristic basis function algorithm by using a discrete Galois method, and performs parallel acceleration on the characteristic basis function algorithm by using the GPU, so that the electromagnetic scattering problem in the separation process of electrically large-size targets and complex targets can be solved, and the calculation has high accuracy and high efficiency.
Description
Technical Field
The invention belongs to the field of computational electromagnetism, and particularly relates to an electromagnetic scattering characteristic analysis method based on a GPU (graphics processing unit) parallel acceleration characteristic basis function algorithm.
Background
With the continuous development of society, the technological progress is changing day by day. In the field of engineering applications, there is an urgent need to study the electromagnetic properties of complex or electrically large targets, and typical applications thereof are as follows: target stealth and anti-stealth design, radar system design, target identification and the like. The research methods mainly include measurement methods and calculation methods. The measurement method has an important irreplaceable effect on the aspect of detecting the electromagnetic property of the target, but has the defects of high test cost, long test period and the like. With the rapid improvement of computer performance, the calculation of electromagnetic characteristics of electrically large targets becomes possible, and the importance of the calculation science is increasingly shown. How to accurately and efficiently solve the electromagnetic characteristics of such complex targets becomes a common concern for students and engineers in radar overall design and stealth and anti-stealth research.
There are two general categories of methods for solving the electromagnetic property problem, one is high frequency methods such as Geometric Optics (GO), geometric diffraction (GTD), Physical Optics (PO) and bound ray method (SBR); another class is the low frequency numerical method of exact solution. The high-frequency method has the characteristics of high solving speed, small storage requirement and the like, but because the methods contain too many approximations, the mutual coupling among the components is not completely considered, and the target with a complex structure cannot be accurately processed. On the contrary, the low-frequency numerical method has the characteristic of accurate calculation, but has slow solution speed and large storage cost.
The low-frequency numerical method is mainly divided into two main categories, namely a differential equation method and an integral equation method. The differential equation method is based on Maxwell partial differential equation system, and directly carries out discrete solution to the field. Representative methods are Finite Element Method (FEM) and finite difference time domain method (FDTD). The methods are widely applied in other fields, are developed more mature, are simpler to realize, and simultaneously, the impedance matrix of a linear equation set formed by the methods is sparse, so that the solution is faster. However, these methods introduce boundaries artificially outside the solution domain, and have a large unknown quantity when the solution domain is physically divided, and they have the inherent disadvantages of the differential method: the grid dispersion error is large, and as the solution domain is increased, the dispersion error accumulation is larger, so that the method is not suitable for solving the electromagnetic property problem of the electrically large target. The integral equation method is represented by the moment method (MoM), which is a source-based method that requires a small amount of unknowns and does not have the problem of grid dispersion errors of the differential equation method. However, the impedance matrix obtained by the MoM method is a full matrix, and the storage complexity is O (N)2) The computational complexity is O (N)2) Or O (N)3) Thus, conventional MThe oM method is also only capable of analyzing electromagnetic properties of electrically small targets.
Fast algorithms based on the moment method are rapidly developed, such as a Fast Multipole Method (FMM) and a multi-layer fast multipole method (MLFMA), when an electrically large target is analyzed, impedance matrixes of far-zone mutual coupling are not filled explicitly, an iterative method is needed to solve a linear equation set, iterative convergence is very slow usually when the target is complex, and the disadvantage is further shown when an iterative solver method is used for solving the electromagnetic response problem of the target under multiple incidence. In 2003, the american scholars Raj misttra proposed a Characteristic Basis Function Method (CBFM), which is based on the following principles: the target is firstly divided into a plurality of small blocks, the current response on each block is calculated to be used as a first-order basis function when the coupling between the blocks is not considered, then the response on each block can be obtained by taking the first-order basis functions of other blocks as excitation and the response current as a second-order basis function when the coupling between the blocks is considered, and a high-order basis function can be obtained by the same method for improving the calculation accuracy. The method relies on the initial incident wave, and the Characteristic Basis Functions (CBFs) are rebuilt many times for the multiple incidence problem, which is a prototype of the characteristic basis function method. A series of plane waves are used as excitation of the blocks, the obtained CBFs are independent of the excitation, and when the multi-incidence problem is solved, the direct method can be used for quickly solving the problem.
In the last decade, the appearance of many fields is new due to the rapid development of GPU massive high-performance parallel computing technology, and researchers in computational electromagnetism are trying to accelerate fast algorithms by using the technology. In 2005, professor Krakiwsky first utilizes a GPU parallel technology to realize an FDTD algorithm and solves a two-dimensional scattering problem on the basis of the FDTD algorithm, and the speed-up ratio is up to several tens of times compared with the speed-up ratio obtained by computing only by using a CPU. Since the CBFM has very good parallelism, it is accelerated and optimized using the GPU.
Disclosure of Invention
The invention aims to provide an electromagnetic scattering characteristic analysis method capable of calculating electromagnetic scattering problems in the separation process of electrically large-size targets and complex targets.
The technical solution for realizing the purpose of the invention is as follows: an electromagnetic scattering characteristic analysis method based on a GPU parallel acceleration characteristic basis function algorithm comprises the following steps:
step 1, carrying out three-dimensional modeling on a target to be detected;
step 2, performing mesh generation on the model of the target to be detected, which is obtained in the step 1, based on the RWG basis function;
step 3, obtaining mesh generation information based on the step 2, and optimizing a characteristic basis function algorithm by using a discrete Galois algorithm;
step 4, carrying out parallel acceleration on the characteristic basis function algorithm by using a GPU;
and 5, taking the mesh generation information obtained in the step 2 as the input of the feature basis function algorithm after parallel acceleration, and outputting the electromagnetic scattering property of the target to be detected.
Further, step 3 is to obtain mesh generation information based on step 2, and optimize the feature basis function algorithm by using a discrete galileo method, and specifically comprises the following steps:
step 3-1, introducing an internal penalty term at the common edge of the monopole RWG basis function:
tmn·Jm(r)＝-tnm·Jn(r) r∈Cmn
in the formula, CmnFor mth monopole RWG basis function contour CmAnd the nth monopole RWG basis function contour CnOverlap contour between tmnIs CmnIs directed from CmPoint of direction Cn，tnmIs CmnIs directed from CnPoint of direction Cm，Jm(r) is the current in the mth triangular bin, Jn(r) is the current on the nth triangular bin;
3-2, representing the current residual R at the boundary of the monopole RWG basis function according to the internal penalty term1And residual charge R accumulated at these boundaries2：
In the formula, 1/j ω ε0Is the amplitude coefficient, fmIs the mth monopole RWG basis function, tmIs a and fmThe outer normal vector related to the contour, G (r, r ') is the green's function of free space, where r and r ' are the position vectors of the field point and the source point, respectively;
step 3-3, combining said residual current R1And residual charge R2The weak form of the Galileo test constructed by the discrete Galileo method is as follows:
wherein,
in the formula, EFIE and MFIE are an electric field integral equation and a magnetic field integral equation generated by induced current on the surface of an ideal conductor in free space respectively, α, β and gamma are coefficients, and N iseE and H are respectively an electric field and a magnetic field related to incident plane waves and are the number of the monopole RWG basis functions; i is a unit parallel vector; j' is the distribution of surface current; mu.s0And ε0N is a normal vector of the surface of the scatterer, ▽ and ▽ ' are Hamilton operators in a field region and a source region respectively, omega ' is an integral domain of a source region area integral, dS ' is an integral surface element of the source region;
3-4, constructing a characteristic basis function matrix equation according to the weak form of the Galileo test, wherein an impedance matrix ZmnAnd an excitation matrix VmRespectively as follows:
Vm＝<fm,αE+(1-α)n×H>
of formula (II) to'mAnd f'nThe mth and nth monopole RWG basis functions in the source region, respectively.
Compared with the prior art, the invention has the following remarkable advantages: 1) the model of the target to be detected is subjected to triangular mesh subdivision with the precision of one tenth of the wavelength, so that a better characteristic basis function can be obtained; 2) optimizing a characteristic basis function algorithm by using a discrete Galois method, so that the algorithm can solve the problem of a binding surface in the separation process of the complex target, and further calculate the electromagnetic scattering problem in the separation process of the complex target; 3) the GPU is used for carrying out parallel acceleration on the characteristic basis function algorithm, so that the algorithm can calculate the electromagnetic scattering problem of the large-size target; 4) the method has high accuracy and high efficiency in calculation.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flowchart of an electromagnetic scattering property analysis method based on a GPU parallel acceleration characteristic basis function algorithm.
FIG. 2 is a schematic diagram of a characteristic basis function algorithm CPU + GPU heterogeneous computing model.
Fig. 3 is a schematic diagram of a separation process of a target to be detected in the embodiment, where fig. (a) is an initial posture in the separation process of the target to be detected, fig. (b) is a 2 nd posture in the separation process of the target to be detected, fig. (c) is a 3 rd posture in the separation process of the target to be detected, fig. (d) is a 4 th posture in the separation process of the target to be detected, and fig. (e) is a 5 th posture in the separation process of the target to be detected.
FIG. 4 is a schematic diagram of CUDA platform construction in the embodiment.
FIG. 5 is a graph comparing the results of FEKO calculation of the method of the present invention and commercial software in the VV polarization mode in the examples.
FIG. 6 is a graph comparing the results of FEKO calculation of the method of the present invention and the commercial software in HH polarization mode in the examples.
Detailed Description
With reference to fig. 1, the present invention provides an electromagnetic scattering property analysis method based on a GPU parallel acceleration feature basis function algorithm, which includes the following steps:
the radar transmits electromagnetic waves to a target to be detected;
step 1, carrying out three-dimensional modeling on a target to be detected;
step 2, performing mesh generation on the model of the target to be detected, which is obtained in the step 1, based on the RWG basis function;
step 3, obtaining mesh generation information based on the step 2, and optimizing a characteristic basis function algorithm by using a discrete Galois algorithm;
step 4, carrying out parallel acceleration on the characteristic basis function algorithm by using the GPU;
and 5, taking the mesh generation information obtained in the step 2 as the input of the feature basis function algorithm after parallel acceleration, and outputting the electromagnetic scattering property of the target to be detected.
Further preferably, the step 2 performs mesh generation on the model of the target to be detected obtained in the step 1 based on the RWG basis function, specifically: and (4) performing triangular mesh subdivision on the model of the target to be detected, which is obtained in the step (1), based on the RWG basis function.
Further preferably, the step 2 performs mesh generation on the model of the target to be detected obtained in the step 1 based on the RWG basis function, specifically: and performing triangular mesh subdivision with the precision of one tenth of the wavelength on the target model to be detected based on the RWG basis function, wherein the wavelength is the wavelength of a radar emission signal.
Further, for electromagnetic scattering property analysis of complex target separation processes, the problem of using monopole RWG basis functions to deal with the junction surface is different from the conventional RWG basis functions, the monopole RWG basis functions only contain one triangular bin instead of a triangular bin pair, and the continuity of the current passing through the common edge of the two monopole RWG basis functions cannot be guaranteed. In order to ensure the current continuity of the target surface and meet the boundary condition of the target surface, a weak form of a Galois field test is established by using a discrete Galois field method, and an impedance matrix and an excitation matrix in a characteristic basis function are constructed by using the weak form.
From the above analysis, step 3 obtains mesh generation information based on step 2, and optimizes the feature basis function algorithm by using a discrete galileo method, which specifically comprises:
step 3-1, introducing an internal penalty term at the common edge of the monopole RWG basis function:
tmn·Jm(r)＝-tnm·Jn(r) r∈Cmn
in the formula, CmnFor mth monopole RWG basis function contour CmAnd the nth monopole RWG basis function contour CnOverlap contour between tmnIs CmnIs directed from CmPoint of direction Cn，tnmIs CmnIs directed from CnPoint of direction Cm，Jm(r) is the current in the mth triangular bin, Jn(r) is the current on the nth triangular bin;
step 3-2, representing the current residual R at the boundary of the monopole RWG basis function according to the internal penalty term1And residual charge R accumulated at these boundaries2：
In the formula, 1/j ω ε0Is the amplitude coefficient, fmIs the mth monopole RWG basis function, tmIs a and fmThe outer normal vector related to the contour, G (r, r ') is the green's function of free space, where r and r ' are the position vectors of the field point and the source point, respectively;
step 3-3, combining the residual current R1And residual charge R2The weak form of the Galileo test constructed by the discrete Galileo method is as follows:
wherein,
in the formula, EFIE and MFIE are an electric field integral equation and a magnetic field integral equation generated by induced current on the surface of an ideal conductor in free space respectively, α, β and gamma are coefficients, and N iseE and H are respectively an electric field and a magnetic field related to incident plane waves and are the number of the monopole RWG basis functions; i is a unit parallel vector; j' is the distribution of surface current; mu.s0And ε0N is a normal vector of the surface of the scatterer, ▽ and ▽ ' are Hamilton operators in a field region and a source region respectively, omega ' is an integral domain of a source region area integral, dS ' is an integral surface element of the source region;
3-4, constructing a characteristic basis function matrix equation according to the weak form of the Galileo test, wherein the impedance matrix ZmnAnd an excitation matrix VmRespectively as follows:
Vm＝<fm,αE+(1-α)n×H>
of formula (II) to'mAnd f'nThe mth and nth monopole RWG basis functions in the source region, respectively.
Further exemplary, in step 2-3, α is 0.2, β is 0.5 λ, γ is- α, where λ is the wavelength of the radar emission signal.
Further, with reference to fig. 2, step 3 is to perform parallel acceleration on the feature basis function algorithm by using the GPU, specifically: and (3) utilizing the GPU to perform parallel acceleration on the impedance matrix calculation in the characteristic basis function algorithm so as to simultaneously operate all the impedance matrices. Other tasks such as geometric partitioning of the space in which the target is located, generation of characteristic basis functions, preparation and transmission of necessary data, and the manner of initiation of the designated kernel function are conventionally performed by the CPU.
The present invention will be described in further detail with reference to examples.
Examples
The object to be detected analyzed in this embodiment is a composite of a plurality of cuboids, the length of the cuboid at the bottom is 1.6m, the width is 1.6m, the height is 0.3m, the length of the cuboid at the top is 0.3m, the width is 0.3m, the height is 0.9m, the frequency of a radar transmitting signal is 300MHz, the incident direction is 0 ° in the vertical direction, and the radar transmitting signals are uniformly distributed in the range of 0 ° to 180 ° at intervals of 1 °. The receiving direction is matched with the incident direction, and the polarization modes are HH polarization and VV polarization respectively. The model and the separation process of target are as shown in fig. 3, bottom cuboid remains motionless in the separation process, the upper cuboids are sequentially far away according to the quadrant sequence, two adjacent postures are compared, if the upper cuboid in the previous posture is far away or is ready to be far away, the upper cuboid corresponding to the next posture is far away from 0.25m on the basis, otherwise, the upper cuboid remains motionless until finally all the bottom cuboids are left. In this embodiment, a simulation environment under the CUDA architecture shown in fig. 4 is built.
Calculation results are shown in fig. 5 and 6 by using the method and the commercial software FEKO of the invention for HH polarization and VV polarization respectively, and the calculation results are almost not different from each other, thereby verifying the correctness of the method of the invention. And the time taken for the calculation is shown in table 1 below:
TABLE 1 comparison of calculated time for each pose of the separation process
As can be seen from Table 1 above, the computation time of the present invention is significantly less than that of the commercial software FEKO, verifying the efficiency of the present invention.
The method optimizes the characteristic basis function algorithm by using a discrete Galois method, and performs parallel acceleration on the characteristic basis function algorithm by using the GPU, so that the electromagnetic scattering problem in the separation process of electrically large-size targets and complex targets can be solved, and the calculation has high accuracy and high efficiency.
Claims (6)
1. An electromagnetic scattering characteristic analysis method based on a GPU parallel acceleration characteristic basis function algorithm is characterized by comprising the following steps:
step 1, carrying out three-dimensional modeling on a target to be detected;
step 2, performing mesh generation on the model of the target to be detected, which is obtained in the step 1, based on the RWG basis function;
step 3, obtaining mesh generation information based on the step 2, and optimizing a characteristic basis function algorithm by using a discrete Galois algorithm;
step 4, carrying out parallel acceleration on the characteristic basis function algorithm by using a GPU;
and 5, taking the mesh generation information obtained in the step 2 as the input of the feature basis function algorithm after parallel acceleration, and outputting the electromagnetic scattering property of the target to be detected.
2. The electromagnetic scattering property analysis method based on the GPU parallel acceleration feature basis function algorithm according to claim 1, wherein step 2 is to perform mesh generation on the model of the target to be detected obtained in step 1 based on the RWG basis function, specifically: and (4) performing triangular mesh subdivision on the model of the target to be detected, which is obtained in the step (1), based on the RWG basis function.
3. The electromagnetic scattering property analysis method based on the GPU parallel acceleration feature basis function algorithm according to claim 1 or 2, characterized in that in step 2, the mesh generation is performed on the model of the target to be detected obtained in step 1 based on the RWG basis function, specifically: and performing triangular mesh subdivision with the precision of one tenth of the wavelength on the target model to be detected based on the RWG basis function, wherein the wavelength is the wavelength of the radar emission signal.
4. The electromagnetic scattering property analysis method based on the GPU parallel acceleration feature basis function algorithm according to claim 1, wherein step 3 obtains mesh generation information based on step 2, and optimizes the feature basis function algorithm by using a discrete galileo method, specifically comprising:
step 3-1, introducing an internal penalty term at the common edge of the monopole RWG basis function:
tmn·Jm(r)＝-tnm·Jn(r) r∈Cmn
in the formula, CmnFor mth monopole RWG basis function contour CmAnd the nth monopole RWG basis function contour CnOverlap contour between tmnIs CmnIs directed from CmPoint of direction Cn，tnmIs CmnIs directed from CnPoint of direction Cm，Jm(r) is the current in the mth triangular bin, Jn(r) is the current on the nth triangular bin;
3-2, representing the current residual R at the boundary of the monopole RWG basis function according to the internal penalty term1And residual charge R accumulated at these boundaries2：
In the formula, 1/j ω ε0Is the amplitude coefficient, fmIs the mth monopole RWG basis function, tmIs a and fmThe outer normal vector related to the contour, G (r, r ') is the green's function of free space, where r and r ' are the position vectors of the field point and the source point, respectively;
step 3-3, combining said residual current R1And residual charge R2The weak form of the Galileo test constructed by the discrete Galileo method is as follows:
wherein,
EFIE:
MFIE:
in the formula, EFIE and MFIE are an electric field integral equation and a magnetic field integral equation generated by induced current on the surface of an ideal conductor in free space respectively, α, β and gamma are coefficients, and N iseE and H are respectively an electric field and a magnetic field related to incident plane waves and are the number of the monopole RWG basis functions; i is a unit parallel vector; j' is the distribution of surface current; mu.s0And ε0Respectively the magnetic permeability and the dielectric constant of the free space; omega is the oscillation angular frequency; n is the normal vector of the surface of the diffuser,
and
hamiltonian operators in the field region and the source region respectively; omega' is an integral domain of the area integral of the source region; dS' is an integral surface element of the source region;
3-4, constructing a characteristic basis function matrix equation according to the weak form of the Galileo test, wherein an impedance matrix ZmnAnd an excitation matrix VmRespectively as follows:
Vm＝<fm,αE+(1-α)n×H>
of formula (II) to'mAnd f'nThe mth and nth monopole RWG basis functions in the source region, respectively.
5. The method for analyzing electromagnetic scattering properties based on the GPU-based parallel acceleration feature basis function algorithm according to claim 4, wherein α -0.2, β -0.5 λ, γ - α in step 2-3, wherein λ is the wavelength of the radar transmission signal.
6. The electromagnetic scattering property analysis method based on the GPU parallel acceleration feature basis function algorithm according to claim 1 or 4, wherein the step 3 of utilizing the GPU to perform parallel acceleration on the feature basis function algorithm specifically comprises the following steps: and (3) utilizing the GPU to perform parallel acceleration on the impedance matrix calculation in the characteristic basis function algorithm so as to simultaneously operate all the impedance matrices.
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Application publication date: 20200421 |