基于图形硬件的快速电磁计算方法与系统
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摘要
目标电磁散射特性分析,特别是雷达散射截面估算,是计算电磁学的重要研究内容之一。电磁散射特性分析可应用于天线的辐射和散射分析等民用领域,还广泛应用于目标的隐身和反隐身设计等国防领域,具有重要的理论研究意义和实用价值。
本文主要研究频域数值计算方法,可分为高频近似方法和低频数值方法。当前广泛应用的高频近似方法为图形电磁计算方法和弹跳射线法。然而,图形电磁计算方法存在计算未能达到实时和可见棱边判断不够准确等问题,弹跳射线法存在射线追踪耗时和射线管分裂等问题,这些问题削弱了高频近似方法在快速估算上的优势。矩量法是最为常用的低频数值方法之一,离散麦克斯韦积分方程为复系数稠密阻抗矩阵求解,但由于受到计算机存储量和运算速度的限制,矩量法局限于求解电小尺寸目标的散射问题。
针对上述问题,本文分析比较了频域数值计算方法和图形学绘制算法的相似性,借鉴图形学绘制算法的思想,并把图形硬件作为计算平台,对上述方法进行了相应的改进。对于图形电磁计算方法,本文提出了在图形硬件上统一处理目标可见性判断和电磁散射计算框架,能够正确地判断可见棱边,并且真正实现了实时一阶高频电磁散射计算。
本文提出的基于统一计算设备架构(CUDA)的弹跳射线法,采用无堆栈的kd树遍历算法,用来加速射线追踪过程,同时也在CUDA上实现了并行射线管积分,显著提高了弹跳射线法的计算效率。
本文还提出了基于光束跟踪的弹跳射线法,该方法变换了射线管划分和射线管追踪的顺序,在射线管追踪过程中,根据目标几何结构动态划分射线管,从而避免了射线管分裂问题,提高了弹跳射线法的计算精度。光束跟踪也可以用于目标可见棱边的正确判断,并利用截断—增量长度绕射系数计算棱边绕射场,弹跳射线法和截断—增量长度绕射系数相结合可解决大部分高频电磁散射计算问题。对目标表面的涂覆材料,本文给出了分层结构表面涂层的等效反射系数计算公式,扩展了高频近似方法的应用范围。
对于低频数值方法,本文研究了基于CUDA的矩量法,利用图形硬件强大的数值计算能力,提高矩量法的计算效率,通过阻抗矩阵分块和out-of-core等内存管理技术,扩大矩量法在单机上的计算规模。
最后,本文介绍了集成上述频域数值计算方法的电磁散射估算系统emX的开发工作,该系统具有几何处理、电磁散射计算、目标成像、数据后处理及可视化等功能。
本文的研究工作有机地结合了频域数值计算方法、图形学绘制算法思想和图形硬件计算平台,为解决电大尺寸复杂目标的电磁散射特性分析问题提供了有效的途径,大量的算例结果也证实了计算机图形学与计算电磁学的结合提高了电磁散射计算的精度、效率和计算规模。
The analysis of the electromagnetic scattering characteristic of the target, especially the prediction of Radar Cross Section (RCS), is one of the important research areas in computational electromagnetics. It has wide application in many different fields, ranging from the scattering and radiation analysis of the antenna to the design of stealth and anti-stealth. Thus, it is vital important in theory and practice to study the electromagnetic scattering characteristic of the target.
This thesis focuses on the frequency-domain numerical methods, which can be classified into high-frequency asymptotic methods and low-frequency numerical methods. Graphical electromagnetic computing (GRECO) and shooting and bounce ray method (SBR) are two widely used high-frequency asymptotic methods in nowadays. However, GRECO still fails to predict RCS in real time and to identify all visible wedges exactly, and SBR has the problem of time-consuming ray tube tracing and the split ray tube. These problems significantly affect the computational efficiency of high-frequency asymptotic methods. The method of moments (MoM), which is one of the most popular low-frequency numerical methods, solves the scattering problem by discretizing Maxwell's integral equation into the dense impedance matrix. However, due to the limited memory and low computing power of the computer, only the RCS of electrically small targets can be predicted by MoM.
Aiming at the above-mentioned issues, we compare and analyze the similarity of the frequency-domain numerical methods and rendering algorithms in computer graphics, and try to improve the frequency-domain numerical methods by adopting the idea of real-time rendering algorithms and employing graphics hardware as the compute platform. In order to accelerate GRECO, we present a new architecture unifying the visibility computing and electromagnetic computing on GPUs. This architecture can detect visible wedges more exactly and predict the first-order scattered field in real-time.
The proposed CUDA-based SBR fully implements the ray tube tracing and electromagnetic computing in CUDA. The ray tube tracing is based on the stackless kd-tree traversal algorithm and this implementation greatly accelerates the RCS prediction. We also introduce the beam-tracing based SBR, which inverses the conventional order of the ray tube generation and the ray tube tracing. During the ray tube tracing, the ray tube is dynamically divided into several ray tubes according to the geometry of the target, which results in avoiding the problem of the split ray tube and improving the computational accuracy of the scattering field. Moreover, beam tracing is also able to identify visible wedges, and the diffracted field of these visible wedges can be evaluated using TW-ILDC. In fact, SBR and TW-ILDC together can obtain a high-fidelity RCS result for most high-frequency scattering problems. Besides the PEC targets, the equivalent reflection coefficients of a layered medium is also presented and it extends the application of SBR to the coated target.
For low-frequency numerical methods, we propose a CUDA-based MoM, which exploits the formidable of computing power on GPUs to enhance the computational efficiency. Additionally, memory management techniques, i.e., block-based impedance matrix and out-of-core, enlarge the electrical size of the target that can be solved on a single computer.
Finally, the electromagnetic modeling and simulation software emX is introduced. emX not only integrates the frequency-domain numerical methods above, but also offers various features, such as geometric processing, target imaging, visualization, etc.
The research of this thesis effectively integrates the frequency-domain numerical methods with rendering algorithms in computer graphics and graphics hardware, and provides a new direction to solve scattering problems of electrically large and complex targets. A large number of numerical results demonstrate that the combination of computational electromagnetics and computer graphics could improve the computational efficiency, accuracy, and scale of scattering problems.
本文主要研究频域数值计算方法,可分为高频近似方法和低频数值方法。当前广泛应用的高频近似方法为图形电磁计算方法和弹跳射线法。然而,图形电磁计算方法存在计算未能达到实时和可见棱边判断不够准确等问题,弹跳射线法存在射线追踪耗时和射线管分裂等问题,这些问题削弱了高频近似方法在快速估算上的优势。矩量法是最为常用的低频数值方法之一,离散麦克斯韦积分方程为复系数稠密阻抗矩阵求解,但由于受到计算机存储量和运算速度的限制,矩量法局限于求解电小尺寸目标的散射问题。
针对上述问题,本文分析比较了频域数值计算方法和图形学绘制算法的相似性,借鉴图形学绘制算法的思想,并把图形硬件作为计算平台,对上述方法进行了相应的改进。对于图形电磁计算方法,本文提出了在图形硬件上统一处理目标可见性判断和电磁散射计算框架,能够正确地判断可见棱边,并且真正实现了实时一阶高频电磁散射计算。
本文提出的基于统一计算设备架构(CUDA)的弹跳射线法,采用无堆栈的kd树遍历算法,用来加速射线追踪过程,同时也在CUDA上实现了并行射线管积分,显著提高了弹跳射线法的计算效率。
本文还提出了基于光束跟踪的弹跳射线法,该方法变换了射线管划分和射线管追踪的顺序,在射线管追踪过程中,根据目标几何结构动态划分射线管,从而避免了射线管分裂问题,提高了弹跳射线法的计算精度。光束跟踪也可以用于目标可见棱边的正确判断,并利用截断—增量长度绕射系数计算棱边绕射场,弹跳射线法和截断—增量长度绕射系数相结合可解决大部分高频电磁散射计算问题。对目标表面的涂覆材料,本文给出了分层结构表面涂层的等效反射系数计算公式,扩展了高频近似方法的应用范围。
对于低频数值方法,本文研究了基于CUDA的矩量法,利用图形硬件强大的数值计算能力,提高矩量法的计算效率,通过阻抗矩阵分块和out-of-core等内存管理技术,扩大矩量法在单机上的计算规模。
最后,本文介绍了集成上述频域数值计算方法的电磁散射估算系统emX的开发工作,该系统具有几何处理、电磁散射计算、目标成像、数据后处理及可视化等功能。
本文的研究工作有机地结合了频域数值计算方法、图形学绘制算法思想和图形硬件计算平台,为解决电大尺寸复杂目标的电磁散射特性分析问题提供了有效的途径,大量的算例结果也证实了计算机图形学与计算电磁学的结合提高了电磁散射计算的精度、效率和计算规模。
The analysis of the electromagnetic scattering characteristic of the target, especially the prediction of Radar Cross Section (RCS), is one of the important research areas in computational electromagnetics. It has wide application in many different fields, ranging from the scattering and radiation analysis of the antenna to the design of stealth and anti-stealth. Thus, it is vital important in theory and practice to study the electromagnetic scattering characteristic of the target.
This thesis focuses on the frequency-domain numerical methods, which can be classified into high-frequency asymptotic methods and low-frequency numerical methods. Graphical electromagnetic computing (GRECO) and shooting and bounce ray method (SBR) are two widely used high-frequency asymptotic methods in nowadays. However, GRECO still fails to predict RCS in real time and to identify all visible wedges exactly, and SBR has the problem of time-consuming ray tube tracing and the split ray tube. These problems significantly affect the computational efficiency of high-frequency asymptotic methods. The method of moments (MoM), which is one of the most popular low-frequency numerical methods, solves the scattering problem by discretizing Maxwell's integral equation into the dense impedance matrix. However, due to the limited memory and low computing power of the computer, only the RCS of electrically small targets can be predicted by MoM.
Aiming at the above-mentioned issues, we compare and analyze the similarity of the frequency-domain numerical methods and rendering algorithms in computer graphics, and try to improve the frequency-domain numerical methods by adopting the idea of real-time rendering algorithms and employing graphics hardware as the compute platform. In order to accelerate GRECO, we present a new architecture unifying the visibility computing and electromagnetic computing on GPUs. This architecture can detect visible wedges more exactly and predict the first-order scattered field in real-time.
The proposed CUDA-based SBR fully implements the ray tube tracing and electromagnetic computing in CUDA. The ray tube tracing is based on the stackless kd-tree traversal algorithm and this implementation greatly accelerates the RCS prediction. We also introduce the beam-tracing based SBR, which inverses the conventional order of the ray tube generation and the ray tube tracing. During the ray tube tracing, the ray tube is dynamically divided into several ray tubes according to the geometry of the target, which results in avoiding the problem of the split ray tube and improving the computational accuracy of the scattering field. Moreover, beam tracing is also able to identify visible wedges, and the diffracted field of these visible wedges can be evaluated using TW-ILDC. In fact, SBR and TW-ILDC together can obtain a high-fidelity RCS result for most high-frequency scattering problems. Besides the PEC targets, the equivalent reflection coefficients of a layered medium is also presented and it extends the application of SBR to the coated target.
For low-frequency numerical methods, we propose a CUDA-based MoM, which exploits the formidable of computing power on GPUs to enhance the computational efficiency. Additionally, memory management techniques, i.e., block-based impedance matrix and out-of-core, enlarge the electrical size of the target that can be solved on a single computer.
Finally, the electromagnetic modeling and simulation software emX is introduced. emX not only integrates the frequency-domain numerical methods above, but also offers various features, such as geometric processing, target imaging, visualization, etc.
The research of this thesis effectively integrates the frequency-domain numerical methods with rendering algorithms in computer graphics and graphics hardware, and provides a new direction to solve scattering problems of electrically large and complex targets. A large number of numerical results demonstrate that the combination of computational electromagnetics and computer graphics could improve the computational efficiency, accuracy, and scale of scattering problems.
引文
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