时域有限元的二维导体微波成像及其图形处理器（GPU）加速的探索
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摘要
本文以标量和矢量时域有限元(TDFEM)分别作为电磁散射正问题的求解基础,以全局优化算法——遗传算法和实数微分进化策略来处理电磁逆散射问题(即微波成像问题),在充分应用从时域获得的超宽带信息的基础上实现标量、矢量时域有限元与遗传算法和实数微分进化策略的有机结合,完成对理想导电体(PEC)二维目标几何形状的重构。此外,本文还对使用图形处理器(GPU)对时域有限元运算加速进行了探讨。
论文首先讨论散射体的描述方法。重点论述文中提出的离散点描述法,并对其优势予以阐述,并最终应用到课题中去。然后,我们将时域MEI(不变量测试方程)方法引入到时域有限元,并以实例说明时域MEI方法应用到时域有限元中是可行的,同时讨论在成像中使用时会产生的问题。
接下来重点阐述以标量、矢量时域有限元方法(TDFEM)作为电磁散射正问题的求解基础,获得目标散射场的近场和远场信息。并通过对散射信息的频域分析得到目标的大致尺寸,进而为下一步优化提供必要的约束条件,以确定优化算法的搜索范围,使之能够更高效的寻找到全局最优解。在做具体优化之前,将首先对当今较为流行的几种优化算法进行介绍和比较分析,在此基础上,选择优化算法中寻优效果较为稳定的遗传算法以及寻优效率较高的实数微分进化策略作为逆过程的求解方法,并将它们分别和标量、矢量时域有限元结合来进行成像。接下来,通过我们对近场、远场解空间的特性分析,可以看到近场和远场解空间有着很大的差别,远场解空间的情况要远比近场解空间复杂,而这样的情况就必然导致了远场成像过程的复杂性,也必然导致优化算法需要更长的时间来寻找最优解。由文中算例可以看到,我们能够得到较为令人满意的成像效果,只要给逆过程以足够的寻优时间。但是成像过程所耗费的时间过多,这也是不容回避的问题。
再者,由于时域有限元繁重的运算量,论文对时域有限元运算的GPU加速进行了一个前瞻性的探索。由于GPU具有一定的并行性、高密集的运算能力、高计算精度,通过对GPU这些优良性能的充分利用,使TD-FEM的运算速度得到数倍的提升。
最后,将对于本课题做一个全面的总结和展望。归纳出本课题的发展前景以及今后需要进一步解决的问题。
In this project,the forward scattering problem is treated via.scalar Time-Domain Finite Element Method(TDFEM) and vector Time-Domain Finite Element Method,while inversion microwave imaging is implemented by global optimization algorithm,genetic algorithm and real differential evolution strategy. And completed reconstruction of the shape information of unknown scatterer is presented by the perfect union of scalar TDFEM,vector TDFEM and genetic algorithm(GA),real differential evolution strategy based on obtaining the ultra-band information through time-domain.Furthermore,we investigate Graphics Processor Unit(GPU) acceleration of TDFEM algorithm.And significant reduction of the computation time of TDFEM is obtained by GPU.
Firstly,we introduce methods that characterize the shape of scatterer.Our focus is on discrete points method put forward by author and its merits.And then the method is used in this project.After this,we introduce time domain measured equation of invariance(MEI) into TDFEM,and bear out the analysis result by some examples. Finally,discuss some questions as we achieve microwave imaging through it.
Secondly,focal point is obtaining the scattering information of near-field and far-field by scalar TDFEM and vector TDFEM.We can get the restrictions of optimization algorithm by extrapolating the approximate size of scatterer from the far-field scattering information,and upon that we can obtain the definite search coverage and find the globe optimum solution faster.We should first simply introduce and analysis the popular optimization algorithm in present-day.And then, GA and real differential evolution strategy are choosed to combine with scalar TDFEM and vector TDFEM respectively achieve imaging.And we will analysis the near-field and far-field next.There has big difference between them.As a result,the circumstances of far-firld solution space are more complicated than near-field solution space.For this reason,the far-field imaging is more difficult,and need more time to find optimum solution.In this paper,we will find the shape reconstructed agrees well with the shape of scatterer,so long as time is enough.But the question that can not skirt round is too much time is spent on imaging process.
In addition,since the complicated computing of the time-domain finite element, GPU accelerated method is applied in the time-domain finite element calculation for prospective study.As the parallelism property of GPU,high-intensive computing capability and high accuracy,through full utilizing the excellent performance of GPU,the TD-FEM computational speed can multiplied.
At last,we sum up and look forward to vistas of the project.And put forward the question should be solved in the future.
论文首先讨论散射体的描述方法。重点论述文中提出的离散点描述法,并对其优势予以阐述,并最终应用到课题中去。然后,我们将时域MEI(不变量测试方程)方法引入到时域有限元,并以实例说明时域MEI方法应用到时域有限元中是可行的,同时讨论在成像中使用时会产生的问题。
接下来重点阐述以标量、矢量时域有限元方法(TDFEM)作为电磁散射正问题的求解基础,获得目标散射场的近场和远场信息。并通过对散射信息的频域分析得到目标的大致尺寸,进而为下一步优化提供必要的约束条件,以确定优化算法的搜索范围,使之能够更高效的寻找到全局最优解。在做具体优化之前,将首先对当今较为流行的几种优化算法进行介绍和比较分析,在此基础上,选择优化算法中寻优效果较为稳定的遗传算法以及寻优效率较高的实数微分进化策略作为逆过程的求解方法,并将它们分别和标量、矢量时域有限元结合来进行成像。接下来,通过我们对近场、远场解空间的特性分析,可以看到近场和远场解空间有着很大的差别,远场解空间的情况要远比近场解空间复杂,而这样的情况就必然导致了远场成像过程的复杂性,也必然导致优化算法需要更长的时间来寻找最优解。由文中算例可以看到,我们能够得到较为令人满意的成像效果,只要给逆过程以足够的寻优时间。但是成像过程所耗费的时间过多,这也是不容回避的问题。
再者,由于时域有限元繁重的运算量,论文对时域有限元运算的GPU加速进行了一个前瞻性的探索。由于GPU具有一定的并行性、高密集的运算能力、高计算精度,通过对GPU这些优良性能的充分利用,使TD-FEM的运算速度得到数倍的提升。
最后,将对于本课题做一个全面的总结和展望。归纳出本课题的发展前景以及今后需要进一步解决的问题。
In this project,the forward scattering problem is treated via.scalar Time-Domain Finite Element Method(TDFEM) and vector Time-Domain Finite Element Method,while inversion microwave imaging is implemented by global optimization algorithm,genetic algorithm and real differential evolution strategy. And completed reconstruction of the shape information of unknown scatterer is presented by the perfect union of scalar TDFEM,vector TDFEM and genetic algorithm(GA),real differential evolution strategy based on obtaining the ultra-band information through time-domain.Furthermore,we investigate Graphics Processor Unit(GPU) acceleration of TDFEM algorithm.And significant reduction of the computation time of TDFEM is obtained by GPU.
Firstly,we introduce methods that characterize the shape of scatterer.Our focus is on discrete points method put forward by author and its merits.And then the method is used in this project.After this,we introduce time domain measured equation of invariance(MEI) into TDFEM,and bear out the analysis result by some examples. Finally,discuss some questions as we achieve microwave imaging through it.
Secondly,focal point is obtaining the scattering information of near-field and far-field by scalar TDFEM and vector TDFEM.We can get the restrictions of optimization algorithm by extrapolating the approximate size of scatterer from the far-field scattering information,and upon that we can obtain the definite search coverage and find the globe optimum solution faster.We should first simply introduce and analysis the popular optimization algorithm in present-day.And then, GA and real differential evolution strategy are choosed to combine with scalar TDFEM and vector TDFEM respectively achieve imaging.And we will analysis the near-field and far-field next.There has big difference between them.As a result,the circumstances of far-firld solution space are more complicated than near-field solution space.For this reason,the far-field imaging is more difficult,and need more time to find optimum solution.In this paper,we will find the shape reconstructed agrees well with the shape of scatterer,so long as time is enough.But the question that can not skirt round is too much time is spent on imaging process.
In addition,since the complicated computing of the time-domain finite element, GPU accelerated method is applied in the time-domain finite element calculation for prospective study.As the parallelism property of GPU,high-intensive computing capability and high accuracy,through full utilizing the excellent performance of GPU,the TD-FEM computational speed can multiplied.
At last,we sum up and look forward to vistas of the project.And put forward the question should be solved in the future.
引文
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