时域积分方程及其并行算法的研究与应用
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摘要
晚时不稳定、计算量大等问题,是制约时域积分方程算法发展的重要原因。本文以解决其晚时不稳定问题、拓展算法的应用领域使其能分析较大规模电磁场散射、辐射问题为目的,对时域积分方程及其并行算法的理论和应用中的关键问题进行了研究。
本文可分为三部分。第一部分研究了显式时间递推算法结合基于RWG三角基函数的矩量法的时域求解技术;第二部分研究了金属、介质以及会属介质混合目标的时域求解技术,并研究了其晚时不稳定问题;第三部分研究了时域积分方程算法的并行求解技术。
在第一部分中,首先从电磁场的基本理论出发,基于等效原理和边界条件,以统一的方法建立了用于分析金属、介质及金属与介质混合结构的时域积分方程;在此基础上,给出了使用基于RWG三角基函数的矩量法求解各种时域积分方程的一般过程;研究了基于时间递推技术时域积分方程求解的显式算法,通过对简单目标的仿真计算,验证了平滑滤波技术改善晚时不稳定问题的有效性。
在第二部分中,首先阐述了导致时域积分方程求解产生晚时不稳定问题的原因;然后以解决这一问题为目标,研究了当前通用的两种消除晚时不稳定现象的算法,并将其应用于对金属、介质以及金属、介质混合目标电磁特性的求解当中。结果表明,两种算法都可以解决晚时不稳定问题。
在第三部分中,以利用局域网内数台计算机协同参与解决较大规模电磁问题的数值计算为目标,研究了时域积分方程算法的并行计算技术,在实验室局域网络连接的三台PC机上实现了时域积分方程的并行算法;随后,将程序移植到我校高性能计算应用研究中心具有64节点的“银河”超级计算机集群系统和上海超级计算中心的曙光4000A超级计算机集群系统上,测试了算法的并行效率,计算了未知量达到60,000量级的目标的电磁特性。
The late-time-oscillations and need large quantity of computation are the important reasons which restrict the progress of the Time-Domain-Integral-Equation(IETD) arithmetic.In order to solve the late-time-oscillations problem and expand its application so that large scale computation problems about scattering and radiation in electromagnetic field can be analyzed using numerical methods,some key problems about theory and application of the arithmetic and its parallel implementation techniques were studied in this paper.
The content of this thesis can be divided into three parts.In the first part,we studied the solution techniques of the IETD named the Explicit Marching-On-in-Time (MOT) method,which is combined with the Method Of Moment(MOM) based on the RWG triangular basis function.In the second part,we studied the solution technique of scattering and radiation problems about metallic objects,dielectric objects and the composite metallic and dielectric objects,as well as the late-time-oscillations problem. In the third part,the parallel solution techniques of IETD were studied.
In the first part of this thesis,the time domain integral equations for metallic objects,dielectric objects and the composite metallic and dielectric objects are elaborated uniformly based on the surface equivalence principle and boundary conditions firstly.Then the solving procedures of various IETDs which based on the RWG triangular basis function were given.Lastly,the Explicit MOT technique was studied and a method to accelerate the iterative solution speed through adding a moving time window in the time steps was proposed.
In the second part of this thesis,the cause of the late-time-oscillations problem coming into being was elaborated firstly.Then,aimed at how to solving the late-time-oscillations problem,two arithmetics which are universally used in solving this problem named Implicit MOT method and Marching-On-in-Degree(MOD) method which using the Laguerre polynomial as the temporal basis function were studied,and these two arithmetics were applied into solving electromagnetic characters of the metallic objects,dielectric objects and the composite metallic and dielectric objects.The results show that both the two arithmetics can eliminate the late-time-oscillations problem preferably.
In the third part of this thesis,in order to solving cosmically numerical calculation by using the PCs in LAN,parallel computation technique was studied,program based on the Message-Passing-Interface(MPI) model and C++ language was established, through the analysis of the results and efficiency of parallel technique,the program were optimized and calculation efficiency were improved.And then,transplant the program onto the Super Computer Cluster of "YinHe" High Performance Compute Center, testing the efficiency of the parallel technique under 64 nodes' Linux system.Lastly,we transplant the program onto Cluster of Drwan 4000A of Shanghai Super Computer Center(SSC),and calculated the electromagnetic character of the objects with unknowns more than 60,000.
本文可分为三部分。第一部分研究了显式时间递推算法结合基于RWG三角基函数的矩量法的时域求解技术;第二部分研究了金属、介质以及会属介质混合目标的时域求解技术,并研究了其晚时不稳定问题;第三部分研究了时域积分方程算法的并行求解技术。
在第一部分中,首先从电磁场的基本理论出发,基于等效原理和边界条件,以统一的方法建立了用于分析金属、介质及金属与介质混合结构的时域积分方程;在此基础上,给出了使用基于RWG三角基函数的矩量法求解各种时域积分方程的一般过程;研究了基于时间递推技术时域积分方程求解的显式算法,通过对简单目标的仿真计算,验证了平滑滤波技术改善晚时不稳定问题的有效性。
在第二部分中,首先阐述了导致时域积分方程求解产生晚时不稳定问题的原因;然后以解决这一问题为目标,研究了当前通用的两种消除晚时不稳定现象的算法,并将其应用于对金属、介质以及金属、介质混合目标电磁特性的求解当中。结果表明,两种算法都可以解决晚时不稳定问题。
在第三部分中,以利用局域网内数台计算机协同参与解决较大规模电磁问题的数值计算为目标,研究了时域积分方程算法的并行计算技术,在实验室局域网络连接的三台PC机上实现了时域积分方程的并行算法;随后,将程序移植到我校高性能计算应用研究中心具有64节点的“银河”超级计算机集群系统和上海超级计算中心的曙光4000A超级计算机集群系统上,测试了算法的并行效率,计算了未知量达到60,000量级的目标的电磁特性。
The late-time-oscillations and need large quantity of computation are the important reasons which restrict the progress of the Time-Domain-Integral-Equation(IETD) arithmetic.In order to solve the late-time-oscillations problem and expand its application so that large scale computation problems about scattering and radiation in electromagnetic field can be analyzed using numerical methods,some key problems about theory and application of the arithmetic and its parallel implementation techniques were studied in this paper.
The content of this thesis can be divided into three parts.In the first part,we studied the solution techniques of the IETD named the Explicit Marching-On-in-Time (MOT) method,which is combined with the Method Of Moment(MOM) based on the RWG triangular basis function.In the second part,we studied the solution technique of scattering and radiation problems about metallic objects,dielectric objects and the composite metallic and dielectric objects,as well as the late-time-oscillations problem. In the third part,the parallel solution techniques of IETD were studied.
In the first part of this thesis,the time domain integral equations for metallic objects,dielectric objects and the composite metallic and dielectric objects are elaborated uniformly based on the surface equivalence principle and boundary conditions firstly.Then the solving procedures of various IETDs which based on the RWG triangular basis function were given.Lastly,the Explicit MOT technique was studied and a method to accelerate the iterative solution speed through adding a moving time window in the time steps was proposed.
In the second part of this thesis,the cause of the late-time-oscillations problem coming into being was elaborated firstly.Then,aimed at how to solving the late-time-oscillations problem,two arithmetics which are universally used in solving this problem named Implicit MOT method and Marching-On-in-Degree(MOD) method which using the Laguerre polynomial as the temporal basis function were studied,and these two arithmetics were applied into solving electromagnetic characters of the metallic objects,dielectric objects and the composite metallic and dielectric objects.The results show that both the two arithmetics can eliminate the late-time-oscillations problem preferably.
In the third part of this thesis,in order to solving cosmically numerical calculation by using the PCs in LAN,parallel computation technique was studied,program based on the Message-Passing-Interface(MPI) model and C++ language was established, through the analysis of the results and efficiency of parallel technique,the program were optimized and calculation efficiency were improved.And then,transplant the program onto the Super Computer Cluster of "YinHe" High Performance Compute Center, testing the efficiency of the parallel technique under 64 nodes' Linux system.Lastly,we transplant the program onto Cluster of Drwan 4000A of Shanghai Super Computer Center(SSC),and calculated the electromagnetic character of the objects with unknowns more than 60,000.
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