A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such m...A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.展开更多
In this paper, a class of real-time parallel combined methods (RTPCM) of the digital simulation for a partitioned large system is presented. By means of combination of the parallelism across the system with the parall...In this paper, a class of real-time parallel combined methods (RTPCM) of the digital simulation for a partitioned large system is presented. By means of combination of the parallelism across the system with the parallelism across the method, stiff and non-stiff subsystems are solved in parallel on parallel computer by a parallel Rosenbrock method and a parallel RK method, respectively. Their construction, convergence and numerical stability are discussed, and the digitalsimulation experiments are conducted.展开更多
In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear...In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear multistep method, which overcomes the defect of the 3rd order parallel Runge-Kutta method discussed in [1].展开更多
Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusse...Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.展开更多
A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and rela...A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosen-brock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.展开更多
针对随机激励下振动系统的减振问题,提出了考虑摩擦与非线性阻尼的混联Ⅱ型惯容非线性能量阱(nonlinear energy sink,简称NES),建立了含新型NES主系统的动力学控制方程。首先,采用蒙特卡洛数值方法,研究了非线性刚度对减振性能的影响,...针对随机激励下振动系统的减振问题,提出了考虑摩擦与非线性阻尼的混联Ⅱ型惯容非线性能量阱(nonlinear energy sink,简称NES),建立了含新型NES主系统的动力学控制方程。首先,采用蒙特卡洛数值方法,研究了非线性刚度对减振性能的影响,当非线性刚度比κ_(21)逐渐增大时,主结构和混联Ⅱ型惯容NES的位移概率密度函数出现了双峰变为单峰,以及速度概率密度函数由单峰变为双峰的随机跳跃现象。主结构的位移概率密度函数对非线性刚度κ_(22)的敏感性比κ_(21)更高,κ_(22)最佳取值区间为200~1 000。其次,研究了噪声强度、阻尼比和惯质比对减振性能的影响,当噪声强度小于0.1或惯质比μ在0.1左右时,惯容NES的减振效果较好。虽然线性阻尼比λ_(1)和非线性阻尼比λ_(21)、λ_(22)增大会导致主结构和混联Ⅱ型惯容NES的概率密度函数出现分岔不稳定现象,但增大非线性阻尼比有助于改善惯容NES的减振性能。最后,采用差分进化法对惯容NES的参数进行了优化。本研究可为受随机激励的振动系统减振研究提供技术参考。展开更多
文摘A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.
文摘In this paper, a class of real-time parallel combined methods (RTPCM) of the digital simulation for a partitioned large system is presented. By means of combination of the parallelism across the system with the parallelism across the method, stiff and non-stiff subsystems are solved in parallel on parallel computer by a parallel Rosenbrock method and a parallel RK method, respectively. Their construction, convergence and numerical stability are discussed, and the digitalsimulation experiments are conducted.
文摘In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear multistep method, which overcomes the defect of the 3rd order parallel Runge-Kutta method discussed in [1].
文摘Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.
基金This project was supported by the National Natural Science Foundation of China (19871080).
文摘A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosen-brock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.
文摘针对随机激励下振动系统的减振问题,提出了考虑摩擦与非线性阻尼的混联Ⅱ型惯容非线性能量阱(nonlinear energy sink,简称NES),建立了含新型NES主系统的动力学控制方程。首先,采用蒙特卡洛数值方法,研究了非线性刚度对减振性能的影响,当非线性刚度比κ_(21)逐渐增大时,主结构和混联Ⅱ型惯容NES的位移概率密度函数出现了双峰变为单峰,以及速度概率密度函数由单峰变为双峰的随机跳跃现象。主结构的位移概率密度函数对非线性刚度κ_(22)的敏感性比κ_(21)更高,κ_(22)最佳取值区间为200~1 000。其次,研究了噪声强度、阻尼比和惯质比对减振性能的影响,当噪声强度小于0.1或惯质比μ在0.1左右时,惯容NES的减振效果较好。虽然线性阻尼比λ_(1)和非线性阻尼比λ_(21)、λ_(22)增大会导致主结构和混联Ⅱ型惯容NES的概率密度函数出现分岔不稳定现象,但增大非线性阻尼比有助于改善惯容NES的减振性能。最后,采用差分进化法对惯容NES的参数进行了优化。本研究可为受随机激励的振动系统减振研究提供技术参考。
