Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisatio...Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.展开更多
By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully charac...By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-? and Newmark-? methods. Therefore, this new algorithm is a highly efficient one with better computational performance.展开更多
用时域有限元差分的子域合成法(Synthetic subdomain method of FDTD)对大规模的光波导模拟,把仿真的光波导划分成两个或多个区域,在不影响仿真精度的条件下,删除对仿真对象影响不大的区域,并相应改变吸收边界条件进行时域有限元差分法...用时域有限元差分的子域合成法(Synthetic subdomain method of FDTD)对大规模的光波导模拟,把仿真的光波导划分成两个或多个区域,在不影响仿真精度的条件下,删除对仿真对象影响不大的区域,并相应改变吸收边界条件进行时域有限元差分法数值模拟,考查光的传播和损耗状况,并与常规方法的运算结果相比较,结果一致且不影响计算精度。与常规方法相比,两段子域合成法所占内存约为前者的55%,时间约为前者的60%,三段子域合成法所占内存约为前者的31%,时间约为前者的28%,可见子域合成法比常规方法更有利于应用于大规模集成光波导的数值模拟仿真,对节省硬件及时间资源具有实际意义,提高工作效率。展开更多
文摘Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.
基金the National Natural Seienee Foundation of China(Grant Nos10172097,19902022,19672074)
文摘By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-? and Newmark-? methods. Therefore, this new algorithm is a highly efficient one with better computational performance.
文摘用时域有限元差分的子域合成法(Synthetic subdomain method of FDTD)对大规模的光波导模拟,把仿真的光波导划分成两个或多个区域,在不影响仿真精度的条件下,删除对仿真对象影响不大的区域,并相应改变吸收边界条件进行时域有限元差分法数值模拟,考查光的传播和损耗状况,并与常规方法的运算结果相比较,结果一致且不影响计算精度。与常规方法相比,两段子域合成法所占内存约为前者的55%,时间约为前者的60%,三段子域合成法所占内存约为前者的31%,时间约为前者的28%,可见子域合成法比常规方法更有利于应用于大规模集成光波导的数值模拟仿真,对节省硬件及时间资源具有实际意义,提高工作效率。
