文中将坐标伸缩完全匹配层CPML引入到弱无条件稳定算法HIE-FDTD中研究其吸波性能。详细推导了2维TE波模型中CPML在HIE-FDTD算法中应用的差分公式。为检验本文所提方法的吸波效能,建立了计算模型,将其与其它吸收边界条件的吸波性能进行...文中将坐标伸缩完全匹配层CPML引入到弱无条件稳定算法HIE-FDTD中研究其吸波性能。详细推导了2维TE波模型中CPML在HIE-FDTD算法中应用的差分公式。为检验本文所提方法的吸波效能,建立了计算模型,将其与其它吸收边界条件的吸波性能进行了综合比较,计算了HIE-FDTD算法选取不同条件数时的反射误差,并详细说明如何合理选取α,κmax和σmax来实现最佳相对误差。结果显示:当将本文所提方法的CPML层数设置为8时,其反射误差为-62 d B,低于传统FDTD方法的-58 d B;当选取α=0.05,κmax=10,σmax/σopt=1.3可以实现低至-83 d B的最大相对误差;在仿真中,其比传统FDTD方法也约减少48%的计算时间。展开更多
文中将CPML引入3维弱无条件稳定算法HIE-FDTD中,详细推到了CPML在3维弱无条件稳定HIE-FDTD中的差分公式。为了验证CPML在3维HIE-FDTD中的吸波性能,建立了数值计算模型,并将CPML的吸波性能同其它几种常用的吸收边界条件进行了比较。结果...文中将CPML引入3维弱无条件稳定算法HIE-FDTD中,详细推到了CPML在3维弱无条件稳定HIE-FDTD中的差分公式。为了验证CPML在3维HIE-FDTD中的吸波性能,建立了数值计算模型,并将CPML的吸波性能同其它几种常用的吸收边界条件进行了比较。结果显示,当将CPML层数设置为8时,其最大反射误差为-72 d B,远低于传统FDTD方法的反射误差。另外,当匹配层参数设置为α=0.05,可以在一个较大范围内选取κmax和σmax来实现最佳误差,从而使得在选值时易于预测反射情况。展开更多
A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate th...A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix’s method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.展开更多
文摘文中将坐标伸缩完全匹配层CPML引入到弱无条件稳定算法HIE-FDTD中研究其吸波性能。详细推导了2维TE波模型中CPML在HIE-FDTD算法中应用的差分公式。为检验本文所提方法的吸波效能,建立了计算模型,将其与其它吸收边界条件的吸波性能进行了综合比较,计算了HIE-FDTD算法选取不同条件数时的反射误差,并详细说明如何合理选取α,κmax和σmax来实现最佳相对误差。结果显示:当将本文所提方法的CPML层数设置为8时,其反射误差为-62 d B,低于传统FDTD方法的-58 d B;当选取α=0.05,κmax=10,σmax/σopt=1.3可以实现低至-83 d B的最大相对误差;在仿真中,其比传统FDTD方法也约减少48%的计算时间。
文摘文中将CPML引入3维弱无条件稳定算法HIE-FDTD中,详细推到了CPML在3维弱无条件稳定HIE-FDTD中的差分公式。为了验证CPML在3维HIE-FDTD中的吸波性能,建立了数值计算模型,并将CPML的吸波性能同其它几种常用的吸收边界条件进行了比较。结果显示,当将CPML层数设置为8时,其最大反射误差为-72 d B,远低于传统FDTD方法的反射误差。另外,当匹配层参数设置为α=0.05,可以在一个较大范围内选取κmax和σmax来实现最佳误差,从而使得在选值时易于预测反射情况。
文摘A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix’s method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.
