We extend LeVeque's wave propagation algorithm,a widely used finite volume method for hyperbolic partial differential equations,to a third-order accurate method.The resulting scheme shares main properties with the...We extend LeVeque's wave propagation algorithm,a widely used finite volume method for hyperbolic partial differential equations,to a third-order accurate method.The resulting scheme shares main properties with the original method,i.e.,it is based on a wave decomposition at grid cell interfaces,it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of a wave limiter.展开更多
Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the meth...Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
入射余角是利用抛物方程模型研究地形条件下电波传播问题的重要参数,但该参数估计具有单次快拍、信号相干和实时性要求高的特点,传统的估计算法难以同时满足上述要求.针对上述问题,提出了基于单次快拍的空间平滑旋转不变性的信号参数估...入射余角是利用抛物方程模型研究地形条件下电波传播问题的重要参数,但该参数估计具有单次快拍、信号相干和实时性要求高的特点,传统的估计算法难以同时满足上述要求.针对上述问题,提出了基于单次快拍的空间平滑旋转不变性的信号参数估计(Estimating Signal Parameters via Rotational Invariance Techniques,ESPRIT)算法.直接采用单次数据的前后向空间平滑子阵构造centro-Hermitian伪协方差矩阵以实现信号解相干,应用酉变换将复数域的奇异值分解转换为实数域求解,利用ESPRIT算法代替多重信号分类算法估计入射余角.仿真结果表明:该算法能够实现电波传播入射余角的快速估计,准确反映地形起伏对入射余角的影响,与现有算法相比提高了实时性和估计精度.展开更多
基金This work was supported by the DFG through HE 4858/4-1
文摘We extend LeVeque's wave propagation algorithm,a widely used finite volume method for hyperbolic partial differential equations,to a third-order accurate method.The resulting scheme shares main properties with the original method,i.e.,it is based on a wave decomposition at grid cell interfaces,it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of a wave limiter.
文摘Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.
文摘入射余角是利用抛物方程模型研究地形条件下电波传播问题的重要参数,但该参数估计具有单次快拍、信号相干和实时性要求高的特点,传统的估计算法难以同时满足上述要求.针对上述问题,提出了基于单次快拍的空间平滑旋转不变性的信号参数估计(Estimating Signal Parameters via Rotational Invariance Techniques,ESPRIT)算法.直接采用单次数据的前后向空间平滑子阵构造centro-Hermitian伪协方差矩阵以实现信号解相干,应用酉变换将复数域的奇异值分解转换为实数域求解,利用ESPRIT算法代替多重信号分类算法估计入射余角.仿真结果表明:该算法能够实现电波传播入射余角的快速估计,准确反映地形起伏对入射余角的影响,与现有算法相比提高了实时性和估计精度.
