基于二维弹性波方程的高阶NAD-SPRK算法

A High-Order NAD-SPRK Algorithm Based on the Two Dimensions Elastic Wave Equation

基于哈密尔顿系统的二维弹性波方程,结合离散空间高阶偏导数的NAD算子和离散时间导数的辛分部Runge-Kutta算法,获得八阶NAD-SPRK算法。针对该方法,从理论和数值计算两方面研究了其稳定性条件、数值频散和计算效率。数值结果表明:同四阶NSPRK算法、八阶Lax-Wendroff算法和八阶交错网格算法相比,八阶NAD-SPRK算法压制数值频散的能力显著优于传统数值计算方法,且具有最小的数值误差和最高的计算效率。

Based on the two dimensions elastic wave equation with the Hamiltonian system,an eighth-order NAD-SPRK algorithm is obtained by combining the NAD operator for higher order partial derivatives of discrete space and the symplectic partitioned Runge-Kutta algorithm of discrete time derivative.The stability conditions,numerical dispersion and computational efficiency of the algorithm are studied theoretically and numerically.The results show that compared with the fourth-order NSPRK algorithm,the eighth-order Lax-Wendroff algorithm and the eighth-order staggered grid algorithm,the eighth-order NAD-SPRK algorithm is significantly superior to the traditional numerical algorithm in suppressing the numerical dispersion,and has the minimum numerical error and the highest computational efficiency.