二维波动方程的高精度隐格式及其多重网格算法  

Multigrid Solutions Based on High-order Implicit Schemes of Two Dimensional Wave Equation

作　　者：葛永斌[1] 吴文权[1] 田振夫[2] 

机构地区：[1]上海理工大学动力工程学院,上海200093 [2]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《厦门大学学报（自然科学版）》2003年第6期691-696,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(59876023)资助

摘　　要：提出了数值求解二维波动方程的两种高精度三层紧致隐格式,利用Fourier分析方法证明了格式均是无条件稳定的.并在此基础上提出了求解该问题的多重网格算法,从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷,大大加快了迭代收敛速度,提高了求解效率.数值实验结果验证了方法的精确性和可靠性.Two classes of highorder threelevel implicit compact difference schemes for the twodimensional wave equation are proposed and proved to be unconditional stable by Fourier analysis. Multigrid accelerating techniques are employed to overcome the difficulties when traditional relaxation methods are used to resolve the implicit difference schemes, and fast solutions are obtained. Numerical results prove their efficiency and dependability.

关 键 词：二维波动方程 高精度紧致隐格式 多重网格法 数值解 

分 类 号：O241.82[理学—计算数学]