三维Helmholtz方程的高阶紧致差分方法  

High-Order Compact Difference Method for Three Dimensional Helmholtz Equation

作　　者：马廷福[1] 葛永斌[2] 

机构地区：[1]中国矿业大学银川学院,宁夏银川750011 [2]宁夏大学应用数学与力学研究所,宁夏银川750021

出　　处：《河南科技大学学报（自然科学版）》2012年第1期84-87,9,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10502026)

摘　　要：提出了三维Helmholtz方程等距网格上的一种四阶精度19点紧致差分格式。结合多重网格V循环算法和红黑高斯-塞德尔迭代法进行求解,并与二阶中心差分格式进行了比较。计算结果验证了本文方法的精确性和有效性。A fourth-order compact 19-point finite difference formula for solving the three dimensional Helmholtz equation was developed on uniform meshes.This scheme was compared with the second-order center difference scheme to show the dramatic improvement in both computed accuracy and convergence by multigrid V-cycle algorithm and Red-Black Gauss-Seidel iterative method.Numerical experiments prove the accuracy and efficiency of the method.

关 键 词：三维Helmholtz方程 高阶紧致格式 有限差分法 多重网格方法 

分 类 号：O241.82[理学—计算数学]