| 三维Helmholtz方程的高阶紧致差分方法 |
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| 引用本文： | 马廷福,葛永斌.三维Helmholtz方程的高阶紧致差分方法[J].河南科技大学学报(自然科学版),2012(1):84-87,9. |
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| 作者姓名： | 马廷福 葛永斌 |
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| 作者单位： | 中国矿业大学银川学院;宁夏大学应用数学与力学研究所 |
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| 基金项目： | 国家自然科学基金项目(10502026) |
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| 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。
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| 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 |
High-Order Compact Difference Method for Three Dimensional Helmholtz Equation |
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| MA Ting-Fu,GE Yong-Bin.High-Order Compact Difference Method for Three Dimensional Helmholtz Equation[J].Journal of Henan University of Science & Technology:Natural Science,2012(1):84-87,9. |
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| Authors: | MA Ting-Fu GE Yong-Bin |
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| Institution: | 1.Yinchuan College,China University of Mining & Technology,Yinchuan 750011,China;2.Institute of Applied Mathematics & Mechanics,Ningxia University,Yinchuan 750021,China) |
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| Abstract: | 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. |
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| Keywords: | 3D Helmholtz equation High-order compact scheme Finite difference method Multigrid method |
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