| 求解Helmholtz方程的新型稀疏近似逆预条件算法 |
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| 引用本文： | 李月卉,詹红霞.求解Helmholtz方程的新型稀疏近似逆预条件算法[J].半导体光电,2012,33(5):663-666. |
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| 作者姓名： | 李月卉 詹红霞 |
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| 作者单位： | 西华大学数学与计算机学院,成都,610039;西华大学电气信息学院,成都,610039 |
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| 基金项目： | 四川省教育厅科研基金项目(09ZC016,10226020) |
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| 摘 要： | 提出了一种新型预条件算法,用于对有限元法离散Helmholtz方程所产生的大型稀疏复对称且高度不定的线性系统进行高效迭代求解。该新型预条件子是在复拉普拉斯偏移算子的基础上结合改进的稀疏近似逆算法来得到。通过改善矢量有限元线性系统自身的谱特性,该预条件算法既可避免迭代中的不稳定情况,同时也能较大提高迭代求解效率。数值结果表明,与若干常用预条件算法相比,所提出的预条件算法更加有效。
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| 关 键 词： | 预条件 拉普拉斯偏移算子 稀疏近似逆 有限元 |
| 收稿时间： | 2012/4/28 0:00:00 |
A New Approximate Inverse Preconditioning Algorithm for Solving Helmholtz Equation |
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| LI Yuehui and ZHAN Hongxia.A New Approximate Inverse Preconditioning Algorithm for Solving Helmholtz Equation[J].Semiconductor Optoelectronics,2012,33(5):663-666. |
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| Authors: | LI Yuehui and ZHAN Hongxia |
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| Affiliation: | 1.School of Mathematics and Computer Engineering; 2.School of Electrical and Information Engineering,Xihua University,Chengdu,Sichuan 610039,CHN) |
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| Abstract: | A new preconditioning algorithm is presented for effectively solving the large complex symmetric and always highly indefinite linear equations arising from the finite element method(FEM) discretizing Helmholtz equation.The proposed preconditioner is constructed by combing the complex shifted Laplace(CSL) operator with a modified AINV(MAINV) approximate inverse algorithm.By improving the FEM linear system’s eigenvalue spectrum,the proposed preconditioner can avoid most of the breakdowns during the iterative process,and enhance the solving efficiency.Numerical examples demonstrate the proposed preconditioning algorithm is more effective than some standard ones. |
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| Keywords: | preconditioner CSL operator AINV finite element |
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