Multilevel preconditioning for the finite volume method
Multilevel preconditioning for the finite volume method
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DOI：
10.1090/s0025-5718-2012-02582-8
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发表时间：
2012-09
期刊：
影响因子：
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通讯作者：
Yonghai Li;S. Shu;Yuesheng Xu;Q. Zou
中科院分区：
文献类型：
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作者：
Yonghai Li;S. Shu;Yuesheng Xu;Q. Zou
本文讨论了椭圆边值问题有限体积法（FVM）中线性方程组的预条件。借助于有限体积法的试空间到测试空间的插值算子和由有限体积法双线性形式导出的算子，我们证明了原来为边值问题的有限元法设计的小波预处理器和多级预处理器都可以用于对同一边值问题的有限体积法进行预处理.我们证明了这样的预条件，确保所得到的系数矩阵的有限体积法有一个一致有界的条件数。我们提出了七个数值例子来证实我们的理论研究结果。
We consider the precondition of linear systems which resulted from the finite volume method (FVM) for elliptic boundary value problems. With the help of the interpolation operator from the trial space to the test space of the FVM and the operator induced by the FVM bilinear form, we show that both wavelet preconditioners and multilevel preconditioners designed originally for the finite element method (FEM) of a boundary value problem can be used to precondition the FVM of the same boundary value problem. We prove that such preconditioners ensure that the resulting coefficient matrix of the FVM has a uniformly bounded condition number. We present seven numerical examples to confirm our theoretical findings.