Multi-neighboring grids schemes for solving PDE eigen-problems
Multi-neighboring grids schemes for solving PDE eigen-problems
复制标题
DOI：
10.1007/s11425-013-4731-9
复制
发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
Jiachang Sun
中科院分区：
文献类型：
--
作者：
Jiachang Sun
为了解决现有网格上的偏微分方程组特征问题，提出了一种新的前处理方法，称为多八孔网格(MNG)。第一阶段K1hUh=λ1hM1hUh，采用基于箱样条的线性或多线性单元。本文将第j级相邻网格格式定义为Kjh=λjhMjhUh，其中Kjh：=Mj−1h⊗K1handMjhU是第j级相邻网格上较好的质量分布，Kjh可以看作是第j级相邻网格上K1h相对于第(j−1)质量分布Mj−1h的展开。结果表明，对于常微分方程组模型的本征问题，采用2j阶B样条基的第j阶格式通过摄动质量矩阵可以达到2j阶精度和偶数(2j+2)阶精度。该参数可以扩展到具有可分离变量情况的高维问题。对于一些二维和三维结构均匀网格的拉普拉斯特征问题，给出了J⩽3的一些2J阶格式。
Instead of most existing postprocessing schemes, a new preprocessing approach, called multineighboring grids (MNG), is proposed for solving PDE eigen-problems on an existing grid. The linear or multi-linear element, based on box-splines, are taken as the first stageK1hUh=λ1hM1hUh. In this paper, thej-th stage neighboring-grid scheme is defined asKjh=λjhMjhUh, whereKjh:=Mj−1h⊗K1handMjhUhis to be found as a better mass distribution over thej-th stage neighboring-grid, andKjhcan be seen as an expansion ofK1hon thej-th neighboring-grid with respect to the (j− 1)-th mass distributionMj−1h. It is shown that for an ODE model eigen-problem, thej-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even (2j+2)-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented forj⩽ 3.