Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities

Authors:	Susanne C Brenner

Institution:	Department of Mathematics, University of South Carolina, Columbia, SC 29208

Abstract:	We consider the Poisson equation $-\Delta u=f$ with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain $\Omega$ with re-entrant angles. A multigrid method for the computation of singular solutions and stress intensity factors using piecewise linear functions is analyzed. When $f\in L^{2}(\Omega )$ , the rate of convergence to the singular solution in the energy norm is shown to be ${\mathcal{O}}(h)$ , and the rate of convergence to the stress intensity factors is shown to be ${\mathcal{O}}(h^{1+(\pi /\omega )-\epsilon })$ , where $\omega$ is the largest re-entrant angle of the domain and $\epsilon >0$ can be arbitrarily small. The cost of the algorithm is ${\mathcal{O}}(h^{-2})$ . When $f\in H^{1}(\Omega )$ , the algorithm can be modified so that the convergence rate to the stress intensity factors is ${\mathcal{O}}(h^{2-\epsilon })$ . In this case the maximum error of the multigrid solution over the vertices of the triangulation is shown to be ${\mathcal{O}}(h^{2-\epsilon })$ .

Keywords:	Multigrid corner singularities stress intensity factors superconvergence

	点击此处可从《Mathematics of Computation》浏览原始摘要信息
	点击此处可从《Mathematics of Computation》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏