Spectral-Element Agglomerate Coarsening in AMGe.

Vaassilevski, P. S.

Technical Information Center Oak Ridge Tennessee

关键词: Lectures;    Algorithms;    Mathematical models;    Equations;    Multigrid methods;   

RP-ID  :  DE200415006289

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

In this talk the authors present a highly accurate coarsening algorithm for constructing coarse finite element spaces to be used in algebraic multigrid methods designed for finite element problems on generally unstructured meshes. The new algorithm relies on removing certain percentage of the high oscillating components from the spectrum of local stiffness matrices corresponding to element agglomerations. By doing so, one is guaranteed that the hierarchical complement finite element subspace gives rise to a well conditioned matrix. The coarsening consists of an agglomeration step and of computing a few minimal eigenvectors of the corresponding assembled agglomerate stiffness matrix. The method requires access to the individual element matrices. Based on the topological agglomeration algorithms they employed one is able to define coarse elements and coarse element matrices thus allowing for recursive use of the same algorithm. Some numerical illustration for elliptic problems is also given.