Robust BDDC algorithms for finite volume element methods

Electronic Transactions on Numerical Analysis

article

Yingxiang Xu¹  Yanru Su²  Xuemin Tu² 

[1] School of Mathematics and Statistics, Northeast Normal University;Department of Mathematics, University of Kansas

关键词: finite volume element methods;    domain decomposition;    BDDC;    deluxe scaling;   

DOI  :  10.1553/etna_vol58s66

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

The balancing domain decomposition by constraints (BDDC) method is applied to the linear system arising from the finite volume element method (FVEM) discretization of a scalar elliptic equation. The FVEMs share nice features of both finite element and finite volume methods and are flexible for complicated geometries with good conservation properties. However, the resulting linear system usually is asymmetric. The generalized minimal residual (GMRES) method is used to accelerate convergence. The proposed BDDC methods allow for jumps of the coefficient across subdomain interfaces. When jumps of the coefficient appear inside subdomains, the BDDC algorithms adaptively choose the primal variables deriving from the eigenvectors of some local generalized eigenvalue problems. The adaptive BDDC algorithms with advanced deluxe scaling can ensure good performance with highly discontinuous coefficients. A convergence analysis of the BDDC method with a preconditioned GMRES iteration is provided, and several numerical experiments confirm the theoretical estimate.

【 授权许可】

Unknown