Stress-aware large-scale mesh editing using a domain-decomposed multigrid solver

作     者：Xu, Weiwei Yang, Haifeng Yang, Yin Wang, Yiduo Zhou, Kun 

作者机构：[a]State Key Lab of CAD&CG Zhejiang University China [b]Electrical and Computer Engineering Department University of New Mexico USA 

出 版 物：《COMPUTER AIDED GEOMETRIC DESIGN》 (计算机辅助几何设计)

年 卷 期：2018年第63卷

页      面：17-30页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：NSFC [61732016, 61502133] Fundamental Research Funds for the Central Universities [2017XZZX009-03] NSF [CHS-1464306, CHS-1717972, CNS-1637092] Nvidia GPU grant 

主　　题：Domain Decomposition Multigrid solver Stress analysis 

摘      要：In this paper, we develop a domain-decomposed subspace and multigrid solver to analyze the stress distribution for large-scale finite element meshes with millions of degrees of freedom. Through the domain decomposition technique, the shape editing directly updates the data structure of local finite element matrices. Doing so avoids the expensive factorization step in a direct solver and provides users with a progressive feedback of the stress distribution corresponding to the mesh operations: a fast preview is achieved through the subspace solver, and the multigrid solver refines the preview result if the user needs to examine the stress distribution carefully at certain design stages. Our system constructs the subspace for stress analysis using reduced constrained modes and builds a three-level multigrid solver through the algebraic multigrid method. We remove mid-edge nodes and lump unknowns with the Schur complement method. The updating and solving of the large global stiffness matrix are implemented in parallel after the domain decomposition. Experimental results show that our solver outperforms the parallel Intel MKL solver. Speedups of 50%-100% can be achieved for large-scale meshes with reasonable pre-computation costs when setting the stopping criterion of the multigrid solver to be 1e-3 relative error. (C) 2018 Elsevier B.V. All rights reserved.