Large Scale Finite Element Analysis Via Assembly-Free Deflated Conjugate Gradient
Large Scale Finite Element Analysis Via Assembly-Free Deflated Conjugate Gradient
复制标题
通过无装配紧缩共轭梯度进行大规模有限元分析
DOI：
10.1115/1.4028591
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
K. Suresh
中科院分区：
文献类型：
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作者：
Praveen Yadav;K. Suresh
百万自由度大尺度有限元分析（FEA）在固体力学研究中日益普及。这类问题的主要计算瓶颈是求解大型线性方程组。在本文中，我们提出了一个无装配版本的放气共轭梯度（DCG）来求解这类方程，其中刚度矩阵和放气矩阵都不装配。虽然无装配有限元分析是一个众所周知的概念，但本文所追求的新颖之处在于使用无装配放气。由此产生的实现特别适合于大规模问题，并且可以很容易地移植到多核中央处理单元（CPU）和图形可编程单元（GPU）体系结构中。为了演示，我们展示了可以在单个GPU卡上解决50 × 106自由度的系统，配备3gb内存。第二个贡献是将DCG中使用的“刚体团聚”概念扩展为“曲率敏感团聚”。后者利用经典的板和梁理论来有效地解决由薄结构引起的高度病态问题。
Large-scale finite element analysis (FEA) with millions of degrees of freedom (DOF) is becoming commonplace in solid mechanics. The primary computational bottleneck in such problems is the solution of large linear systems of equations. In this paper, we propose an assembly-free version of the deflated conjugate gradient (DCG) for solving such equations, where neither the stiffness matrix nor the deflation matrix is assembled. While assembly-free FEA is a well-known concept, the novelty pursued in this paper is the use of assembly-free deflation. The resulting implementation is particularly well suited for large-scale problems and can be easily ported to multicore central processing unit (CPU) and graphics-programmable unit (GPU) architectures. For demonstration, we show that one can solve a 50 × 106 degree of freedom system on a single GPU card, equipped with 3 GB of memory. The second contribution is an extension of the “rigid-body agglomeration” concept used in DCG to a “curvature-sensitive agglomeration.” The latter exploits classic plate and beam theories for efficient deflation of highly ill-conditioned problems arising from thin structures.