Large Scale Finite Element Analysis Via Assembly Free Deflated Conjugate Gradient

Abstract

Largescale 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 assemblyfree version of the deflated conjugate gradient (DCG) for solving such equations, where neither the stiffness matrix nor the deflation matrix is assembled. While assemblyfree FEA is a wellknown concept, the novelty pursued in this paper is the use of assemblyfree deflation. The resulting implementation is particularly well suited for largescale problems and can be easily ported to multicore central processing unit (CPU) and graphicsprogrammable unit (GPU) architectures. For demonstration, we show that one can solve a 50 أ— 106 degree of freedom system on a single GPU card, equipped with 3 GB of memory. The second contribution is an extension of the “rigidbody agglomerationâ€‌ concept used in DCG to a “curvaturesensitive agglomeration.â€‌ The latter exploits classic plate and beam theories for efficient deflation of highly illconditioned problems arising from thin structures.