Research Papers

Large Scale Finite Element Analysis Via Assembly-Free Deflated Conjugate Gradient

[+] Author and Article Information
Praveen Yadav

Department of Mechanical Engineering,
Madison, WI 53706

Krishnan Suresh

Department of Mechanical Engineering,
Madison, WI 53706
e-mail: suresh@engr.wisc.edu

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received June 27, 2014; final manuscript received September 10, 2014; published online October 7, 2014. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 14(4), 041008 (Oct 07, 2014) (9 pages) Paper No: JCISE-14-1225; doi: 10.1115/1.4028591 History: Received June 27, 2014; Revised September 10, 2014

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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

A two-level geometric multigrid

Grahic Jump Location
Fig. 2

(a) Finite element mesh and (b) agglomeration of mesh nodes into four groups

Grahic Jump Location
Fig. 3

Example of “thick” solids

Grahic Jump Location
Fig. 4

Examples of “thin” solids

Grahic Jump Location
Fig. 5

Curvature effects in thin structures

Grahic Jump Location
Fig. 6

Congruency in a finite element mesh

Grahic Jump Location
Fig. 7

Most of the distinct elements are localized

Grahic Jump Location
Fig. 8

Partitioning mesh-nodes into groups. (a) Finite element mesh. (b) Partitioning into 32 groups. (c) Partitioning into 64 groups.

Grahic Jump Location
Fig. 9

SpMV implementation in GPU

Grahic Jump Location
Fig. 10

GPU implementation of prolongation

Grahic Jump Location
Fig. 11

GPU implementation for restriction

Grahic Jump Location
Fig. 12

A beam geometry and its mesh

Grahic Jump Location
Fig. 13

Assembly-free SpMV on the CPU with and without exploiting element-congruency

Grahic Jump Location
Fig. 14

(a) Knuckle geometry and loading. (b) Voxel mesh with 3.16 × 106 DOF.

Grahic Jump Location
Fig. 15

Static displacement and stress for knuckle

Grahic Jump Location
Fig. 16

Visual representation of 100 and 1000 agglomeration groups

Grahic Jump Location
Fig. 17

Convergence of DCG versus Jacobi-PCG

Grahic Jump Location
Fig. 18

Loading on a thin plate

Grahic Jump Location
Fig. 19

Convergence of DCG versus Jacobi-PCG for thin plate

Grahic Jump Location
Fig. 20

CUDA profile for RBM deflation

Grahic Jump Location
Fig. 21

Structural problem over a Thomas engine

Grahic Jump Location
Fig. 22

Deflection from a 50 × 106 DOF system




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In