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Research Papers

Assembly-Free Large-Scale Modal Analysis on the Graphics-Programmable Unit

[+] Author and Article Information
Krishnan Suresh

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

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received July 11, 2012; final manuscript received December 1, 2012; published online January 7, 2013. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 13(1), 011003 (Jan 07, 2013) (7 pages) Paper No: JCISE-12-1108; doi: 10.1115/1.4023168 History: Received July 11, 2012; Revised December 01, 2012

Popular eigensolvers such as block-Lanczos require repeated inversion of an eigenmatrix. This is a bottleneck in large-scale modal problems with millions of degrees of freedom. On the other hand, the classic Rayleigh–Ritz conjugate gradient method only requires a matrix-vector multiplication, and is therefore potentially scalable to such problems. However, as is well-known, the Rayleigh–Ritz has serious numerical deficiencies, and has largely been abandoned by the finite-element community. In this paper, we address these deficiencies through subspace augmentation, and consider a subspace augmented Rayleigh–Ritz conjugate gradient method (SaRCG). SaRCG is numerically stable and does not entail explicit inversion. As a specific application, we consider the modal analysis of geometrically complex structures discretized via nonconforming voxels. The resulting large-scale eigenproblems are then solved via SaRCG. The voxelization structure is also exploited to render the underlying matrix-vector multiplication assembly-free. The implementation of SaRCG on multicore central processing units (CPUs) and graphics-programmable units (GPUs) is discussed, followed by numerical experiments and case-studies.

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Figures

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Fig. 1

A thin gear housing whose eigenspectrum is desired

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Fig. 2

Complex thin-structures require a fine-mesh

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Fig. 3

Brute-force voxelization of the structure

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Fig. 4

First four modes computed via SolidWorks

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Fig. 5

Nonconforming voxelization of a beam

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Fig. 6

First eigenmode of a connecting-rod at 529.6 Hz

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Fig. 7

(a) A knuckle component, (b) conforming mesh, and (c) voxel-mesh

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Fig. 8

The first five modes computed via SolidWorks

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Fig. 9

The first five modes computed via proposed method

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Fig. 10

The first mode of the structure in Fig. 1

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