Computational strategies for iterative solutions of large FEM applications employing voxel data

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Van Rietbergen, B.¹; Weinans, H.¹; Huiskes, R.¹; Polman, B. J. W.²

Computational strategies for iterative solutions of large FEM applications employing voxel data

Int J Num Meth Eng. August 30, 1996;39(16):2743-2767

©1996 John Wiley & Sons, Ltd.

Affiliations

¹Biomechanics Section, Institute of Orthopaedics, University of Nijmegen, The Netherlands

²Department of Mathematics, University of Nijmegen, The Netherlands
Abstract and keywords

FE-models for structural solid mechanics analyses can be readily generated from computer images via a "voxel conversion" method, whereby voxels in a two- or three-dimensional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithms that can compensate for a large number of elements. The solving methods described in this paper are based on an iterative solving algorithm in combination with a unique-element Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of 10⁵ 3-D brick elements on a workstation and on the order of 10⁶ elements on a Cray computer.

The methods are demonstrated for the Boussinesq problem and for FE-models that represent a porous trabecular bone structure. The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques.

Keywords: structural mechanics; voxel conversion; large FEM applications; iterative solving; element‐by‐element; row‐by‐row
Links

DOI: 10.1002/(SICI)1097-0207(19960830)39:16<2743::AID-NME974>3.0.CO;2-A

WoS: A1996VB59000003
History

Received: 1994-04-01

Revised: 1995-10-04

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Cited By (47)

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2002	van Rietbergen B, Majumdar S, Newitt D, MacDonald B. High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment. Clin Biomech (Bristol, Avon). February 2002;17(2):81-88.
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1998	Van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Relationships between bone morphology and bone elastic properties can be accurately quantified using high‐resolution computer reconstructions. J Orthop Res. January 1998;16(1):23-28.
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2013	Madi K, Tozzi G, Zhang Q, Tong J, Cossey A, Au A, Hollis D, Hild F. Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis. Med Eng Phys. September 2013;35(9):1298.
2001	Homminga J, Weinans H, Gowin W, Felsenberg D, Huiskes R. Ostehoporosis changes the amount of vertebral trabecular bone at risk of fracture but not the vertebral load distribution. Spine. July 2001;26(14):1555-1560.
1997	Ulrich D, Hildebrand T, Van Rietbergen B, Müller R, Rüegsegger P. The quality of trabecular bone evaluated with micro-computed tomography, FEA and mechanical testing. Stud Health Technol Inform. 1997;40:97-112.
1998	van Rietbergen B, Majumdar S, Pistoia W, Newitt DC, Kothari M, Laib A, Rüegsegger P. Assessment of cancellous bone mechanical properties from micro-FE models based on micro-CT, pQCT and MR images. Technol Health Care. December 1998;6(5-6):413-420.
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2006	Nagaraja S. Microstructural Stresses and Strains Associated With Trabecular Bone Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; December 2006.
2011	O'Neal JM. The Effects of Aging and Remodeling on Bone Quality and Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; August 2011.
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