A Study of preconditioned Krylov subspace methods with reordering for linear systems from a biphasic v-p finite element formulation

A study was conducted on combinations of preconditioned iterative methods with matrix reordering to solve the linear systems arising from a biphasic velocity-pressure (v-p) finite element formulation used to simulate soft hydrated tissues in the human musculoskeletal system. Krylov subspace methods...

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Bibliographic Details
Published in:Computer methods in biomechanics and biomedical engineering 2007-02, Vol.10 (1), p.13-24, Article 13
Main Authors: Yang, Taiseung, Spilker, Robert L.
Format: Article
Language:English
Subjects:
Animals
Biphasic theory
Body Water - physiology
Cartilage, Articular - physiology
Computer Simulation
Connective Tissue - physiology
Elasticity
Finite Element Analysis
Humans
Humeral head cartilage
Incomplete LU factorization preconditioning
Linear Models
Models, Biological
Preconditioned Krylov subspace methods
Reorderings
Stress, Mechanical
Velocity-pressure finite element formulation
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Summary:A study was conducted on combinations of preconditioned iterative methods with matrix reordering to solve the linear systems arising from a biphasic velocity-pressure (v-p) finite element formulation used to simulate soft hydrated tissues in the human musculoskeletal system. Krylov subspace methods were tested due to the symmetric indefiniteness of our systems, specifically the generalized minimal residual (GMRES), transpose-free quasi-minimal residual (TFQMR), and biconjugate gradient stabilized (BiCGSTAB) methods. Standard graph reordering techniques were used with incomplete LU (ILU) preconditioning. Performance of the methods was compared on the basis of convergence rate, computing time, and memory requirements. Our results indicate that performance is affected more significantly by the choice of reordering scheme than by the choice of Krylov method. Overall, BiCGSTAB with one-way dissection (OWD) reordering performed best for a test problem representative of a physiological tissue layer. The preferred methods were then used to simulate the contact of the humeral head and glenoid tissue layers in glenohumeral joint of the shoulder, using a penetration-based method to approximate contact. The distribution of pressure and stress fields within the tissues shows significant through-thickness effects and demonstrates the importance of simulating soft hydrated tissues with a biphasic model.
ISSN:1025-5842
1476-8259
DOI:10.1080/10255840601086416