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ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

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error at a fixed time step by a reduction order of 99.9 %. The reduced simulation needs<br />

only 44 % of the computational time of the unreduced simulation. The largest relative<br />

errors are located where the absolute values of the corresponding variable have its<br />

smallest value. For a surgical application where the absolute value of the error is<br />

important these areas are negligible. Therefore the POD method is able to approximate<br />

the required behavior of this biomechanical system very well and simultaneously allows<br />

an enormous reduction of the computational effort.<br />

8. REFERENCES<br />

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the Karhunen-Loéve expansion and dual-weighted-residual methods, Computational<br />

Mechanics, 2003, Vol. 31, 179-191.<br />

3. Mourelatos, Z. P., An efficient crankshaft dynamic analysis using substructuring<br />

with Ritz vectors, Journal of Sound and Vibration, 2000, Vol. 238, 495-527.<br />

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7. Chatterjee, A., An introduction to the proper orthogonal decomposition, Current<br />

Science, 2000, Vol. 78, 808-817.<br />

8. Niroomandi, S., Alfaro, I., Cueto, E., Chinesta, F., Real-time deformable models of<br />

non-linear tissues by model reduction techniques, Computer Methods and Programs<br />

in Biomedicine, 2008, Vol. 91, 223-231<br />

9. Dogan, F., Serdar Celebi, M., Real-time deformation simulation of non-linear<br />

viscoelastic soft tissues, Simulation, 2011, Vol. 87, 179-187.<br />

10. Willcox, K., Peraire, J., Balanced model reduction via the proper orthogonal<br />

decomposition, AIAA Journal, 2002, Vol. 40, 2323-2330.<br />

11. Radermacher, A., Reese, S., Model Reduction for Complex Continua – At the<br />

Example of Modeling Soft Tissue in the Nasal Area, In: Advances in Extended and<br />

Multifield Theories for Continua (Eds.: Markert, B.), Lecture Notes in Applied and<br />

Computational Mechanics, 2011, Vol. 59, 197-217.<br />

12. Edward L. Wilson, E. L., A new method of dynamic analysis for linear and<br />

nonlinear systems, Finite Elements in Analysis and Design, 1985, Vol. 1, 21-23.<br />

13. Breuer, K. S., Sirovich, L., The use of the Karhunen-Loéve procedure for the<br />

calculation of linear eigenfunctions, Journal of Computational Physics, 1991, Vol.<br />

96, 277-296.

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