Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Sensitivity analysis in poro-elastic and poro-visco-elastic models with respect to boundary data


Authors: H. T. Banks, K. Bekele-Maxwell, L. Bociu, M. Noorman and G. Guidoboni
Journal: Quart. Appl. Math. 75 (2017), 697-735
MSC (2010): Primary 49K40, 49Q12, 74B20, 35Q92, 46N60, 62P10
DOI: https://doi.org/10.1090/qam/1475
Published electronically: July 28, 2017
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Abstract: In this article we consider poro-elastic and poro-visco-elastic models inspired by problems in medicine and biology, and we perform sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the imposed boundary data, which are the main drivers of the system. Moreover, we compare the results obtained in the elastic case vs. visco-elastic case, as it is known that structural viscosity of biological tissues decreases with age and disease. Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is our ultimate goal.


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Additional Information

H. T. Banks
Affiliation: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8212
Email: htbanks@ncsu.edu

K. Bekele-Maxwell
Affiliation: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8212
Email: ktzeleke@ncsu.edu

L. Bociu
Affiliation: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8212
Email: lvbociu@ncsu.edu

M. Noorman
Affiliation: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8212
Email: mjnoorma@ncsu.edu

G. Guidoboni
Affiliation: Indiana University Purdue University Indianapolis, 402 N. Blackford St, LD270, Indianapolis, Indiana 46202-3267
Email: gguidobo@iupui.edu

DOI: https://doi.org/10.1090/qam/1475
Keywords: Sensitivity, poro-elastic, poro-visco-elastic, biological tissues, complex-step method
Received by editor(s): April 28, 2017
Published electronically: July 28, 2017
Article copyright: © Copyright 2017 Brown University

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