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Description: |
In this seminar we present a finite volume method enriched with a fully
adaptive
multiresolution scheme, a Runge-Kutta-Fehlberg adaptive scheme, and a locally
varying time stepping, for solving the widely known monodomain and bidomain
equations modeling the electrical activity of the myocardial tissue. Two
simple models for the membrane and ionic currents are considered, one proposed
by Mitchell and Schaeffer [1] and the simple FitzHugh-Nagumo model [2]. We
firstly
prove, following [3], well-posedness for a class of these problems consisting in
a
strongly coupled and degenerate parabolic-elliptic system. We also prove
existence,
uniqueness of approximate solution
and its convergence to the corresponding weak
solution, obtaining in this way, an alternative proof for the well-posedness
result.
As in [4], After introducing the multiresolution technique, an optimal threshold
for
discarding non-significant information is derived and the efficiency and
accuracy of the numerical method is viewed in terms of CPU time speed-up,
memory compression and errors in different norms.
[1] C. Mitchell and D. Schaeffer, A two-current model for the dynamic of cardiac
membrane,
Bull. Math. Bio., 65 (2001) 767--793.
[2] R. FitzHugh, Impulses and physiological states in theoretical models of
nerve membrane,
Biophys. J., 1 (1961) 445--465.
[3] M. Bendahmane and K.H. Karlsen, Analysis of a class of degenerate
reaction-diffusion systems
and the bidomain model of cardiac tissue, Netw. Heterog. Media, 1 (2006)
185--218.
[4] R. BÌrger, R. Ruiz, K. Schneider and M. Sepúlveda, Fully adaptive
multiresolution schemes for
strongly degenerate parabolic equations with discontinuous flux, J.\ Engrg.\
Math., 60 (2008) 365--385.
Area(s):
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Date: |
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| Start Time: |
11:30 |
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Speaker: |
Ricardo Ruiz Baier (Universidad de Concepción, Chile)
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Place: |
5.5
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| Research Groups: |
-Numerical Analysis and Optimization
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See more:
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