An order optimal solver for the discretized bidomain equations

2007 ◽  
Vol 14 (2) ◽  
pp. 83-98 ◽  
Author(s):  
Kent-Andre Mardal ◽  
Bjørn Fredrik Nielsen ◽  
Xing Cai ◽  
Aslak Tveito
Keyword(s):  
Bidomain Equations

Homogenization of the Cell Cytoplasm: The Calcium Bidomain Equations

2006 ◽  
Vol 5 (4) ◽  
pp. 1045-1062 ◽  
Author(s):  
Pranay Goel ◽  
James Sneyd ◽  
Avner Friedman
Keyword(s):  
Cell Cytoplasm ◽  
Bidomain Equations

scholarly journals Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

2009 ◽  
Vol 56 (10) ◽  
pp. 2404-2412 ◽  
Author(s):  
James A. Southern ◽  
Gernot Plank ◽  
Edward J. Vigmond ◽  
Jonathan P. Whiteley
Keyword(s):  
Computational Efficiency ◽  
Coupled System ◽  
Bidomain Equations

Delayed Residual Compensation for Bidomain Equations

2010 ◽  
Author(s):  
Martin Weiser ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Bidomain Equations

scholarly journals Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

2018 ◽  
Vol 28 (05) ◽  
pp. 979-1035 ◽  
Author(s):  
Annabelle Collin ◽  
Sébastien Imperiale
Keyword(s):  
Mathematical Analysis ◽  
Cardiac Electrophysiology ◽  
Convergence Theory ◽  
Bidomain Model ◽  
Periodic Homogenization ◽  
Homogenization Procedure ◽  
Uniform Estimates ◽  
Bidomain Equations ◽  
Homogenization Process

The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in cardiac electrophysiology. We consider space-dependent and tensorial electric conductivities as well as space-dependent physiological and phenomenological nonlinear ionic models. We provide the nondimensionalization of the bidomain equations and derive uniform estimates of the solutions. The homogenization procedure is done using 2-scale convergence theory which enables us to study the behavior of the nonlinear ionic models in the homogenization process.

scholarly journals Strong time-periodic solutions to the bidomain equations with arbitrary large forces

2019 ◽  
Vol 47 ◽  
pp. 398-413 ◽  
Author(s):  
Yoshikazu Giga ◽  
Naoto Kajiwara ◽  
Klaus Kress
Keyword(s):  
Periodic Solutions ◽  
Bidomain Equations ◽  
Time Periodic Solutions ◽  
Time Periodic

Error estimates and communication overhead in the computation of the bidomain equations on the distributed memory parallel Blue Gene/L supercomputer

2008 ◽  
Author(s):  
M. Reumann ◽  
B.G. Fitch ◽  
A. Rayshubskiy ◽  
D.L. Weiss ◽  
G. Seemann ◽  
...  
Keyword(s):  
Error Estimates ◽  
Distributed Memory ◽  
Communication Overhead ◽  
Bidomain Equations ◽  
Blue Gene
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