Corrado, Cesare; Lassoued, Jamila; Mahjoub, Moncef; Zemzemi, Néjib Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology. (English) Zbl 1332.92013 Math. Biosci. 272, 81-91 (2016). MSC: 92C30 35K20 35B45 35K57 35K60 35B65 49M27 PDFBibTeX XMLCite \textit{C. Corrado} et al., Math. Biosci. 272, 81--91 (2016; Zbl 1332.92013) Full Text: DOI HAL
Krause, Dorian; Dickopf, Thomas; Potse, Mark; Krause, Rolf Towards a large-scale scalable adaptive heart model using shallow tree meshes. (English) Zbl 1349.76940 J. Comput. Phys. 298, 79-94 (2015). MSC: 76Z05 76M25 65Y05 92C30 92-08 PDFBibTeX XMLCite \textit{D. Krause} et al., J. Comput. Phys. 298, 79--94 (2015; Zbl 1349.76940) Full Text: DOI
Scacchi, Simone; Franzone, Piero Colli; Pavarino, Luca F.; Taccardi, B. Computing cardiac recovery maps from electrograms and monophasic action potentials under heterogeneous and ischemic conditions. (English) Zbl 1194.92050 Math. Models Methods Appl. Sci. 20, No. 7, 1089-1127 (2010). MSC: 92C55 65M60 92C50 65C20 68U20 35Q92 PDFBibTeX XMLCite \textit{S. Scacchi} et al., Math. Models Methods Appl. Sci. 20, No. 7, 1089--1127 (2010; Zbl 1194.92050) Full Text: DOI
Fernández, Miguel A.; Zemzemi, Nejib Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation. (English) Zbl 1193.92024 Math. Biosci. 226, No. 1, 58-75 (2010). MSC: 92C30 35Q92 92C05 92C55 65C20 PDFBibTeX XMLCite \textit{M. A. Fernández} and \textit{N. Zemzemi}, Math. Biosci. 226, No. 1, 58--75 (2010; Zbl 1193.92024) Full Text: DOI Link
Pennacchio, Micol; Simoncini, Valeria Algebraic multigrid preconditioners for the bidomain reaction-diffusion system. (English) Zbl 1171.92017 Appl. Numer. Math. 59, No. 12, 3033-3050 (2009). MSC: 92C30 92C05 35K57 37N25 34A34 PDFBibTeX XMLCite \textit{M. Pennacchio} and \textit{V. Simoncini}, Appl. Numer. Math. 59, No. 12, 3033--3050 (2009; Zbl 1171.92017) Full Text: DOI
Belhamadia, Youssef; Fortin, André; Bourgault, Yves Towards accurate numerical method for monodomain models using a realistic heart geometry. (English) Zbl 1168.92003 Math. Biosci. 220, No. 2, 89-101 (2009). MSC: 92C05 65C20 78A70 PDFBibTeX XMLCite \textit{Y. Belhamadia} et al., Math. Biosci. 220, No. 2, 89--101 (2009; Zbl 1168.92003) Full Text: DOI
Scacchi, S.; Franzone, P. Colli; Pavarino, L. F.; Taccardi, B. A reliability analysis of cardiac repolarization time markers. (English) Zbl 1168.92014 Math. Biosci. 219, No. 2, 113-128 (2009). MSC: 92C30 92C05 65C20 92C50 PDFBibTeX XMLCite \textit{S. Scacchi} et al., Math. Biosci. 219, No. 2, 113--128 (2009; Zbl 1168.92014) Full Text: DOI
Bourgault, Yves; Coudière, Yves; Pierre, Charles Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology. (English) Zbl 1154.35370 Nonlinear Anal., Real World Appl. 10, No. 1, 458-482 (2009). MSC: 35K50 92C50 35K57 PDFBibTeX XMLCite \textit{Y. Bourgault} et al., Nonlinear Anal., Real World Appl. 10, No. 1, 458--482 (2009; Zbl 1154.35370) Full Text: DOI HAL
Pennacchio, Micol; Simoncini, Valeria Substructuring preconditioners for mortar discretization of a degenerate evolution problem. (English) Zbl 1203.65173 J. Sci. Comput. 36, No. 3, 391-419 (2008). MSC: 65M55 92D15 PDFBibTeX XMLCite \textit{M. Pennacchio} and \textit{V. Simoncini}, J. Sci. Comput. 36, No. 3, 391--419 (2008; Zbl 1203.65173) Full Text: DOI
Nielsen, Bjørn Fredrik; Ruud, Tomas Syrstad; Lines, Glenn Terje; Tveito, Aslak Optimal monodomain approximations of the bidomain equations. (English) Zbl 1115.92005 Appl. Math. Comput. 184, No. 2, 276-290 (2007). MSC: 92C05 65N99 93B30 35Q92 78A70 PDFBibTeX XMLCite \textit{B. F. Nielsen} et al., Appl. Math. Comput. 184, No. 2, 276--290 (2007; Zbl 1115.92005) Full Text: DOI Link
Franzone, P. Colli; Pavarino, L. F.; Savaré, G. Computational electrocardiology: mathematical and numerical modeling. (English) Zbl 1387.92056 Quarteroni, Alfio (ed.) et al., Complex systems in biomedicine. Milano: Springer (ISBN 978-88-470-0394-1/hbk). 187-241 (2006). MSC: 92C55 PDFBibTeX XMLCite \textit{P. C. Franzone} et al., in: Complex systems in biomedicine. Milano: Springer. 187--241 (2006; Zbl 1387.92056) Full Text: DOI
Coudière, Yves; Pierre, Charles Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology. (English) Zbl 1109.35056 Nonlinear Anal., Real World Appl. 7, No. 4, 916-935 (2006). Reviewer: Qin Mengzhao (Beijing) MSC: 35K57 74S10 92C10 65M12 PDFBibTeX XMLCite \textit{Y. Coudière} and \textit{C. Pierre}, Nonlinear Anal., Real World Appl. 7, No. 4, 916--935 (2006; Zbl 1109.35056) Full Text: DOI HAL
Jakobsen, E. R.; Karlsen, K. H. Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source teams. (English) Zbl 1079.65094 BIT 45, No. 1, 37-67 (2005). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M12 65M06 35L60 65M20 35K65 49J25 PDFBibTeX XMLCite \textit{E. R. Jakobsen} and \textit{K. H. Karlsen}, BIT 45, No. 1, 37--67 (2005; Zbl 1079.65094) Full Text: DOI
Sundnes, Joakim; Lines, Glenn Terje; Tveito, Aslak An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso. (English) Zbl 1063.92018 Math. Biosci. 194, No. 2, 233-248 (2005). MSC: 92C30 78A70 65M60 92C05 PDFBibTeX XMLCite \textit{J. Sundnes} et al., Math. Biosci. 194, No. 2, 233--248 (2005; Zbl 1063.92018) Full Text: DOI
Spiteri, Raymond J.; MacLachlan, Mary C. An efficient non-standard finite difference scheme for an ionic model of cardiac action potentials. (English) Zbl 1319.65069 J. Difference Equ. Appl. 9, No. 12, 1069-1081 (2003). MSC: 65L12 92C30 PDFBibTeX XMLCite \textit{R. J. Spiteri} and \textit{M. C. MacLachlan}, J. Difference Equ. Appl. 9, No. 12, 1069--1081 (2003; Zbl 1319.65069) Full Text: DOI
Sundnes, Joakim; Lines, Glenn Terje; Tveito, Aslak Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells. (English) Zbl 0984.92010 Math. Biosci. 172, No. 2, 55-72 (2001). MSC: 92C30 92C05 65L05 PDFBibTeX XMLCite \textit{J. Sundnes} et al., Math. Biosci. 172, No. 2, 55--72 (2001; Zbl 0984.92010) Full Text: DOI