2009
DOI: 10.1098/rsta.2008.0306
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Numerical solution of the bidomain equations

Abstract: Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra-and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysi… Show more

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Cited by 48 publications
(24 citation statements)
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“…An additional approximation is made in [35,54] by substituting the mass matrix with the identity. A recap of some splitting and uncoupling approaches can be found in the review papers [5,20,28,53].…”
Section: Time Discretizationmentioning
confidence: 99%
See 1 more Smart Citation
“…An additional approximation is made in [35,54] by substituting the mass matrix with the identity. A recap of some splitting and uncoupling approaches can be found in the review papers [5,20,28,53].…”
Section: Time Discretizationmentioning
confidence: 99%
“…Alternatively, most previous works have considered IMEX time discretizations and/or operator splitting schemes, where the reaction and diffusion terms are treated separately, see e.g. [4,6,8,14,20,22,28,35,38,45,47,[53][54][55]. The advantage of IMEX and operator splitting schemes is that they only require the solution of a linear system for the parabolic and elliptic PDEs at each time step.…”
Section: Introductionmentioning
confidence: 99%
“…For self-adjoint, linear PDEs, optimal solvers are well understood (e.g., see the review papers [59,60] for the theory of saddle point problems). In simulating cardiac tissue, optimal solvers exist for both the monodomain model and the bidomain model (e.g., [11,61,62]). …”
Section: Optimal Solversmentioning
confidence: 99%
“…There exists a large body of literature concerning the development of parallel cardiac electrophysiology solvers (see Bordas et al (2009) ;Linge et al (2009) and Clayton et al (2011) for surveys). Examples of early contributions to parallel solution approaches are Fishler and Thakor (1991), Pollard and Barr (1991), Winslow et al (1993), Ng et al (1995), Saleheen et al (1997), Quan et al (1998) and Cai and Lines (2002).…”
Section: Introductionmentioning
confidence: 99%