Implicit parallel solvers in computational electrocardiology

Applied Analysis and Differential Equations: Lasi, Romania, 4-9 September 2006

Volumn , Issue , 2007, Pages 255-266

  Munteanu, Marilena ^a   Pavarino, Luca Franco ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Finite elements; Implicit time discretization; Monodomain and bidomain models; Newton Krylov methods; Parallel solver

Indexed keywords

COMPUTER OPERATING SYSTEMS; FINITE ELEMENT METHOD; ION BEAMS; LINEAR EQUATIONS; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; NON NEWTONIAN FLOW; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

BIDOMAIN MODELS; BIO-ELECTRICAL ACTIVITY; COMPUTATIONAL ELECTROCARDIOLOGY; NEWTON KRYLOV METHOD; NONLINEAR PARABOLIC REACTION; PARALLEL SOLVER; STABILITY CONSTRAINTS; TIME DISCRETIZATION;

PARALLEL PROCESSING SYSTEMS;

EID: 50049086235     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812708229_0021     Document Type: Chapter

References (18)

1. C. Luo, Y. Rudy, A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction, Circ. Res., 68 (1991), 15011526.
2. G. Akrivis, M. Crouzeix, C. Makridakis, Implicit-explicit multistep finite element methods for nonlinear parabolic problems, Math. Comp., 67, 2 (1998) 457-477.
3. J. Pormann, A simulation system for the Bidomain equations, PhD thesis, Duke University, Dep. of Electr. Comp. Eng., (1999).
4. P. Colli Franzone, L.F. Pavarino, A parallel solver for reaction-diffusion equations in computational electrocardiology, Math. Models Methods Appl. Sci., 14, 6 (2004), 883-911.
5. J. Lang, J. Verwer, Ros3P-An accurate third-order Rosenbrock solver designed for parabolic problems, BIT, 41, 4 (2001), 731-738.
6. M. Murillo, X.-C. Cai, A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart, Numer. Linear Algebra Appl., 11, 2-4 (2004), 261-277.
7. P. Colli Franzone, G. Savare, Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level, Evolution equations, semigroups and functional analysis (Milano, 2000), 49-78, Progr. Nonlinear Differential Equations Appl., 50, (Birkhäuser, Basel, 2002).
8. M. Pennacchio, G. Savaré, P. Colli Franzone, Multiscale modeling for the bioelectric activity of the Heart, SIAM J. Math. Anal., 37, 4 (2006), 1333-1370.
9. S. Sanfelici, Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology, Numer. Meth. Part. Differ. Equ., 18, 2 (2002), 218-240.
10. R.H. Nochetto, G. Savarè, C. Verdi, A posteriori error estimates for variable time-step discretizations for nonlinear evolution equations, Comm. Pure Appl. Math., 53, 5 (2000), 525-589.
11. X.-C. Cai, W.D. Gropp, D.E. Keyes, M.D. Tidriri, Newton-Krylov-Schwarz methods in CFD, in Proceedings of the International Workshop on Numerical Methods for the Navier-Stokes equations, (Vieweg, Braunschweig, 1995), 183-200.
12. D.A. Knoll, D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approches and applications, J. Comput. Phys., 193, 2 (2004), 357-397.
13. P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, 35, (Springer-Verlag, Berlin, 2004).
14. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, 14, (Springer-Verlag, Berlin, 1996).
15. Ch. Lubich, M. Roche, Rosenbrock methods for differential-algebraic systems with solution-dependent singular matrix multiplying the derivative, Computing, 43, 4 (1990), 325-342.
16. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M. Knepley, L.Cufman McInnes, B.F. Smith and H.Zhang, PETSc user manual, Tech. Rep ANL-95/11-Revision 2.1.5, Argonne National Laboratory (2002).
17. N. Hooke, Efficient simulation of action potential propagation in a Bidomain, PhD thesis, Duke Univ., Dept. of Comput. Sci., (1992).
18. P.Colli Franzone, P. Deuflhard, B. Erdmann, J. Lang, L.F. Pavarino, Adaptivity in space and time for reaction-diffusion systems in electrocardiology, SIAM J. Sci. Comput., 28, 3 (2006), 942-962.