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Section B

Hexagonal grid methods with applications to partial differential equations

, , &
Pages 1986-2009 | Received 02 Apr 2013, Accepted 03 Nov 2013, Published online: 26 Mar 2014

References

  • R.R. Aliev and A.V. Panfilov, A simple two-variables model of cardiac excitation, Chaos, Solitons Fractals 7(3) (1996), pp. 293–301. doi: 10.1016/0960-0779(95)00089-5
  • F.L. Bauer and C.T. Fike, Norms and exclusion theorems, Numer. Math. 2 (1960), pp. 137–141. doi: 10.1007/BF01386217
  • A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994.
  • B. He, Modeling and Imaging of Bio-electrical Activity: Principle and Applications, Kluwer Academic/Plenum Publishers, New York, 2004.
  • S. Karaa and J. Zhang, Analysis of stationary iterative methods for the discrete convection-diffusion equation with a 9-point compact scheme, J. Comp. Appl. Math. 154 (2003), pp. 447–476. doi: 10.1016/S0377-0427(02)00863-4
  • I.J. LeGrice, B.H. Smaill, L.Z. Chai, S.G. Edgar, J.B. Gavin, and P.J. Hunter, Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog, Am. J. Physiol. 269(2) Pt 2 (1995), pp. H571–82.
  • M. Lorange and R.M. Gulrajani, A computer heart model incorporating anisotropic propagation. I. Model construction and simulation of normal activation, J Electrocardiol. 26(4) (1993), pp. 245–261. doi: 10.1016/0022-0736(93)90047-H
  • G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl. 13(3) (1992), pp. 707–728.
  • W.M. Pickering, On the solution of Poisson's equation on a regular hexagonal grid using FFT methods, JCP 64 (1986), pp. 320–333. doi: 10.1139/p86-056
  • M. Postse, B. Dube, J. Richer, A. Vinet, and R.M. Gulrajani, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart, IEEE Trans. Biomed. Eng. 53(12) (2006), pp. 2425–2435. doi: 10.1109/TBME.2006.880875
  • W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed., Cambridge University Press, New York, NY, 2002.
  • J.R. Rice and R.F. Boisvert, Solving Elliptic Problems with ELLPACK, Springer-Verlag, New York, NY, 1985.
  • H.J. Ritsema van Eck, J.A. Kors, and G. van Herpen, The U wave in the electrocardiogram: A solution for a 100-year-old riddle, Cardiovasc Res. 67(2) (2005), pp. 256–262. doi: 10.1016/j.cardiores.2005.04.010
  • J.B. Roser, Nine point difference solutions for Poisson's equation, Comp. Math. Appl. 1 (1975), pp. 351–360. doi: 10.1016/0898-1221(75)90035-8
  • Y. Saad, Iterative Methods for Sparse Linear System, 2nd ed., SIAM, Philadelphia, PA, 2003.
  • H. Sakaguchi and T. Fujimoto, Elimination of spiral chaos by periodic force for the Aliev-Panfilov model, Phys. Rev. E 71 (2005), p. 052901. doi: 10.1103/PhysRevE.71.052901
  • L.F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, New York, NY, 2003.
  • Jia-chang Sun, On approximation of Laplacian eigenproblem over a regular hexagon with zero boundary condition, J. Clin. Microbiol. 22(2) (2004), pp. 275–286.
  • L. Tung, A bi-domain model for describing ischemic myocardial D-C potentials, Ph.D. diss., MIT, Cambridge, MA, 1978.
  • K.H.W.J. ten Tusscher and A.V. Panfilov, Wave propagation in excitable media with randomly distributed obstacles, Multiscale Model Simul. 3(2) (2005), pp. 265–282. doi: 10.1137/030602654
  • H.K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, the Finite Volume Method, Longman Group Ltd, New York, NY, 1995.
  • E.J. Vigmond, R.W.d. Santos, A.J. Prassl, M. Deocw, and G. Plank, Solvers for the cardiac bidomain equations, Prog. Biophys. Mol. Biol. 96 (2008), pp. 3–18. doi: 10.1016/j.pbiomolbio.2007.07.012

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