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Volumn 22, Issue 2, 2006, Pages 435-448

Spectral smoothed boundary methods: The role of external boundary conditions

Author keywords

Domain embedding methods; Irregular domains; Reaction diffusion equations; Spectral methods

Indexed keywords


EID: 33645013922     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20103     Document Type: Article
Times cited : (43)

References (25)
  • 1
    • 0003583110 scopus 로고    scopus 로고
    • A practical guide to pseudospectral methods
    • 1 B. Fornberg, A practical guide to pseudospectral methods, Cambridge University Press, Cambridge, 1996.
    • (1996)
    • Fornberg, B.1
  • 2
    • 0007748409 scopus 로고
    • Fourier techniques in numerical methods for evolutionary problems
    • 2 J. M. Sanz‐Serna, Fourier techniques in numerical methods for evolutionary problems, Lecture Notes in Phys. 448, Springer‐Verlag, Berlin, 1995, pp. 145–200.
    • (1995) , vol.448 , pp. 145-200
    • Sanz‐Serna, J.M.1
  • 4
    • 0003600453 scopus 로고
    • Numerical analysis of spectral methods: theory and applications
    • 4 D. Gottlieb, and S. A. Orszag, Numerical analysis of spectral methods: theory and applications, Society for Industrial and Applied Mathematics, Philadelphia, 1977.
    • (1977)
    • Gottlieb, D.1    Orszag, S.A.2
  • 5
    • 0003902398 scopus 로고    scopus 로고
    • Spectral methods and their applications
    • 5 G. Ben‐Yu, Spectral methods and their applications, World Scientific, Singapore, 1998.
    • (1998)
    • Ben‐Yu, G.1
  • 6
    • 0346040186 scopus 로고    scopus 로고
    • On a Fourier method of embedding domains using an optimal distributed control
    • 6 L. Badea and P. Daripa, On a Fourier method of embedding domains using an optimal distributed control, Numer Algo 32 (2003), 261–273.
    • (2003) Numer Algo , vol.32 , pp. 261-273
    • Badea, L.1    Daripa, P.2
  • 7
    • 0015202899 scopus 로고
    • The direct solution of the discrete Poisson equation on irregular regions
    • 7 B. L. Buzbee, F. W. Dorr, J. A. George, and G. H. Golub, The direct solution of the discrete Poisson equation on irregular regions, SIAM J Numer Anal 8 (1971), 722–736.
    • (1971) SIAM J Numer Anal , vol.8 , pp. 722-736
    • Buzbee, B.L.1    Dorr, F.W.2    George, J.A.3    Golub, G.H.4
  • 8
    • 0000684010 scopus 로고
    • Domain embedding methods for the Stokes equations
    • 8 C. Borgers, Domain embedding methods for the Stokes equations, Numer Math 57 (5) (1990), 435–452.
    • (1990) Numer Math , vol.57 , Issue.5 , pp. 435-452
    • Borgers, C.1
  • 9
    • 0030137176 scopus 로고    scopus 로고
    • A spectral embedding method applied to the advection‐diffusion equation
    • 9 M. Elghaoui and R. Pasquetti, A spectral embedding method applied to the advection‐diffusion equation, J Comput Phys 125 (1996), 464–476.
    • (1996) J Comput Phys , vol.125 , pp. 464-476
    • Elghaoui, M.1    Pasquetti, R.2
  • 10
    • 14744294384 scopus 로고    scopus 로고
    • An immersed interface method for anisotropic elliptic problems on irregular domains in 2D
    • 10 M. A. Dumett and J. P. Keener, An immersed interface method for anisotropic elliptic problems on irregular domains in 2D, Numer Meth Part D, E 21 (2005), 397–420.
    • (2005) Numer Meth Part D, E , vol.21 , pp. 397-420
    • Dumett, M.A.1    Keener, J.P.2
  • 11
    • 17744397787 scopus 로고    scopus 로고
    • Modeling wave propagation in realistic heart geometries using the phase‐field method
    • 11 F. H. Fenton, E. M. Cherry, A. Karma, and W. J. Rappel, Modeling wave propagation in realistic heart geometries using the phase‐field method, Chaos 15 (2005), 013502.
    • (2005) Chaos , vol.15 , pp. 013502
    • Fenton, F.H.1    Cherry, E.M.2    Karma, A.3    Rappel, W.J.4
  • 12
    • 85120589030 scopus 로고    scopus 로고
    • 12 A. Bueno‐Orovio, V. M. Pérez‐García, and F. H. Fenton, Spectral methods for partial differential equations in irregular domains: the Spectral Smoothed Boundary Method, SIAM J Sci Comput, submitted. Preprint available at http://arXiv.org/abs/math.NA/0406327.
    • Bueno‐Orovio, A.1    Pérez‐García, V.M.2    Fenton, F.H.3
  • 13
    • 0031636309 scopus 로고    scopus 로고
    • FFTW: An adaptive software architecture for the FFT
    • 13 M. Frigo and S. G. Johnson, FFTW: An adaptive software architecture for the FFT, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE, Seattle, 1998, pp. 1381–1384.
    • (1998) , pp. 1381-1384
    • Frigo, M.1    Johnson, S.G.2
  • 14
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • 14 S. M. Allen and J. W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall Mater 27 (1979), 1084–1095.
    • (1979) Acta Metall Mater , vol.27 , pp. 1084-1095
    • Allen, S.M.1    Cahn, J.W.2
  • 15
    • 36949058437 scopus 로고
    • Concentration wave propagation in two‐dimensional liquid‐phase self‐oscillating system
    • 15 A. N. Zaikin and A. M. Zhabotinsky, Concentration wave propagation in two‐dimensional liquid‐phase self‐oscillating system, Nature 225 (1970), 535–537.
    • (1970) Nature , vol.225 , pp. 535-537
    • Zaikin, A.N.1    Zhabotinsky, A.M.2
  • 16
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • 16 A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J Physiol 117 (1952), 500–544.
    • (1952) J Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 17
    • 0017370379 scopus 로고
    • Reconstruction of the action potential of ventricular myocardial fibres
    • 17 G. W. Beeler and H. Reuter, Reconstruction of the action potential of ventricular myocardial fibres, J Physiol 268 (1977), 177–210.
    • (1977) J Physiol , vol.268 , pp. 177-210
    • Beeler, G.W.1    Reuter, H.2
  • 18
    • 4444320725 scopus 로고    scopus 로고
    • A computational model of the human left ventricular epicardial myocyte
    • 18 V. Iyer, R. Mazhari, and R. L. Winslow, A computational model of the human left ventricular epicardial myocyte, Biophys J 87 (2004), 1507–1525.
    • (2004) Biophys J , vol.87 , pp. 1507-1525
    • Iyer, V.1    Mazhari, R.2    Winslow, R.L.3
  • 19
    • 0001976781 scopus 로고    scopus 로고
    • Vortex dynamics in three‐dimensional continuous myocardium with fiber rotation: filament instability and fibrillation
    • 19 F. Fenton and A. Karma, Vortex dynamics in three‐dimensional continuous myocardium with fiber rotation: filament instability and fibrillation, Chaos 8 (1998), 20–47.
    • (1998) Chaos , vol.8 , pp. 20-47
    • Fenton, F.1    Karma, A.2
  • 20
    • 0032023898 scopus 로고    scopus 로고
    • Three‐dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy
    • 20 F. J. Vetter and A. D. McCulloch, Three‐dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy, Prog Biophys Mol Biol 69 (1998), 157–183.
    • (1998) Prog Biophys Mol Biol , vol.69 , pp. 157-183
    • Vetter, F.J.1    McCulloch, A.D.2
  • 21
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • 21 G. Strang, On the construction and comparison of difference schemes, SIAM J Numer Anal 5 (1968), 506–517.
    • (1968) SIAM J Numer Anal , vol.5 , pp. 506-517
    • Strang, G.1
  • 22
    • 0003683330 scopus 로고    scopus 로고
    • The DFT: an owner's manual for the discrete Fourier transform
    • 22 W. L. Briggs and V. E. Henson, The DFT: an owner's manual for the discrete Fourier transform, Society for Industrial and Applied Mathematics, Philadelphia, 2000.
    • (2000)
    • Briggs, W.L.1    Henson, V.E.2
  • 23
    • 0003417587 scopus 로고
    • Computational frameworks for the fast Fourier transform
    • 23 C. Van Loan, Computational frameworks for the fast Fourier transform, Society for Industrial and Applied Mathematics, Philadelphia, 1992.
    • (1992)
    • Van Loan, C.1
  • 24
    • 0036711265 scopus 로고    scopus 로고
    • Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity
    • 24 F. H. Fenton, E. M. Cherry, H. M. Hastings, and S. J. Evans, Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity, Chaos 12 (2002), 852–892.
    • (2002) Chaos , vol.12 , pp. 852-892
    • Fenton, F.H.1    Cherry, E.M.2    Hastings, H.M.3    Evans, S.J.4
  • 25
    • 85120594575 scopus 로고    scopus 로고
    • Efficient simulations in three dimensional complex geometries using the spectral smoothed boundary method
    • 25 A. Bueno‐Orovio, V. M. Pérez‐García, and F. H. Fenton, Efficient simulations in three dimensional complex geometries using the spectral smoothed boundary method, in preparation.
    • Bueno‐Orovio, A.1    Pérez‐García, V.M.2    Fenton, F.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.