메뉴 건너뛰기




Volumn 220, Issue 2, 2007, Pages 824-838

An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell

Author keywords

Exponential time differencing; Magnetohydrodynamics; Spectral method; Stiff system

Indexed keywords

MAGNETOHYDRODYNAMICS;

EID: 33845646844     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.05.029     Document Type: Article
Times cited : (12)

References (28)
  • 2
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • Cox S.M., and Matthews P.C. Exponential time differencing for stiff systems. J. Comput. Phys. 176 (2002) 430-455
    • (2002) J. Comput. Phys. , vol.176 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 3
    • 85190106744 scopus 로고    scopus 로고
    • B.V. Minchev, W.M. Wright, A review of exponential integrators for first order semi-linear problems, Norwegian University of Science and Tech., Numerics (Rep. 2).
  • 6
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • Hochbruck M., Lubich C., and Selhofer H. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comp. 19 5 (1998) 1552-1574
    • (1998) SIAM J. Sci. Comp. , vol.19 , Issue.5 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, C.2    Selhofer, H.3
  • 7
    • 10844237437 scopus 로고    scopus 로고
    • Generalized integrating factor methods for stiff PDEs
    • Krogstad S. Generalized integrating factor methods for stiff PDEs. J. Comput. Phys. 203 (2005) 72-88
    • (2005) J. Comput. Phys. , vol.203 , pp. 72-88
    • Krogstad, S.1
  • 8
    • 0001025210 scopus 로고    scopus 로고
    • A new class of time discretization schemes for the solution of nonlinear PDEs
    • Beylkin G., Keiser J.M., and Vozovoi L. A new class of time discretization schemes for the solution of nonlinear PDEs. J. Comput. Phys. 147 (1997) 362-387
    • (1997) J. Comput. Phys. , vol.147 , pp. 362-387
    • Beylkin, G.1    Keiser, J.M.2    Vozovoi, L.3
  • 9
    • 22544474620 scopus 로고    scopus 로고
    • Fourth-order time stepping for stiff PDEs
    • Kassam A.-K., and Trefethen L.N. Fourth-order time stepping for stiff PDEs. SIAM J. Sci. Comp. 26 4 (2005) 1214-1233
    • (2005) SIAM J. Sci. Comp. , vol.26 , Issue.4 , pp. 1214-1233
    • Kassam, A.-K.1    Trefethen, L.N.2
  • 10
    • 1842865578 scopus 로고    scopus 로고
    • A Schur-Parlett algorithm for computing matrix functions
    • Davies P., and Higham N.J. A Schur-Parlett algorithm for computing matrix functions. SIAM J. Matrix Anal. Appl. 25 2 (2003) 464-485
    • (2003) SIAM J. Matrix Anal. Appl. , vol.25 , Issue.2 , pp. 464-485
    • Davies, P.1    Higham, N.J.2
  • 11
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 5 (1997) 1911-1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 12
    • 85190160630 scopus 로고    scopus 로고
    • A.-K. Kassam, High order timestepping for stiff semilinear partial differential equations, Ph.D. Thesis, University of Oxford, 2004.
  • 13
    • 0001942937 scopus 로고
    • Spectral methods in time for parabolic problems
    • Tal-Ezer H. Spectral methods in time for parabolic problems. SIAM J. Numer. Anal. 26 1 (1989) 1-11
    • (1989) SIAM J. Numer. Anal. , vol.26 , Issue.1 , pp. 1-11
    • Tal-Ezer, H.1
  • 14
    • 0000130158 scopus 로고
    • Numerical simulations of stellar convective dynamos. I. The model and method
    • Glatzmaier G.A. Numerical simulations of stellar convective dynamos. I. The model and method. J. Comput. Phys. 55 (1984) 461-484
    • (1984) J. Comput. Phys. , vol.55 , pp. 461-484
    • Glatzmaier, G.A.1
  • 15
    • 0034655860 scopus 로고    scopus 로고
    • A spectral solution of the magneto-convection equations in spherical geometry
    • Hollerbach R. A spectral solution of the magneto-convection equations in spherical geometry. Int. J. Numer. Meth. Fluids 32 (2000) 773-797
    • (2000) Int. J. Numer. Meth. Fluids , vol.32 , pp. 773-797
    • Hollerbach, R.1
  • 16
    • 0033618580 scopus 로고    scopus 로고
    • Spectral methods for the simulations of incompressible flows in spherical shells
    • Tilgner A. Spectral methods for the simulations of incompressible flows in spherical shells. Int. J. Numer. Meth. Fluids 30 (1999) 713-724
    • (1999) Int. J. Numer. Meth. Fluids , vol.30 , pp. 713-724
    • Tilgner, A.1
  • 17
    • 30844466160 scopus 로고    scopus 로고
    • A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry
    • Livermore P.W., and Jackson A. A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry. Geophys. Astrophys. Fluid Dyn. 99 6 (2005) 467-480
    • (2005) Geophys. Astrophys. Fluid Dyn. , vol.99 , Issue.6 , pp. 467-480
    • Livermore, P.W.1    Jackson, A.2
  • 18
    • 0347511542 scopus 로고    scopus 로고
    • A fast transform for spherical harmonics
    • Mohlenkamp M. A fast transform for spherical harmonics. J. Fourier Anal. Appl. 5 2/3 (1999) 159-184
    • (1999) J. Fourier Anal. Appl. , vol.5 , Issue.2-3 , pp. 159-184
    • Mohlenkamp, M.1
  • 19
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, Twenty five years later
    • Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, Twenty five years later. SIAM Rev. 45 1 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 22
    • 23944514603 scopus 로고    scopus 로고
    • Application of the pseudo-spectral method for a 2D eigenvalue problems in elasticity
    • Talbot C.J., and Crampton A. Application of the pseudo-spectral method for a 2D eigenvalue problems in elasticity. Numer. Alg. 38 (2005) 95-110
    • (2005) Numer. Alg. , vol.38 , pp. 95-110
    • Talbot, C.J.1    Crampton, A.2
  • 23
    • 0000689353 scopus 로고
    • The psuedospectral method for solving differential eigenvalue problems
    • Huang W., and Sloan D.M. The psuedospectral method for solving differential eigenvalue problems. J. Comput. Phys. 111 (1994) 399-409
    • (1994) J. Comput. Phys. , vol.111 , pp. 399-409
    • Huang, W.1    Sloan, D.M.2
  • 25
    • 85190162493 scopus 로고    scopus 로고
    • B.V. Minchev, Computing analytic matrix functions for a class of exponential integrators, Department of Informatics, University of Bergen, Norway: Reports in Informatics (Rep. 278).
  • 26
    • 0032010619 scopus 로고    scopus 로고
    • Expokit: A software package for computing matrix exponentials
    • Sidje R.B. Expokit: A software package for computing matrix exponentials. ACM Trans. Math. Soft. 24 1 (1998) 130-156
    • (1998) ACM Trans. Math. Soft. , vol.24 , Issue.1 , pp. 130-156
    • Sidje, R.B.1
  • 28
    • 4243913217 scopus 로고
    • Numerical evidence of fast dynamo action in a spherical shell
    • Hollerbach R., Galloway D.J., and Proctor M.R.E. Numerical evidence of fast dynamo action in a spherical shell. Phys. Rev. Lett. 74 16 (1995) 3145-3148
    • (1995) Phys. Rev. Lett. , vol.74 , Issue.16 , pp. 3145-3148
    • Hollerbach, R.1    Galloway, D.J.2    Proctor, M.R.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.