메뉴 건너뛰기




Volumn 229, Issue 23, 2010, Pages 8666-8683

An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere

Author keywords

Basis function; Convergence; Eigenvalue; Galerkin method; Jacobi polynomial; Kinematic dynamo; Zel'dovich theorem

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HARMONIC ANALYSIS; HARMONIC FUNCTIONS; KINEMATICS; POLYNOMIALS; RADIAL BASIS FUNCTION NETWORKS; REYNOLDS NUMBER; SPHERES;

EID: 77956898293     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.07.039     Document Type: Article
Times cited : (33)

References (39)
  • 1
    • 35348908359 scopus 로고    scopus 로고
    • Spectral solvers for spherical elliptic problems
    • Auteri F., Quartapelle L. Spectral solvers for spherical elliptic problems. J. Comput. Phys. 2007, 227:36-54.
    • (2007) J. Comput. Phys. , vol.227 , pp. 36-54
    • Auteri, F.1    Quartapelle, L.2
  • 2
    • 68549112694 scopus 로고    scopus 로고
    • Navier Stokes spectral solver in a sphere
    • Auteri F., Quartapelle L. Navier Stokes spectral solver in a sphere. J. Comput. Phys. 2009, 228:7197-7214.
    • (2009) J. Comput. Phys. , vol.228 , pp. 7197-7214
    • Auteri, F.1    Quartapelle, L.2
  • 3
    • 0002807741 scopus 로고
    • The principle of minimized iterations in the solution of the matrix eigenvalue problem
    • Arnoldi W.E. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quart. Appl. Math. 1951, 9:17-29.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 17-29
    • Arnoldi, W.E.1
  • 11
    • 0002734811 scopus 로고
    • The magnetic field of sunspots
    • Cowling T.G. The magnetic field of sunspots. Mon. Not. R. Astr. Soc. 1934, 94:39-48.
    • (1934) Mon. Not. R. Astr. Soc. , vol.94 , pp. 39-48
    • Cowling, T.G.1
  • 13
    • 0000594677 scopus 로고
    • Time-dependent kinematic dynamos with stationary flows
    • Dudley M.L., James R.W. Time-dependent kinematic dynamos with stationary flows. Proc. R. Soc. Lond. A 1989, 425:407-429.
    • (1989) Proc. R. Soc. Lond. A , vol.425 , pp. 407-429
    • Dudley, M.L.1    James, R.W.2
  • 15
    • 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. 1984, 55:461-484.
    • (1984) J. Comput. Phys. , vol.55 , pp. 461-484
    • Glatzmaier, G.A.1
  • 16
    • 34249019501 scopus 로고    scopus 로고
    • Mixed Jacobi-spherical harmonic spectral method for Navier Stokes equations
    • Guo B.Y., Huang W. Mixed Jacobi-spherical harmonic spectral method for Navier Stokes equations. Appl. Numer. Math. 2007, 57:939-961.
    • (2007) Appl. Numer. Math. , vol.57 , pp. 939-961
    • Guo, B.Y.1    Huang, W.2
  • 17
    • 0004719847 scopus 로고
    • Numerical solutions of the kinematic dynamo problem
    • Gubbins D. Numerical solutions of the kinematic dynamo problem. Phil. Trans. R. Soc. Lond. A 1973, 274:493-521.
    • (1973) Phil. Trans. R. Soc. Lond. A , vol.274 , pp. 493-521
    • Gubbins, D.1
  • 18
    • 33746394109 scopus 로고    scopus 로고
    • Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry
    • Gubbins D., Barber C.N., Gibbons S., Love J.J. Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry. Proc. R. Soc. Lond. A 2000, 456:1333-1353.
    • (2000) Proc. R. Soc. Lond. A , vol.456 , pp. 1333-1353
    • Gubbins, D.1    Barber, C.N.2    Gibbons, S.3    Love, J.J.4
  • 19
    • 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 2000, 32:773-797.
    • (2000) Int. J. Numer. Meth. Fluids , vol.32 , pp. 773-797
    • Hollerbach, R.1
  • 20
    • 0029416177 scopus 로고
    • Oscillatory internal shear layers in rotating and precessing flows
    • Hollerbach R., Kerswell R. Oscillatory internal shear layers in rotating and precessing flows. J. Fluid Mech. Digital Arch. 1995, 298:327-339.
    • (1995) J. Fluid Mech. Digital Arch. , vol.298 , pp. 327-339
    • Hollerbach, R.1    Kerswell, R.2
  • 21
    • 54349086329 scopus 로고    scopus 로고
    • Helical flow structure in a precessing sphere
    • Kida S., Nakayama K. Helical flow structure in a precessing sphere. J. Phys. Soc. Jpn 2008, 77(1-9):054401.
    • (2008) J. Phys. Soc. Jpn , vol.77 , Issue.1-9 , pp. 054401
    • Kida, S.1    Nakayama, K.2
  • 22
    • 0001224825 scopus 로고
    • A three-dimensional kinematic dynamo
    • Kumar S., Roberts P.H. A three-dimensional kinematic dynamo. Proc. R. Soc. Lond. A 1975, 344:235-238.
    • (1975) Proc. R. Soc. Lond. A , vol.344 , pp. 235-238
    • Kumar, S.1    Roberts, P.H.2
  • 24
    • 30844466160 scopus 로고    scopus 로고
    • A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry
    • Livermore P.W., Jackson A. A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry. Geophys. Astrophys. Fluid Dyn. 2005, 99(6):467-480.
    • (2005) Geophys. Astrophys. Fluid Dyn. , vol.99 , Issue.6 , pp. 467-480
    • Livermore, P.W.1    Jackson, A.2
  • 26
    • 77954456665 scopus 로고    scopus 로고
    • Quasi-L p norm orthogonal Galerkin expansions in sums of Jacobi polynomials, Numerical Algorithms
    • P.W. Livermore, G. Ierley, Quasi-L p norm orthogonal Galerkin expansions in sums of Jacobi polynomials, Numerical Algorithms, 2009, doi:10.1007/s11075-009-9353-5.
    • (2009)
    • Livermore, P.W.1    Ierley, G.2
  • 27
    • 73649120572 scopus 로고    scopus 로고
    • Galerkin orthogonal polynomials
    • Livermore P.W. Galerkin orthogonal polynomials. J. Comput. Phys. 2010, 229:2046-2060.
    • (2010) J. Comput. Phys. , vol.229 , pp. 2046-2060
    • Livermore, P.W.1
  • 28
    • 0000627077 scopus 로고
    • A spectral method for polar coordinates
    • Matsushima T., Marcus P.S. A spectral method for polar coordinates. J. Comput. Phys. 1995, 120(2):365-374.
    • (1995) J. Comput. Phys. , vol.120 , Issue.2 , pp. 365-374
    • Matsushima, T.1    Marcus, P.S.2
  • 29
    • 33845520317 scopus 로고    scopus 로고
    • Small-scale structures in three-dimensional magnetohydrodynamic turbulence
    • Mininni P.D., Pouquet A.G., Montgomery D.C. Small-scale structures in three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett., PRL 2006, 97(1-4):244503.
    • (2006) Phys. Rev. Lett., PRL , vol.97 , Issue.1-4 , pp. 244503
    • Mininni, P.D.1    Pouquet, A.G.2    Montgomery, D.C.3
  • 30
    • 34548458861 scopus 로고    scopus 로고
    • Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere
    • Mininni P.D., Montgomery D.C., Turner L. Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere. New J. Phys. 2007, 9:303.
    • (2007) New J. Phys. , vol.9 , pp. 303
    • Mininni, P.D.1    Montgomery, D.C.2    Turner, L.3
  • 32
    • 0035947945 scopus 로고    scopus 로고
    • Numerical study of the motions within a slowly precessing sphere at low Ekman number
    • Noir J., Jault D., Cardin P. Numerical study of the motions within a slowly precessing sphere at low Ekman number. J. Fluid Mech. 2001, 437:283-299.
    • (2001) J. Fluid Mech. , vol.437 , pp. 283-299
    • Noir, J.1    Jault, D.2    Cardin, P.3
  • 34
    • 67849135037 scopus 로고    scopus 로고
    • An application of one-sided Jacobi polynomials for spectral modeling of vector fields in polar coordinates
    • Sakai T., Redekopp L.G. An application of one-sided Jacobi polynomials for spectral modeling of vector fields in polar coordinates. J. Comput. Phys. 2009, 228:7069-7085.
    • (2009) J. Comput. Phys. , vol.228 , pp. 7069-7085
    • Sakai, T.1    Redekopp, L.G.2
  • 35
    • 0031232443 scopus 로고    scopus 로고
    • A Spectral Model for Two-Dimensional Incompressible Fluid Flow in a Circular Basin I. Mathematical Formulation
    • Verkley W.T.M. A Spectral Model for Two-Dimensional Incompressible Fluid Flow in a Circular Basin I. Mathematical Formulation. J. Comput. Phys. 1997, 136(1):100-114.
    • (1997) J. Comput. Phys. , vol.136 , Issue.1 , pp. 100-114
    • Verkley, W.T.M.1
  • 36
    • 0031232465 scopus 로고    scopus 로고
    • A spectral model for two-dimensional incompressible fluid flow in a circular basin II. Numerical examples
    • Verkley W.T.M. A spectral model for two-dimensional incompressible fluid flow in a circular basin II. Numerical examples. J. Comput. Phys. 1997, 136(1):115-131.
    • (1997) J. Comput. Phys. , vol.136 , Issue.1 , pp. 115-131
    • Verkley, W.T.M.1
  • 37
    • 0037108219 scopus 로고    scopus 로고
    • Inner-core conductivity in numerical dynamo simulations
    • Wicht J. Inner-core conductivity in numerical dynamo simulations. Phys. Earth Planet. Inter. 2002, 132(4):281-302.
    • (2002) Phys. Earth Planet. Inter. , vol.132 , Issue.4 , pp. 281-302
    • Wicht, J.1
  • 38
    • 0001462754 scopus 로고
    • The magnetic field in the two-dimensional motion of a conducting turbulent fluid
    • Zel'dovich Ya.B. The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP 1957, 4:460-462.
    • (1957) Sov. Phys. JETP , vol.4 , pp. 460-462
    • Zel'dovich, Y.B.1
  • 39
    • 33747113980 scopus 로고
    • Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode
    • Zernike F. Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode. Physica 1934, 1:689-704.
    • (1934) Physica , vol.1 , pp. 689-704
    • Zernike, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.