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Volumn 172, Issue 1, 2004, Pages 79-99

Interpolating discrete advection-diffusion propagators at Leja sequences

Author keywords

Advection diffusion problem; Exponential operator; Leja sequence; Polynomial interpolation; Sparse matrix

Indexed keywords

DIFFUSION; FINITE DIFFERENCE METHOD; INTERPOLATION; MATRIX ALGEBRA; SPECTRUM ANALYSIS;

EID: 4444264388     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.11.015     Document Type: Article
Times cited : (63)

References (42)
  • 2
    • 0037253743 scopus 로고    scopus 로고
    • Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems
    • Bergamaschi L. Caliari M. Vianello M. Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems Numer. Linear Algebra Appl. 10 3 2003 271-289
    • (2003) Numer. Linear Algebra Appl. , vol.10 , Issue.3 , pp. 271-289
    • Bergamaschi, L.1    Caliari, M.2    Vianello, M.3
  • 3
    • 0034382829 scopus 로고    scopus 로고
    • Efficient computation of the exponential operator for large, sparse, symmetric matrices
    • Bergamaschi L. Vianello M. Efficient computation of the exponential operator for large, sparse, symmetric matrices Numer. Linear Algebra Appl. 7 1 2000 27-45
    • (2000) Numer. Linear Algebra Appl. , vol.7 , Issue.1 , pp. 27-45
    • Bergamaschi, L.1    Vianello, M.2
  • 4
    • 4444335023 scopus 로고    scopus 로고
    • Ph.D. Thesis in Computational Mathematics, University of Padova, advisors M. Vianello and L. Bergamaschi, URL http://www.math.unipd.it/~mcaliari/pdf/phd.pdf
    • M. Caliari, Efficient implementation of exponential integrators for 2D and 3D advection-diffusion equations, Ph.D. Thesis in Computational Mathematics, University of Padova, advisors M. Vianello and L. Bergamaschi, 2003, URL http://www.math.unipd.it/~mcaliari/pdf/phd.pdf http://www.math.unipd.it/~mcaliari/pdf/phd.pdf
    • (2003) Efficient Implementation of Exponential Integrators for 2D and 3D Advection-diffusion Equations
    • Caliari, M.1
  • 5
    • 84953600891 scopus 로고
    • A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
    • Crank J. Nicolson P. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type Proc. Cambridge Philos. Soc. 43 1947 50-67
    • (1947) Proc. Cambridge Philos. Soc. , vol.43 , pp. 50-67
    • Crank, J.1    Nicolson, P.2
  • 6
    • 0000446481 scopus 로고
    • Two polynomial methods for calculating functions of symmetric matrices
    • Druskin V.L. Knizhnerman L.A. Two polynomial methods for calculating functions of symmetric matrices Comput. Math. Math. Phys. 29 6 1989 112-121
    • (1989) Comput. Math. Math. Phys. , vol.29 , Issue.6 , pp. 112-121
    • Druskin, V.L.1    Knizhnerman, L.A.2
  • 7
    • 84966244685 scopus 로고
    • Computation of Faber series with application to numerical polynomial approximation in the complex plane
    • Ellacott S.W. Computation of Faber series with application to numerical polynomial approximation in the complex plane Math. Comput. 40 162 1983 575-587
    • (1983) Math. Comput. , vol.40 , Issue.162 , pp. 575-587
    • Ellacott, S.W.1
  • 8
    • 84968521861 scopus 로고
    • Newton interpolation in Fejér and Chebyshev points
    • Fischer B. Reichel L. Newton interpolation in Fejér and Chebyshev points Math. Comput. 53 187 1989 265-278
    • (1989) Math. Comput. , vol.53 , Issue.187 , pp. 265-278
    • Fischer, B.1    Reichel, L.2
  • 9
    • 0024779854 scopus 로고
    • A method for exponential propagation of large system of stiff nonlinear differential equations
    • Friesner R.A. Tuckerman L.S. Dornblaser B.C. Russo T.V. A method for exponential propagation of large system of stiff nonlinear differential equations J. Sci. Comput. 4 4 1989 327-354
    • (1989) J. Sci. Comput. , vol.4 , Issue.4 , pp. 327-354
    • Friesner, R.A.1    Tuckerman, L.S.2    Dornblaser, B.C.3    Russo, T.V.4
  • 10
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov subspace methods
    • Gallopoulos E. Saad Y. Efficient solution of parabolic equations by Krylov subspace methods SIAM J. Sci. Statist. Comput. 13 5 1992 1236-1264
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , Issue.5 , pp. 1236-1264
    • Gallopoulos, E.1    Saad, Y.2
  • 11
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential
    • Hochbruck M. Lubich C. On Krylov subspace approximations to the matrix exponential 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
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • Hochbruck M. Lubich C. Selhofer H. Exponential integrators for large systems of differential equations SIAM J. Sci. Comput. 19 5 1998 1552-1574
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.5 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, C.2    Selhofer, H.3
  • 14
    • 0002497330 scopus 로고
    • The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
    • Kershaw D.S. The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations J. Comput. Phys. 26 1 1978 43-65
    • (1978) J. Comput. Phys. , vol.26 , Issue.1 , pp. 43-65
    • Kershaw, D.S.1
  • 15
    • 0033571420 scopus 로고    scopus 로고
    • Analysis of operator splitting for advection-diffusion-reaction problems for air-pollution modelling
    • Lanser D. Verwer J.G. Analysis of operator splitting for advection-diffusion-reaction problems for air-pollution modelling J. Comput. Appl. Math. 111 1-2 1999 201-216
    • (1999) J. Comput. Appl. Math. , vol.111 , Issue.1-2 , pp. 201-216
    • Lanser, D.1    Verwer, J.G.2
  • 16
    • 0033149563 scopus 로고    scopus 로고
    • Modified Krylov acceleration for parallel environments
    • Le Calvez C. Saad Y. Modified Krylov acceleration for parallel environments Appl. Numer. Math. 30 2-3 1999 191-212
    • (1999) Appl. Numer. Math. , vol.30 , Issue.2-3 , pp. 191-212
    • Le Calvez, C.1    Saad, Y.2
  • 18
    • 0040361621 scopus 로고
    • Sur certaines suites liées aux ensembles plans et leur application à la représentation conforme
    • Leja F. Sur certaines suites liées aux ensembles plans et leur application à la représentation conforme Ann. Polon. Math. 4 1957 8-13
    • (1957) Ann. Polon. Math. , vol.4 , pp. 8-13
    • Leja, F.1
  • 19
    • 0001256129 scopus 로고
    • The Tchebychev iteration for nonsymmetric linear systems
    • Manteuffel T.A. The Tchebychev iteration for nonsymmetric linear systems Numer. Math. 28 3 1977 307-327
    • (1977) Numer. Math. , vol.28 , Issue.3 , pp. 307-327
    • Manteuffel, T.A.1
  • 20
    • 34250261642 scopus 로고
    • Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration
    • Manteuffel T.A. Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration Numer. Math. 31 2 1978/1979 183-208
    • (1978) Numer. Math. , vol.31 , Issue.2 , pp. 183-208
    • Manteuffel, T.A.1
  • 22
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • Moler C. van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later SIAM Rev. 45 2003 3-49
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.1    van Loan, C.2
  • 23
    • 0035416395 scopus 로고    scopus 로고
    • The computation of functions of matrices by truncated Faber series
    • Moret I. Novati P. The computation of functions of matrices by truncated Faber series Numer. Funct. Anal. Optim. 22 5-6 2001 697-719
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , Issue.5-6 , pp. 697-719
    • Moret, I.1    Novati, P.2
  • 24
    • 0035360316 scopus 로고    scopus 로고
    • An interpolatory approximation of the matrix exponential based on Faber polynomials
    • Moret I. Novati P. An interpolatory approximation of the matrix exponential based on Faber polynomials J. Comput. Appl. Math. 131 1-2 2001 361-380
    • (2001) J. Comput. Appl. Math. , vol.131 , Issue.1-2 , pp. 361-380
    • Moret, I.1    Novati, P.2
  • 27
    • 0037214140 scopus 로고    scopus 로고
    • A polynomial method based on Fejér points for the computation of functions of unsymmetric matrices
    • Novati P. A polynomial method based on Fejér points for the computation of functions of unsymmetric matrices Appl. Numer. Math. 44 1-2 2003 201-224
    • (2003) Appl. Numer. Math. , vol.44 , Issue.1-2 , pp. 201-224
    • Novati, P.1
  • 28
    • 0037253980 scopus 로고    scopus 로고
    • Solving linear initial value problems by Faber polynomials
    • Novati P. Solving linear initial value problems by Faber polynomials Numer. Linear Algebra Appl. 10 3 2003 247-270
    • (2003) Numer. Linear Algebra Appl. , vol.10 , Issue.3 , pp. 247-270
    • Novati, P.1
  • 29
    • 0035109252 scopus 로고    scopus 로고
    • Arnoldi and Crank-Nicolson methods for integration in time of the transport equation
    • Pini G. Gambolati G. Arnoldi and Crank-Nicolson methods for integration in time of the transport equation Internat. J. Numer. Methods Fluids 35 2001 25-38
    • (2001) Internat. J. Numer. Methods Fluids , vol.35 , pp. 25-38
    • Pini, G.1    Gambolati, G.2
  • 31
    • 0028695631 scopus 로고
    • Pseudospectra of the convection-diffusion operator
    • Reddy S.C. Trefethen L.N. Pseudospectra of the convection-diffusion operator SIAM J. Appl. Math. 54 6 1994 1634-1649
    • (1994) SIAM J. Appl. Math. , vol.54 , Issue.6 , pp. 1634-1649
    • Reddy, S.C.1    Trefethen, L.N.2
  • 32
    • 0012089844 scopus 로고
    • Newton interpolation at Leja points
    • Reichel L. Newton interpolation at Leja points BIT 30 2 1990 332-346
    • (1990) BIT , vol.30 , Issue.2 , pp. 332-346
    • Reichel, L.1
  • 33
    • 0000186540 scopus 로고
    • Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
    • Reichel L. Trefethen L.N. Eigenvalues and pseudo-eigenvalues of Toeplitz matrices Linear Algebra Appl. 162/164 1992 153-185
    • (1992) Linear Algebra Appl. , vol.162 , Issue.164 , pp. 153-185
    • Reichel, L.1    Trefethen, L.N.2
  • 34
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Saad Y. Analysis of some Krylov subspace approximations to the matrix exponential operator SIAM J. Numer. Anal. 29 1 1992 209-228
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 209-228
    • Saad, Y.1
  • 35
    • 0025245135 scopus 로고
    • A polynomial based iterative method for linear parabolic equations
    • Schaefer M.J. A polynomial based iterative method for linear parabolic equations J. Comput. Appl. Math. 29 1 1990 35-50
    • (1990) J. Comput. Appl. Math. , vol.29 , Issue.1 , pp. 35-50
    • Schaefer, M.J.1
  • 36
    • 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. Software 24 1 1998 130-156
    • (1998) ACM Trans. Math. Software , vol.24 , Issue.1 , pp. 130-156
    • Sidje, R.B.1
  • 37
    • 0242510121 scopus 로고
    • An accurate and efficient scheme for propagating the time dependend Schrödinger equation
    • Tal-Ezer H. Kosloff R. An accurate and efficient scheme for propagating the time dependend Schrödinger equation J. Chem. Phys. 81 9 1984 3967-3971
    • (1984) J. Chem. Phys. , vol.81 , Issue.9 , pp. 3967-3971
    • Tal-Ezer, H.1    Kosloff, R.2
  • 38
    • 0009694082 scopus 로고
    • Low-order polynomial approximation of propagators for the time-dependent Schrödinger equation
    • Tal-Ezer H. Kosloff R. Cerien C. Low-order polynomial approximation of propagators for the time-dependent Schrödinger equation J. Comput. Phys. 100 1 1992 179-187
    • (1992) J. Comput. Phys. , vol.100 , Issue.1 , pp. 179-187
    • Tal-Ezer, H.1    Kosloff, R.2    Cerien, C.3
  • 39
    • 85011519633 scopus 로고    scopus 로고
    • Computation of pseudospectra
    • A. Iserles (Ed.), Cambridge University Press, Cambridge
    • L.N. Trefethen, Computation of pseudospectra, in: A. Iserles (Ed.), Acta Numerical, Vol. 8, Cambridge University Press, Cambridge, 1999, pp. 247-295.
    • (1999) Acta Numerical , vol.8 , pp. 247-295
    • Trefethen, L.N.1
  • 40
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • van der Vorst H.A. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 13 2 1992 631-644
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , Issue.2 , pp. 631-644
    • van der Vorst, H.A.1
  • 41
    • 0003339238 scopus 로고
    • Numerical methods for advection-diffusion problems
    • Eds. Friedrivk, Vieweg and Sohn, Braunschweig
    • C.B. Vreugdenhil, B. Koren (Eds.), Numerical methods for advection-diffusion problems, Notes on Numerical Fluid Mechanics, Vol. 45, Friedrivk, Vieweg and Sohn, Braunschweig, 1993.
    • (1993) Notes on Numerical Fluid Mechanics , vol.45
    • Vreugdenhil, C.B.1    Koren, B.2


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