The LEM exponential integrator for advection-diffusion-reaction equations

Journal of Computational and Applied Mathematics

Volumn 210, Issue 1-2, 2007, Pages 56-63

  Caliari, Marco ^a   Vianello, Marco ^a   Bergamaschi, Luca ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Advection diffusion reaction equations; Exponential integrators; Interpolation; Leja points

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; INTERPOLATION; MATRIX ALGEBRA; POLYNOMIAL APPROXIMATION;

ADVECTION-DIFFUSION-REACTION EQUATIONS; EXPONENTIAL INTEGRATORS; LEJA POINTS; MIDPOINT INTEGRATORS;

INTEGRAL EQUATIONS;

EID: 34748841428     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.10.055     Document Type: Article

References (25)

1. Baglama J., Calvetti D., and Reichel L. Fast Leja points. Electron. Trans. Numer. Anal. 7 (1998) 124-140
2. L. Bergamaschi, M. Caliari, A. Martínez, M. Vianello, A parallel exponential integrator for large-scale discretizations of advection-diffusion models, in: Proceedings of Euro PVM MPI 2005, Sorrento, Italy, Lecture Notes in Computer Science, vol. 3666, Springer, Berlin, pp. 483-492.
3. L. Bergamaschi, M. Caliari, A. Martínez, M. Vianello, Comparing Leja and Krylov approximations of large scale matrix exponentials in: Proceedings of ICCS 2006, Reading, UK, Lecture Notes in Computer Science, vol. 3994, Springer, Berlin, pp. 685-692.
4. Bergamaschi L., Caliari M., and Vianello M. Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems. Numer. Linear Algebra Appl. 10 (2003) 271-289
5. L. Bergamaschi, M. Caliari, M. Vianello, The ReLPM exponential integrator for FE discretizations of advection-diffusion equations, in: Proceedings of ICCS 2004, Krakow, Lecture Notes in Computer Science, vol. 3039, Springer, Berlin, part IV, pp. 434-442.
6. Caliari M., Vianello M., and Bergamaschi L. Interpolating discrete advection-diffusion propagators at Leja sequences. J. Comput. Appl. Math. 172 (2004) 79-99
7. Cox S.M., and Matthews P.C. Exponential time differencing for stiff systems. J. Comput. Phys. 176 (2002) 430-455
8. Gallopoulos E., and Saad Y. Efficient solution of parabolic equations by Krylov subspace methods. SIAM J. Sci. Statist. Comput. 13 (1992) 1236-1264
9. González C., Ostermann A., and Thalhammer M. A second-order Magnus type integrator for non-autonomous parabolic problems. J. Comput. Appl. Math. 189 (2006) 142-156
10. Hochbruck M., and Lubich C. On Magnus integrators for time-dependent Schrödinger equations. SIAM J. Numer. Anal. 41 (2003) 945-963
11. Hochbruck M., Lubich C., and Selhofer H. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 19 (1998) 1552-1574
12. Hochbruck M., and Ostermann A. Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43 (2005) 1069-1090
13. Hundsdorfer W. Accuracy and stability of splitting with stabilizing corrections. Appl. Numer. Math. 42 (2002) 213-233
14. W. Hundsdorfer, J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction equations, Springer Series in Computational Mathematics, vol. 33, Springer, Berlin, 2003.
15. Krogstad S. Generalized integrating factor methods for stiff PDEs. J. Comput. Phys. 203 (2005) 72-88
16. Leja F. Sur certaines suites liées aux ensembles plas et leur application á la représentation conforme. Ann. Polon. Math. 4 (1957) 8-13
17. Moret I., and Novati P. An interpolatory approximation of the matrix exponential based on Faber polynomials. J. Comput. Appl. Math. 131 (2001) 361-380
18. Novati P. A polynomial method based on Feiér points for the computation of functions of unsymmetric matrices. Appl. Numer. Math. 44 (2003) 201-224
19. Pini G., and Gambolati G. Arnoldi and Crank-Nicolson methods for integration in time of the transport equation. Internat. J. Numer. Methods Fluids 35 (2001) 25-38
20. Reichel L. Newton interpolation at Leja points. BIT 30 (1990) 332-346
21. Schaefer M.J. A polynomial based iterative method for linear parabolic equations. J. Comput. Appl. Math. 29 (1990) 35-50
22. M. Thalhammer, A second-order Magnus type integrator for non-autonomous semilinear parabolic problems, preprint, University of Innsbruck, 2005.
23. R.S. Varga, Gershgorin and His Circles, Springer Series in Computational Mathematics, vol. 36, Springer, Berlin, 2004.
24. J.L. Walsh, Interpolation and approximation by rational functions in the complex domain, AMS Colloquium Publications, vol. XX, American Mathematical Society, Providence, RI, 1935.
25. Yeh G.T. Computational Subsurface Hydrology (1999), Kluwer, Dordrecht