Implementation of exponential Rosenbrock-type integrators

Applied Numerical Mathematics

Volumn 59, Issue 3-4, 2009, Pages 568-581

  Caliari, Marco ^a,b   Ostermann, Alexander ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Exponential integrators; Implementation of matrix functions; Newton interpolation; Parabolic evolution equations; Real Leja points; Rosenbrock type methods

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; FUNCTIONS; INTERPOLATION; MATLAB; PROBABILITY DENSITY FUNCTION;

EXPONENTIAL INTEGRATORS; IMPLEMENTATION OF MATRIX FUNCTIONS; NEWTON INTERPOLATION; PARABOLIC EVOLUTION EQUATIONS; REAL LEJA POINTS; ROSENBROCK-TYPE METHODS;

NUMERICAL METHODS;

EID: 58249085985     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.03.021     Document Type: Article

References (21)

1. Abdulle A., and Medovikov A.A. Second order Chebyshev methods based on orthogonal polynomials. Numer. Math. 90 (2001) 1-18
2. Bergamaschi L., Caliari M., Martínez A., and Vianello M. A parallel exponential integrator for large-scale discretizations of advection-diffusion models. In: Di Martino B., et al. (Ed). Recent Advances in Parallel Virtual Machine and Message Passing Interface. Lecture Notes in Computer Science vol. 3666 (2005), Springer, Berlin 483-492
3. Bergamaschi L., Caliari M., Martínez A., and Vianello M. Comparing Leja and Krylov approximations of large scale matrix exponentials. In: Alexandrov V.N., et al. (Ed). Computational Science. ICCS 2006. Lecture Notes in Computer Science vol. 3994 (2006), Springer, Berlin 685-692
4. Berland H., Skaflestad B., and Wright W. Expint - A Matlab package for exponential integrators. ACM Trans. Math. Software 33 1 (2007) Article 4
5. Caliari M., Vianello M., and Bergamaschi L. Interpolating discrete advection-diffusion propagators at Leja sequences. J. Comput. Appl. Math. 172 (2004) 79-99
6. Calvo M.P., and Palencia C. A class of explicit multistep exponential integrators for semilinear problems. Numer. Math. 102 (2006) 367-381
7. Gallopoulos E., and Saad Y. Efficient solution of parabolic equations by Krylov subspace methods. SIAM J. Sci. Statist. Comput. 13 (1992) 1236-1264
8. Hairer E., and Wanner G. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. second edition (1996), Springer, Berlin
9. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics vol. 840 (1981), Springer, Berlin
10. Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 (1997) 1911-1925
11. Hochbruck M., and Ostermann A. Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43 (2005) 1069-1090
12. Hochbruck M., and Ostermann A. Exponential integrators of Rosenbrock-type. Oberwolfach Reports 3 (2006) 1107-1110
13. M. Hochbruck, A. Ostermann, J. Schweitzer, Exponential Rosenbrock-type methods (2008), submitted for publication
14. A. Martínez, L. Bergamaschi, M. Caliari, M. Vianello, Efficient massively parallel implementation of the ReLPM exponential integrator for advection-diffusion models, 2006, Technical report
15. Novati P., and Moret I. RD-rational approximation of the matrix exponential operator. BIT 44 (2004) 595-615
16. Ostermann A., Thalhammer M., and Wright W. A class of explicit exponential general linear methods. BIT 46 (2006) 409-431
17. Reichel L. Newton interpolation at Leja points. BIT 30 (1990) 332-346
18. Schmelzer T., and Trefethen L.N. Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals. ETNA 29 (2007) 1-18
19. Sommeijer B.P., Shampine L.F., and Verwer J.G. RKC: An explicit solver for parabolic PDEs. J. Comp. Appl. Math. 88 (1997) 315-326
20. Tal-Ezer H. High degree polynomial interpolation in Newton form. SIAM J. Sci. Statist. Comput. 12 (1991) 648-667
21. van den Eshof J., and Hochbruck M. Preconditioning Lanczos approximations to the matrix exponential. SIAM J. Sci. Comp. 27 (2006) 1438-1457