Computing general companion matrices and stability regions of multirate methods

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 2, 2004, Pages 255-273

  Rodríguez Gómez, Gustavo ^a   González Casanova, Pedro ^b   Martínez Carballido, Jorge ^a  

^a INSTITUTO NACIONAL DE ASTROFÍSICA   (Mexico)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Absolute stability; Coupled systems; Semi implicit multirate methods; Simulation; Subcycling methods

Indexed keywords

DIFFERENTIAL SYSTEMS; DISCRETIZATIONS; SEMI-IMPLICIT MULTIRATE LINEAR DISCRETIZATIONS;

COMPUTATIONAL METHODS; INTERPOLATION; STABILITY;

MATRIX ALGEBRA;

MATHEMATICAL METHOD;

EID: 4444261911     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1065     Document Type: Article

References (24)

1. Gear CW. Numerical solution of ordinary differential equations: is there anything left to do? SIAM Review 1981; 23(l):10-24.
2. Rükgauer A, Schiehlen W. Simulation of modular dynamic systems. Mathematics and Computers in Simulation 1998; 46(5):535-542.
3. Günter M, Rentrop P. Multirate ROW methods and latency of electric circuits. Applied Numerical Mathematics 1993; 13(1):83-102.
4. Belytschko T, Yen HJ, Mullen R. Mixed methods for time integration. Computer Methods in Applied Mechanical Engineering 1979; 17:259-275.
5. Smolinski P, Sleith S, Belytschko T. Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations. Computational Mechanics 1996; 18(3):236-243.
6. Daniel WJT. The subcycled Newmark algorithm. Computational Mechanics 1997; 20(3):272-281.
7. Kværnø A. Stability of multirate Runge-Kutta schemes. International Journal of Differential Equations and Applications 2000; 1(1):97-105.
8. Hughes TJR, Belytschko T, Liu WK. Convergence of an element-partitioned subcycling algorithm for the semi-discrete heat equation. Numerical Methods for Partial Differential Equations 1987; 3(2):131-137.
9. Combescure A, Gravouil A. A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis study of the stability of subcycling algorithms in structural dynamics. Computer Methods in Applied Mechanics and Engineering 2002; 191:1129-1157.
10. Daniel WJT. A study of the stability of subcycling algorithms in structural dynamics. Computer Methods in Applied Mechanics and Engineering 1998; 156(1-4):1-13.
11. Wu YS, Smolinski P. A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule. Computer Methods in Applied Mechanics and Engineering 2000; 1877(3-4):641-660.
12. Andrus JF. Stability of a multirate method for numerical integration of ODE's. Computers and Mathematics with Applications 1993; 25(2):3-14.
13. Skelboe S, Andersen PU. Stability properties of backward Euler multirate formulas. SIAM Journal on Scientific and Statistical Computing 1989; 10(5):1000-1009.
14. Gear CW, Wells DR. Multirate linear multistep methods. BIT 1984; 24(4):484-502.
15. Wells DR. Multirate linear multistep methods for the solution of systems of ordinary differential equations. Report No. UIUCDCS-R-82-1093, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, 1982.
16. Gomm W. Stability analysis of explicit multirate methods. Mathematics and Computers in Simulation 1981; 23(1):34-50.
17. Owren B. Stability of multirate Runge-Kutta methods used in modular integration. Journal of Computational and Applied Mathematics 1995; 62(1):89-101.
18. Gear CW. Multirate methods for ordinary differential equations. Report No. UIUCDCS-F-74-880, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, 1974.
19. Skelboe S. The numerical solution of stiff systems of ordinary differential equations by multirate integration methods. Report No. ECR-150, ElektronikCentralen, Venlighedsvej 4, DK-2970 Hørsholm, Denmark, 1984.
20. Sand J, Skelboe S. Stability of backward Euler multirate methods and convergence of waveform relaxation. BIT 1992; 32(2):350-366.
21. Gear CW. Automatic multirate methods for ordinary differential equations. Report No. UIUCDCS-R-80-1000, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, 1980.
22. Golub GH, Loan CFV. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, London, 1996.
23. Zahreddine Z. On the Γ-stability of systems of differential equations in the Routh-Hurwitz and the Schur-Cohn cases. Bulletin of the Belgian Mathematical Society 1996; 3(3):363-368.
24. Lambert JD. Numerical Methods for Ordinary Differential Systems. Wiley: New York, 1991