Order reduction of stiff solvers at elastic multibody systems

Dedicated to W.C. Rheinboldt on the occasion of his 70th birthday
https://doi.org/10.1016/S0168-9274(98)00060-9Get rights and content

Abstract

Elastic multibody systems arise in the simulation of vehicles, robots, air- and spacecrafts. After semidiscretization in space, a partitioned differential-algebraic system of index 3 with large stiffness terms has to be solved. We investigate the behavior of numerical methods for stiff ODEs and DAEs at this problem class and show that strong order reductions may occur. Examples from structural dynamics and multibody systems illustrate the results.

References (26)

  • C. Lubich

    Extrapolation integrators for constrained multibody systems

    Impact Comput. Sci. Engrg.

    (1991)
  • B. Owren et al.

    Alternative integration methods for problems in structural dynamics

    Comput. Methods Appl. Mech. Engrg.

    (1995)
  • C. Arévalo et al.

    Stabilized multistep methods for index 2 Euler-Lagrange DAEs

    BIT

    (1996)
  • M. Arnold

    Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2

    BIT

    (1998)
  • J.C. Butcher

    The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods

    (1987)
  • S.L. Campbell et al.

    The index of an infinite dimensional implicit system

  • R. Courant et al.

    Methoden der Mathematischen Physik I

    (1968)
  • B.L. Ehle

    A-stable methods and Padé approximations to the exponential

    SIAM J. Math. Anal.

    (1973)
  • E. Hairer et al.

    The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

  • E. Hairer et al.

    Solving Ordinary Differential Equations II

    (1996)
  • T.J. Hughes

    The Finite Element Method

    (1987)
  • C. Lubich

    Integration of stiff mechanical systems by Runge-Kutta methods

    Z. Angew. Math. Phys.

    (1993)
  • W. Lucht et al.

    Linear partial differential-algebraic equations

  • Cited by (18)

    • On Rosenbrock methods for the time integration of nearly incompressible materials and their usage for nonlinear model reduction

      2014, Journal of Computational and Applied Mathematics
      Citation Excerpt :

      A similar approach has been chosen for standard singularly perturbed systems in [8], which lead to the so-called Scholz conditions, see below. Compare also the analysis for unconstrained second order systems in [4]. Another approach was given by Scholz [8] who suggested the use of methods which do fulfill the following conditions.

    • Mechanisms of coupling in river flow simulation systems

      2004, Journal of Computational and Applied Mathematics
      Citation Excerpt :

      RODASP is also able to solve the aforementioned index-2 problems efficiently. Similar observations have been made in [13]. The whole flow simulation and forecast system of the German Federal Institute of Hydrology is implemented in Fortran90 on a PC.

    View all citing articles on Scopus
    View full text