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Coupled Systems Mechanics
  Volume 3, Number 1, March 2014 , pages 1-25

Formulation, solution and CTL software for coupled thermomechanics systems
R. Niekamp, A. Ibrahimbegovic and H.G. Matthies

    In this work, we present the theoretical formulation, operator split solution procedure and partitioned software development for the coupled thermomechanical systems. We consider the general case with nonlinear evolution for each sub-system (either mechanical or thermal) with dedicated time integration scheme for each sub-system. We provide the condition that guarantees the stability of such an operator split solution procedure for fully nonlinear evolution of coupled thermomechanical system. We show that the proposed solution procedure can accommodate different evolution time-scale for different sub-systems, and allow for different time steps for the corresponding integration scheme. We also show that such an approach is perfectly suitable for parallel computations. Several numerical simulations are presented in order to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed-up of parallel computations, which follow from the adequate choice of the time step for each sub-problem. This work confirms that one can make the most appropriate selection of the time step with respect to the characteristic time-scale, carry out the separate computations for each sub-system, and then enforce the coupling to preserve the stability of the operator split computations. The software development strategy of direct linking the (existing) codes for each sub-system via Component Template Library (CTL) is shown to be perfectly suitable for the proposed approach.
Key Words
    coupled thermomechanical system; operator split procedure; nonlinear stability analysis; multiscale in time; code-coupling via CTL
R. Niekamp, A. Ibrahimbegovic and H.G. Matthies : Technical University Braunschweig, D-38092 Braunschweig, Germany
A. Ibrahimbegovic: Ecole Normale Superieure de Cachan, 94235 Cachan Cedex, France

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