A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems

Authors:
Zheming Zheng;Bernd Simeon;Linda Petzold
Affiliations:
Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA;Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, D-85748 Garching bei München, Germany;Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A fully explicit, stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations (PDEs) is presented. Writing the semi-discretized equations as a differential-algebraic equation (DAE) system where the interface continuity constraints between subdomains are enforced by Lagrange multipliers, the method uses the Runge-Kutta-Chebyshev projection scheme to integrate the DAE explicitly and to enforce the constraints by a projection. With mass lumping techniques and node-to-node matching grids, the method is fully explicit without solving any linear system. A stability analysis is presented to show the extended stability property of the method. The method is straightforward to implement and to parallelize. Numerical results demonstrate that it has excellent performance.