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

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.