Bulletin of the
Korean Mathematical Society BKMS

Based on a particular overlapping domain decomposition \linebreak technique, a parallel finite element discretization algorithm for the generalized Stokes equations is proposed and investigated. In this algorithm, each processor computes a local approximate solution in its own subdomain by solving a global problem on a mesh that is fine around its own subdomain and coarse elsewhere, and hence avoids communication with other processors in the process of computations. This algorithm has low communication complexity. It only requires the application of an existing sequential solver on the global meshes associated with each subdomain, and hence can reuse existing sequential software. Numerical results are given to demonstrate the effectiveness of the parallel algorithm.

Keywords: generalized Stokes problem, finite element, parallel algorithm, parallel computing, domain decomposition

MSC numbers: Primary 65N30, 65N55, 76D07, 76M10