We consider the parallel solution of elliptic boundary value problems discretized by domain decomposition methods on nonmatching grids involving mortar finite elements. We start from an initial nonoverlapping decomposition of the computational domain and independent triangulations of the subdomains realizing weak continuity conditions on the internal subdomain boundaries by means of appropriately chosen Lagrangean multipliers. The solution process features a preconditioned Lanczos iteration for the resulting saddle point problem using a block diagonal preconditioner and an adaptive local mesh refinement on the basis of residual based or hierarchical a posteriori error estimators.
In the parallel implementation of the code, the data related to the subdomains are appropriately distributed among the available processors.
The efficiency of the parallel implementation and the adaptive grid refinement process is illustrated by numerical simulation results obtained on a IBM SP2 for some selected test problems including potential flow around profiles.
This is joint work with Yu. Vassilevski and B. Wohlmuth.