The Effect of Irregular Interfaces on the BDDC Method for the Navier-Stokes Equations

摘要

We have investigated the influence of an irregular interface on the performance of the BDDC method for Navier-Stokes equations. A benchmark problem of a narrowing channel in 2D and 3D has been proposed to evaluate the impact of aspect ratios of finite elements on the convergence of iterative solvers for the arising system of equations. A simple partitioning strategy based on an application of a regular geometric division of simple sub-blocks of the computational mesh has been presented. This approach was applied to the benchmark channel problems. The number of BiCGstab iterations required when using the geometric partitioner has been compared to the number of iterations required when using a graph partitioner. This rather simple idea has dramatically improved convergence of our BDDCML solver. Our next aim is to apply the idea to real geometries of hydrostatic bearings with block structured meshes. The preliminary results in this direction are very promising.