Domain decomposition with nonlocal interface boundary conditions

Abstract

Numerical algorithms based on domain decomposition are widely used for solving boundary value problems. They are especially efficient in combination with parallel computing algorithms. In addition, as well known, decomposition can work as an effective preconditioner. Among the domain decomposition approaches, non-overlapping algorithms are very attractive since they allow using independent meshes in sub-domains and avoid interpolation of the solution from one mesh to another. On the other hand, the efficiency of these methods strongly depends on the interface boundary conditions. In the current paper, for the first time a non-overlapping algorithm is developed with the use of nonlocal approximations of Steklov–Poincaré operator. The approach can be easily implemented. As demonstrated in the paper, both theoretically and numerically, the proposed approach can effectively be used for near-wall turbulence modeling.