An accelerated domain decomposition procedure based on Robin transmission conditions
An accelerated domain decomposition procedure based on Robin transmission conditions is considered. A new method of convergence acceleration is proposed for some model problems. This method is more effective than that proposed by P. L. Lions. The model boundary value problem \[ -\Delta u= f,\quad x \in \Omega;\qquad u =0,\quad x \in \partial\Omega, \] where the domain \(\Omega=(-\infty,\infty) \times (0,1)\) is the unit strip, is considered. Under reasonable conditions the model problem is equivalent to solving the two problems \[ -\Delta u_i= f,\quad x\in \Omega_i;\qquad u_i=0, \quad x \in \partial\Omega \cap \partial\Omega_i, \quad i=1,2 \] subject to two consistency conditions. Test examples for two- and three-dimensional problems are considered. The results of computation are consistent with the theoretical estimates. Problems of realization for the proposed procedure are considered, too.
accelerated domain decomposition procedure
scientific article; zbMATH DE number 1087024