Improved interface condition for 2D DomainDecomposition with corner

Dr. Chokri Chniti

June 13, 2007, 3:30 p.m. HF 136

We propose a domain decomposition method for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents corner singularities. Starting from the method used for regular interfaces, we derive a local improvement by matching the singularities, which are the first terms of the asymptotic expansion around the corner, provided by Kondratiev’s theory. Next, we compute the coefficients of the interface boundary conditions that minimize the number of iterations of the domain decomposition algorithm. This theoretical approach is tested numerically.