Optimized Schwarz methods for heterogeneous heat transfer problems

Abstract

We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive the error equation and obtain the convergence factor. The optimal transmission operators are nonlocal, and thus inconvenient to use in practice. We introduce three versions of local approximations for the transmission parameter, and provide a detailed analysis at the continuous level in each case to identify the best local transmission conditions. Numerical experiments are presented to illustrate the performance of each local transmission condition. As shown in our analysis, local transmission conditions, which are scaled appropriately with respect to the heterogeneous diffusion coefficients, are more efficient and robust especially when the discontinuity of the diffusion coefficient is large.