Fine tuning interface relaxation methods for elliptic differential equations

Two simple interface relaxation techniques for solving elliptic differential equations are considered. A theoretical analysis is carried out at the differential level and “optimal” relaxation parameters are obtained for model problems. A comprehensive experimental numerical study for 1- and 2-dimensional problems is also presented. We present a complete analysis of convergence and optimum parameters for two 1-dimensional methods applied to Helmholtz equations: the averaging method AVE and the Robin-type method ROB. We then present experimental studies for 1- and 2-dimensional methods and more general equations. These studies confirm the theoretical results and suggest they are valid in these more general cases.