Non-overlapping Schwarz methods with optimized transmission conditions for the Helmholtz equation

摘要

The development of efficient transmission conditions for the Schwarz method without overlap is an important area of current research. The techniques developed in recent years mainly consist of algebraic approximations of the discrete transparent operator or optimized approximations of the continuous transparent operator. These optimized approximations are currently based on an analytical approach involving a minimization problem over all the available frequencies and using the L~∞ - norm. In this paper, new numerical optimization techniques are investigated. These original approaches allow selection of the frequency range for the minimization problem which is based on the L~p-norm. New numerical experiments performed on a model problem demonstrate the performance and the robustness of the proposed optimization techniques in the particular cases p = 1 and p = + ∞. Applications to industrial automotive problems confirm the efficiency of these techniques when using arbitrary mesh partitions.