Domain decomposition methods for mixed finite element approximations of wave problems

The main goal of this paper is to address the numerical solution of wave problems by a numerical method combining a mixed finite element approximation and domain decomposition, possibly with nonmatching grids. The method to be discussed is well suited to heterogeneous media. Due to the use of mixed finite element approximations, crossing vertices do not introduce additional difficulties so that box domain decompositions are as easy to treat as striped decompositions. Interface conditions are treated by a method combining Lagrange multipliers and a conjugate gradient algorithm. The results of numerical experiments will be presented.