Domain decomposition methods for mixed finite element approximations of wave problems (Q1972509)

The authors consider the following hyperbolic problem: \[ \begin{aligned} \rho u_{tt}= \nabla\cdot a(\nabla u) &= f\quad\text{in }\Omega\times (0,T),\\ \sqrt{a\rho}u_t+ a\nabla u\cdot{\mathbf n} &= 0\quad\text{on }\partial\Omega\times (0,T);\;u(0)= 0,\;u_t(0)= 0.\end{aligned} \] Here \(\Omega\) is a bounded domain of \(\mathbb{R}^d\), \(a\) and \(\rho\) are piecewise continuous functions bounded from below by positive constants, and \({\mathbf n}\) the outer normal to the frontier. The aim of the paper is to develop a numerical method to solve the above problem. This method combines a mixed finite element approximation and domain decomposition using both striped and box decompositions. The authors note that the method is well suited to heterogeneous media. A numerical example illustrated the method.