An operator splitting scheme with a distributed Lagrange multiplier based fictitious domain method for wave propagation problems (Q1780679)

The article describes a method for the numerical solution of the time dependent problem of the obstacle scattering based on an extension of the domain and the use of a mixed finite element spatial discretisation together with a central difference time discretisation. The interaction with the obstacle is handled by an operator splitting. The approach is analyzed for a one-dimensional wave problem. Several important properties of the distributed multiplier method are also demonstrated. The efficiency of the method is shown on numerical results for two-dimensional wave problems. The work is related to the paper by \textit{F. Collino, P. Joly} and \textit{F. Millot} [J. Comput. Phys. 138, No. 2, 907--938 (1997; Zbl 1126.78311)].