Efficient Domain Decomposition Method for Acoustic Scattering in Multi-Layered Media

Abstract

The time-harmonic acoustic scattering in multi-layered media is modeled with an inhomogeneous Helmholtz equation for the pressure field. For example, such problems result from acoustic geological surveys. The exterior problem is truncated into a rectangle and an absorbing boundary condition is posed on its boundaries. A low-order finite difference discretization is performed on a uniform grid. Subdomains which overlap only on the interfaces are defined by the domains where the material properties are constants. Each of these subdomains is embedded into a larger rectangular domains with absorbing boundary conditions. The subdomain preconditioner is a Schur complement matrix and problems with it can be solved using a fast direct solver. Based on these subdomain preconditioners a Schwarz-type multiplicative preconditioner is defined. Preconditioned systems are solved using the GMRES iterations which are reduced on a neighborhood of the interfaces. Numerical experiments demonstrate that problems with millions of unknowns can be solved in some tens of seconds on a PC. Furthermore, the convergence rate deteriorates only mildly when frequency is increased.