A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change

A domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces. Inside each subdomain, the method presented coincides with the second-order finite difference schemes traditionally used in geophysical modeling. However, the possibility of assigning to each subdomain its own space-step makes numerical simulations much less expensive. Another interest of the method lies in the fact that its hybrid variational formulation naturally leads to exact equations for gridpoints on the interfaces. Transposing Babuska--Brezzi's formalism on mixed and hybrid finite elements provides a suitable functional framework for this domain decomposition formulation and shows that the inf-sup condition remains the basic requirement for convergence to occur.