A dimensionality reduction method for wave propagation in inhomogeneous media: the planewave layer interaction method

Standard techniques for wave propagation in inhomogeneous media such as finite-difference or finite-element methods usually deal with large size matrices. The author presents a solution method which reduces the problem by one spatial dimension and thereby reduces the computation effort. The method defines a propagator matrix for solution continuation over one space dimension and then uses the propagator to find the solution. The continuation effectively removes one dimension of the problem. The continuations are matrix multiplications which can be easily vectorized for speedy computation. The method is a generalization of the well-known Haskell matrix method associated with layered media. In the Haskell matrix method, the solution within each layer is a sum of decoupled modes, and each mode is propagated by itself. However, in the present method, the modes are coupled due to medium inhomogeneity, and the whole spectrum of modes is propagated simultaneously. The method can be interpreted in terms of plane waves interacting with laterally inhomogeneous layers.<>