Domain decomposition for finite difference solutions of parabolic equations in wave propagation

The numerical determination of propagated fields in an inhomogeneous atmosphere and over irregular terrain requires specialized methods. One such method is the finite difference solution of a parabolic differential equation that approximates the governing elliptic differential equation. This method, as implemented in a computer model called IFDG, has been shown to reproduce the effects of diffraction, ducting, mixed path (e.g. land-sea-land), and multipath, and to agree with experimental results. However, it is not without limitations. Since it must solve a linear system of equations at each step in a marching process, the size of such a system is limited by the memory capacity of the computing machinery available, and by the amount of time one is willing to wait for the results. This can be particularly problematic for high altitudes and small mesh sizes required for higher frequency propagation in the presence of high, thick ducts. Some of these problems can be overcome with the use of parallel processors if the solution method could be properly formulated. One method for "parallelizing" this problem is to divide the solution domain into several sub-domains, with computations on each sub-domain performed by a different processor. The solution on a sub-domain requires a boundary condition to be defined on its inner boundary in a manner that minimizes adverse numerical effects. These aspects are addressed.