SEMI-DIRECT PROCEDURE USING A LOCAL RELAXATION FACTOR AND ITS APPLICATION TO AN INTERNAL FLOW PROBLEM.

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, can be circumvented by a semi-direct procedure, i. e. , an iterative procedure using fast direct solvers. In this paper, an efficient semi-direct procedure is presented which is easy to implement and applicable to a variety of boundary conditions. The current procedure also possesses other highly desirable properties, i. e. , the convergence rate does not decrease with an increase of grid cell aspect ratio, and the convergence rate can be estimated using the coefficients of the partial differential equation being solved.