Abstract
A stepwise coupled-mode solution with the use of the direct global matrix approach is proposed. This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry. With the use of the direct global matrix approach, this method is numerically stable. In addition, by introducing appropriately normalized range solutions, this model is free from the numerical overflow problem. Furthermore, we put forward general source conditions for the line-source problem in plane geometry. As a result, this method is capable of addressing the scenario with a line source on top of a sloping bottom. Closed-form expressions for coupling matrices are derived and applied for handling problems with perfectly reflecting boundaries as well as a homogeneous water column. The numerical simulations indicate that the proposed model is accurate, efficient, and numerically stable. Consequently, this model can serve as a benchmark model in range-dependent propagation modeling.
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