Optimum mesh grading for finite-difference method

The coarseness error of the finite-difference (FD) method is studied analyzing a typical planar waveguide and a rectangular coaxial geometry. Results for equidistant and graded mesh are compared in terms of accuracy and numerical efforts. Because of the field singularities involved a graded mesh proves to be superior compared to the equidistant case. A grading strategy with optimum efficiency is presented. Furthermore, the results show that the most significant improvement in accuracy can be obtained by incorporating the edge behavior into the FD scheme