EXTRAPOLATED SURFACE-CHARGE METHOD FOR CAPACITY CALCULATION OF POLYGONS AND POLYHEDRA

Effectiveness of extrapolation in calculating the electric capacities of polygons and polyhedra by SCM (surface charge method) is represented. In the case of a square, it is divided into n2 small squares as treated by Maxwell (n = 6). Empirically, extrapolation function of the form a1 n + a2 n2 + β1(log n) n + β2(logn) n2 is found to give the best result with the accuracy of more than six decimal figures at n = 28. In conventional methods without extrapolation, forbiddingly large n = 105 should be needed to obtain the same accuracy. Extrapolation without logarithmic terms (β1 = β2 = 0) does not work well. Thus, extrapolation using a logarithmic series and successive refinement leads to both accurate solutions and a saving in computational time. The origin of logarithmic terms is studied. The result of a numerical experiment suggests that logarithmic terms are needed when there are sharp edges in the configuration. © 1992.