Abstract
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 n 2 small squares as treated by Maxwell ( n = 6). Empirically, extrapolation function of the form a 1 n + a 2 n 2 + β 1( log n) n + β 2( logn) n 2 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 = 10 5 should be needed to obtain the same accuracy. Extrapolation without logarithmic terms ( β 1 = β 2 = 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.
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