Using the triple integration scheme typically met in textbooks (see attachment), especially regarding the possibility of zero values of the denominator |r-r'|? Are there any alternatives?
I would consider using an iterative averaging algorithm to solve the differential equation directly given the current.
See http://en.wikipedia.org/wiki/Harmonic_function#The_mean_value_property
The technical term is "relaxation methods": http://en.wikipedia.org/wiki/Relaxation_(iterative_method)
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