The Use of Shadow Regions in Multi Region FDM: High Precision Cylindrically Symmetric Electrostatics
A previously reported multi region FDM process, while producing very accurate solutions to the cylindrically symmetric electrostatic problem for points distant from region boundaries has been found to have abnormally high errors near the region boundaries themselves. A solution to this problem has been found that uses an extension of the definition of a region boundary line to a two line array. The resultant regions are called shadow regions and it is shown that their use in the multi region FDM process reduces the previous errors by ~ two orders of magnitude thus significantly extending the precisional capabilities of the multi region FDM method.
KeywordsFDM High Precision Calculations Multi Region FDM
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