Abstract
The Laplace equation was solved in the interelectrode space for shaped electrodes (two-dimensional case) by the method of finite differences (FDM), Galerkin's method (GM), and collocation method (CM). A comparison shows that for electrode shapes with a continuously changing surface (continuous first and second derivatives), the solutions by all three methods are equivalent, giving identical distribution of local current densities on the electrode surface. The use of GM and CM is, however, not practical because of high requirements on the computer time and memory as compared with FDM. Moreover, the GM and CM fail in the case of discontinuities in the electrode shape.
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