Octupole Last-Passage Algorithm for Charge Density on the Fichera-Corner Conducting Surface

Abstract

In a series of papers, it has been developing last-passage algorithms such as last-passage algorithm and off-centered last-passage algorithm on a flat conducting surface, quadrupole last-passage algorithm on an L-shaped conducting surface and so on, held at (non)constant potentials. In this paper, it further develops the last-passage algorithms on the Fichera-corner (cubic trihedral) conducting flat surface. To demonstrate the algorithm, it computes charge densities on the Fichera-corner conducting surface in 3D space and finds that the results agree very well with the ones from the Given-Hwang's original last-passage algorithm on a flat surface. Compared with the Given-Hwang's last-passage algorithm, the octupole last-passage one is very suitable for computing charge density near the corner of the Fichera-corner conducting surface.