Mesh boundaries in potential problems

An alternative method of handling the intersection of a regular mesh with an irregular boundary is described. Instead of stopping the mesh at the boundary, one extends it one or two meshes beyond, and assigns to the nodes that are exterior to the actual boundary fictitious potentials, which are images of the interior potentials, in such a manner that the potential gradients are correctly maintained up to the boundaries. Use of this method has led to a ray-tracing program in which the description of the boundary to the computer has been reduced to the simplest possible terms, namely, exactly that information that would be needed to draw the boundary with a ruler, compasses, and protractor.<
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