座標を使わない曲面上の3角形格子差分法

抄録

We study numerically a finite difference method (FDM) on 2-dimensional curved surfaces. A 2-dimensional surface is discretized by piecewise linear triangles, to form what is called a triangulated surface. We present a technique for discretization of Poisson's equation on triangulated surfaces. Our technique is examined for Laplace's equation on a flat domain and on a spherical domain, and the results are compared, and found to be in good agreement, with those obtained by known FDMs. The most remarkable feature of our technique is a coordinate-free property, i. e. the only data necessary to carry out a FDM are the lengths of bonds of a triangulated surface.