Spherical finite element analysis

Finite element analysis techniques are applied to the sphere. The sphere is subdivided into non-rectangular linear hexahedra except at the polar axis, where they are wedges. An automatic mesh generation computer program, based on the work of Sepulveda (1984), is used to assign node and element numbers. Equation numbers are assigned to minimize the bandwidth of the “stiffness matrix”. To avoid computation artifacts, it is important to subdivide the sphere into elements whose sides are approximately equal. Two examples are presented, (a) the ideal magnet, and (b) a three-layered conducting sphere. To demonstrate the versatility of the method described in the paper, a low-resistivity region was introduced in the three-layered conducting sphere to show how the equipotential and current flow lines are affected