Automatic Discretization of a Three-Dimensional Domain into Voronoi Polyhedron Elements

Abstract

When a partial differential equation is solved numerically, it is conventional to discretize the calculating domain into many elements by elaborate handwork. For this discretization we devised a new method with which the three-dimensional domain can be automatically divided into Voronoi polyhedron elements enclosing arbitrary nuclear points. The present report describes this method in detail giving an example. When the Voronoi polyhedron elements are used, various types of differential equations can be easily transformed into simultaneous algebraic equations for each of the nuclear points, and parallel processing can be achieved more quickly and accurately. Moreover, the Voronoi polyhedron element table has possibilities for future development : it can be used not only as a direct analytical method of solving a partial differential equation, but also, after being transformed, as an ordinary tetrahedron element table.