Automatic Discretizing of a Three-Dimensional Domain into Voronoi Polyhedron Elements.

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  • 三次元領域のボロノイ多面体要素への自動要素分割
  • 3ジゲン リョウイキ ノ ボロノイ タメンタイ ヨウソ エ ノ ジドウ ヨウソ

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Abstract

When a partial differential equation is solved numerically, it is usual to discretize the calculating domain into many elements by elaborate handwork. For this discretizing, we devised a new method with which the three-dimensional domain can be divided automatically into Voronoi polyhedron elements around arbitrary nuclear points. This method is described in detail giving an example. When Voronoi polyhedron elements are used, the various differential equations can be easily transformed into simultaneous algebraic equations for each of the nuclear points, for which parallel processing can be done more speedily and accurately. Moreover, the Voronoi polyhedron element table has possibilities of future growth; it can be used directly as an analytical method of solving a partial differential equation and it can be transformed into an ordinary tetrahedron element table.

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