Computation Algorithm for the Constraint Matrix Arising in a Fictitious Domain Method : Triangulation Algorithm for the Intersection of a Tetrahedron and a Triangle

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  • Koyama Daisuke
    Department of Computer Science The University of Electro-Communications

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  • 仮想領域法において生ずる制約行列の計算法 : 四面体と三角形との交差部分の三角形分割アルゴリズム
  • カソウ リョウイキホウ ニ オイテ ショウズル セイヤク ギョウレツ ノ ケイサンホウ 4メンタイ ト 3カクケイ ト ノ コウサ ブブン ノ 3カクケイ ブンカツ アルゴリズム

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A fictitious domain method via Lagrange multipliers for solving three-dimensional Dirichlet problems is considered. A computation algorithm for the constraint matrix in discrete problems of the arising saddle-point problem is presented, in which a triangulation algorithm for the intersection of a tetrahedron and a triangle plays an essential role. First such a triangulation algorithm is designed so that it does not generate any degenerate triangles on the assumption that the precision in computation is infinite. Next its simplified algorithm is presented; it can generate degenerate triangles even if it is implemented in precise arithmetic. These two algorithms are compared through numerical experiments.

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