Abstract
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.
