D₃-triangulation for simplicial deformation algorithms for computing solutions of nonlinear equations

We construct a new triangulation of (0, 1] ×Rⁿ, called D₃-triangulation, with continuous refinement of grid sizes for simplicial deformation algorithms for computing solutions of nonlinear equations. It is proved that the D₃-triangulation is superior to the well-known K₃-triangulation and J₃-triangulation in the number of simplices. The surface density of the D₃-triangulation also must be less than that of the K₃-triangulation and the J₃-triangulation. Numerical tests show that the simplicial deformation algorithm based on the D₃-triangulation indeed is much more efficient. © 1992 Plenum Publishing Corporation.