| Asymptotically Efficient Triangulations of the d-Cube (2007) | |||||||||||||||||
Abstract | |||||||||||||||||
| Triangulating the regular d-cube I^d = [0, 1]^d in a "simple" way has many applications, like solving differential equations by finite element methods or calculating fixed points. See, for example, [7]. Determining the smallest number of simplices needed has brought special attention both from a theoretical point of view and from an applied one (see [6, Section 14.5.2] for a recent survey). Before going on, let us clarify that when we speak about triangulations of a polytope P of dimension d we mean decompositions of P into d-simplices (i) using as vertices only the vertices of P , and (ii) intersecting face to face (i.e., forming a geometric simplicial complex). If the second condition is not fulfilled, we call them simplicial dissections of P . The number of d-simplices of a triangulation or dissection T will be called its size and denoted |T|. A general method to obtain the smallest triangulation of a polytope P of dimension d as the optimal integer solution of a ... | |||||||||||||||||
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