In this paper, we expand circular arc triangulations with parabolic arcs, which are triangulations whose edges are circular or parabolic arcs. Creating triangulations this way bears several advantages if angles are to be optimized, especially for finite element method. A typical reason for the occurrence of small angles in a straight line triangulation is that the geometry of the vertex set for...

We examine the eigenstructure of generalized isosceles triangles and explore the possibilities of analytic solutions to the general eigenvalue problem in other triangles. Starting with work based off of Brian McCartin’s paper on equilateral triangles, we first explore the existence of analytic solutions within the space of all isosceles triangles. We find that this method only leads to consiste...

In this paper we study geometrical properties of the iterative 4triangles longest-side partition of triangles (and of a 3-triangles partition), as well as practical algorithms based on these partitions, used both directly for the triangulation refinement problem, and as a basis for point insertion strategies in Delaunay refinement algorithms. The 4-triangles partition is obtained by joining the...

Simplicial complexes consist of a set of vertices together with designated subsets. They can be thought of as embedded in Rn with the induced metric and topology, where n is large enough that the points can all be geometrically independent. The sets of points spanned by these designated subsets then form triangles or their higher or lower dimensional analogues according to some restrictions. By...

We present new algorithms for listing triangles in dense and sparse graphs. The running time of our algorithm for dense graphs is Õ(n + nt), and the running time of the algorithm for sparse graphs is Õ(m + mt), where n is the number of vertices, m is the number of edges, t is the number of triangles to be listed, and ω < 2.373 is the exponent of fast matrix multiplication. With the current boun...