Data Structure for Triangulations
نویسنده
چکیده
We shall discuss the data structure to represent triangulations and facilitate the mesh adaptation procedure. There is a dilemma for the data structure in the implementation level. If more sophisticated data structure is used to easily traverse in the mesh, for example, to save the star of vertices or edges, it will simplify the implementation of most adaptive finite element subroutines. On the other hand, if the triangulation is changed, for example, a triangle is bisected, one has to update those data structure which in turn complicates the implementation. Our solution is to maintain two basic data structure and construct auxiliary data structure inside each subroutine when it is necessary. It is not optimal in terms of the computational cost. But it will benefit the interface of accessing subroutines, simplify the coding and save the memory. Also as we shall see soon, the auxiliary data structure can be constructed by sparse matrixlization efficiently. This is an example we scarify a small factor of efficiency to gain the simplicity.
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