Programming of Finite Element Methods in Matlab

نویسنده

LONG CHEN

چکیده

1.1. Mesh data structure. The matrices node(1:N,1:d) and elem(1:NT,1:d+1) are used to represent a d-dimensional triangulation embedded in R, where N is the number of vertices and NT is the number of elements. These two matrices represent two different structure of a triangulation: elem for the topology and node for the geometric embedding. The matrix elem represents a set of abstract simplices. The index set {1, 2, . . . , N} is called the global index set of vertices. Here an vertex is thought as an abstract entity. For a simplex t, {1, 2, . . . , d + 1} is the local index set of t. The matrix elem is the mapping (pointer) from the local index to the global one, i.e., elem(t,1:d+1) records the global indices of d + 1 vertices which form the abstract d-simplex t. Note that any permutation of vertices of a simplex will represent the same abstract simplex. The matrix node gives the geometric realization of the simplicial complex. For example, for a 2-D triangulation, node(k,1:2) contain xand y-coordinates of the k-th nodes. The geometric realization introduces an ordering of the simplex. For each elem(t,:), we shall always order the vertices of a simplex such that the signed area is positive. That is in 2-D, three vertices of a triangle is ordered counter-clockwise and in 3-D, the ordering of vertices follows the right-hand rule.

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