ABSTRACT
Geometrical operations, namely, those for computing the distance between two simplices of the same or different dimensions, i.e. point-to-line segment and line segment to triangular facet, etc., frequently required in MG along with other useful formulas (for instance, normal at a point, solid angles, determination of intersection points, etc.), are given in Section 2.4. In MG, topological operations are equally if not more important than geometrical operations, as enquiries such as how many elements are connected to a particular node and how to list all the nodes or segments on the boundary of a mesh are always faced. As the number of nodes and the number of elements in a mesh can be very large, efficient topology computation algorithms are crucial to a robust MG scheme. Accordingly, algorithms for the common topological operations including elements connected to a node, adjacency relationship of a mesh, etc., in the form of detailed pseudo-code readily translated into C++ or FORTRAN programs are given in Section 2.5.
