Tech Tip: The NAG Library and Mesh Generation

The NAG libraries include a chapter, D06, which provides routines for generating two-dimensional triangular meshes on arbitrary domains.

The first step is to generate a boundary mesh for the domain. Routine D06BA does this for quite general boundaries, defined as the union of a set of line segments which may be straight lines, curves defined by the equation f(x,y) = 0, or polygonal curves defined by a set of given boundary mesh points.

Once the boundary mesh is computed the routines D06AA, D06AB, or D06AC may be used to generate a 2D triangular mesh using a simple incremental method, the Delaunay-Voronoi process, or the Advancing Front method.

Routines are also provided for mesh smoothing, mesh transformation, mesh stitching, computing the sparsity structure of an associated finite element matrix, and bandwidth reduction.

A NAG Technical Report (TR1/01 [pdf]) illustrates how these routines can be used in combination with sparse iterative solvers from Chapter F11, to solve partial differential equations using the finite element method.

The material in Chapter D06 was derived from the MODULEF software developed by INRIA (Institut National de Recherche en Informatique et Automatique).

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