Finite element mesh generation over analytical curved surfaces

A scheme is proposed for the automatic generation of unstructured triangular meshes of arbitrary density distribution over curved surfaces. Instead of using the widely employed plane to surface mapping method, elements are generated directly on the curved surfaces by the advancing front technique. Given a segment on the boundary, the possibility of forming a new triangle with a node on the boundary or an interior node is examined. The elements formed are optimized in terms of a number of parameters including surface curvature, element quality and the given element density distribution. Two algorithms to bring a spatial point back on the curved surface without affecting the shape and size of the element are described. Some examples are given to illustrate the application of the method to various kinds of surfaces.