The use of the Schwarz-Christoffel transformation in finite element mesh generation
This thesis describes a new computer-based method for the generation of finite element meshes. It relies upon the Schwarz-Christoffel transformation, a conformal mapping from conplex variable theory. This mapping is defined and some examples of its use in classical fluid dynamics are given. A practical method for evaluating the parameters defining this transformation is described and emphasis is placed on the efficiency of the solution process in order that coirputer run times may be kept as short as possible. A theorem in Euclidean geometry is stated and proved which links the theory of the Schwarz-Christoffel mapping and the geometrical use to which it is put here. Two such Schwarz-Christoffel transformations are used to construct a mapping between any two polygons. The desirable properties of a finite element mesh are stated and a method is described which atteirpts to generate such a mesh in any sinply-connected two-dimensional region. Numbering of the nodes is an inherent part of the generation scheme, thus ensuring that the optimum bandwidth of the resulting system of linear equations in the analysis phase is obtained. In order to be able to present example meshes, a particular element type, the three-noded triangle, is used and a section describing the enumeration of hexagons, all of whose internal angles are 2n/3, is included. The thesis includes a brief survey of existing methods of two-dimensional mesh generation as well as several example meshes.