An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co‐ordinates

Abstract

SUMMARYA computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

“…A coordinate-transformation technique that is a natural byproduct of isoparametric mappings used to represent curved-sided finite elements is presented by Zienkiewicz and Phillips (1971). In this method, the entire solution domain is divided into a coarse subdivision cornposed of a few very large isoparametric elements.…”

Electromagnetic Scattering by Surface of Arbitrary Shape.

“…In the topological discussion a number of geometrical quantities are defined and some relationships between them are given. Consideration is then given to a means for mathematically representing a triangulated surface in a form that is convenient whether the surface data is supplied by the modeler or is generated by an automatic surface triangulation computer subprogram [24]. From this representation may be derived an alternative representation which is actually more convenient for the subsequent numerical processing necessary in applying the moment method.…”

The Boundary Integral Equation Method Using Various Approximation Techniques for Problems Governed by Laplace's Equation.

“…In fact , this can be done by using the so-called "isoparametric transformation " [12] , where we use the shape functions used to approx imate the functions to also appr oximate the boundary geometry.…”