A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality

Certain classes of problems result in solution fields of which the characteristic length scales vary with the orientation. Often the orientation of these length scales is related to the orientation of the boundaries. Such solution fields can be captured by the finite element method, using a mesh that is refined in the direction of the short length scales and coarse in the other directions. These meshes contain elements with high aspect ratios in a predefined pattern.The mesh generator presented here can render triangles with high aspect ratios through a paving algorithm. The paving algorithm that is employed applies both triangles and quadrilaterals, combining the advantages of both to render a qualitatively good, oriented triangular mesh, with a concentration of elements in the direction where the internal length scales of the solution field are the shortest.The mesh generator produces triangles with one (almost) orthogonal corner. When low aspect ratio triangles are generated, these are well suited for conversion to quadrilateral elements. Test results indicate that quadrilateral meshes converted from the mesh generator introduced here have a considerably better quality than those converted from several other triangular mesh generators.