Generation of gradation meshes by the background grid technique

Abstract

A new algorithm for the generation of well-graded high-quality finite element mesh for adaptive refinement analysis is presented. The proposed mesh generation scheme is fully automatic and is applicable to any arbitrary 2D planar domains. The element size information of the background mesh is first transferred to a square grid, with which well graded elements with size compatible with the prescribed node spacing function can be generated. The efficiency of the mesh generator is also much improved over the direct interpolation scheme, as a rigorous search on the elements is no longer required in the computation of node spacing values. Moreover, by using different mesh conversion techniques to convert part or all of the triangular elements into quadrilateral elements, gradation quadrilateral meshes can also be obtained. A dimensionless parameter χ is introduced to measure the deviation of the element size of the gradation mesh from the prescribed node spacing function. Mesh generation over domains of various characteristics are given as examples. The χ values of the meshes generated are found to be very close to the ideal value of unity, demonstrating that a rapid variation of element size inside the problem domain can be captured precisely by this background square grid technique. © 1994.