Mesh generation over curved surfaces with explicit control on discretization error

Abstract

A scheme is presented for the automatic generation of triangular meshes over general analytical curved surfaces with explicit control on the discretization error over the interior of the domain. The element size on the curved surface is estimated based on the given allowable discretization error and the surface curvature. The mesh generation starts with the subdivision of the curved boundary of the domain into straight line segments in compliance with the given discretization error constraint. Elements are generated directly over the surface in such a way that the discretization error is kept within the required geometrical tolerance. Those elements violating the given constraint are noted and post‐processed by either element subdivision or node repositioning. Various schemes as to how improvement should be made are proposed, which reduce the discretization error by different strategies depending on the position of the point where the maximum discretization error occurs.

A Hierarchical Adaptive Mesh Generation Strategy for Parametric Surfaces Based on Tree Structures

“…In the first work [8], it is proposed a scheme for automatic generation of triangular meshes with arbitrary distribution of elements on curved surfaces and without the use of a parametric space. The second work [9] brings a similar approach, but proposes more control over the curvature.…”

“…Lau and Lo [8], [9] present a technique for generating finite element meshes using the curvature as a measure to determine the size of the elements and guide the discretization. In the first work [8], it is proposed a scheme for automatic generation of triangular meshes with arbitrary distribution of elements on curved surfaces and without the use of a parametric space.…”

“…Compute the center of E k in 3D space, C E k ; 6 Find parametric coordinates of C E k , (u k , v k ); 7 Determine in which cell (u k , v k ) is located; 8 while size of the cell > h new do 9 Subdivide the cell into four children; 10 Determine in which cell (u k , v k ) is located; 11 Algorithm 5: Computing h new for an element.…”

“…The advancing front was adapted to search only points in the adjacency of the chosen active edge, avoiding the unnecessary work of searching points occluded by the inner cells. This is the last phase of mesh generation for patch P k , and is performed as described in the Algorithm Find the best vertex from the adjacent cell list; 8 Build the triangle; 9 Update the active edge list; 6. Figure 10 (a) illustrates the mesh after the advancing front.…”

Comparative crash simulations incorporating the results of sheet forming analyses

“…Here the mesh generation is performed in the current configuration as illustrated in Lee and Oh (1999), by a projecting procedure where the single nodes are obtained using a subdivision strategy. A procedure for curved surfaces with explicit control of the error coming along with the meshing can be found in Lo and Lau (1998).…”