Efficient Adaptive Meshing of Parametric Models

Abstract

Parametric modeling is becoming the representation of choice for most modern solid modelers. However, when generating the finite-element mesh of the model for simulation and analysis, most meshing tools ignore the parametric information and use only the boundary representation of the model for meshing. This results in re-meshing the model basically from scratch each time a parametric change is instantiated, which happens numerous times throughout the design process. In this paper we look at ways to use the parametric information during the meshing procedure to prevent unnecessary re-meshing. The paper examines existing meshing techniques developed for other purposes, which can be applied to this problem. It also suggests several new mesh modification techniques specifically designed for efficient mesh adjustment after parametric model changes.

Adaptive mesh coarsening for quadrilateral and hexahedral meshes

“…This is, in large part, due to the topology constraints that exist in a conforming all-hexahedral mesh. These constraints make it difficult to modify mesh density without causing topology changes to propagate beyond the boundaries of a defined region [17,18].…”

Guaranteed‐quality triangular mesh generation for domains with curved boundaries

“…A fully automatic mesh generator must handle curved surfaces as readily as planar ones, which requires the use of the exact representation of the boundaries during the meshing process [5]. Otherwise, time is wasted discretizing these curves into sets of linear segments, a process which can also lead to an invalid representation of the boundary.…”

“…To enable meshing from general curved boundaries, we need a framework in which the mesh generation code makes no assumptions about the underlying geometry of boundary patches [5]. This implies a generic interface between mesher and geometry, in which the mesher only needs the results of several geometric queries.…”

Efficient tetrahedral remeshing of feature models for finite element analysis

“…The best examples we know of are [14,15]. The first work proposes two strategies of which the first is akin to mesh morphing.…”

“…The second strategy is only effective for changes with a local geometric scope. The work in [15] offers no single, generic approach, but discusses a range of techniques that can be applied in several different situations. The focus is specifically on parametric model modification.…”