Civil Engineering Reference
In-Depth Information
triangles can be guaranteed (Rivara 1984). However, the idea of bisection of the LE cannot
be extended to higher dimensions as the quality of the resulting tetrahedra is unbounded,
i.e. very poor tetrahedral elements may be created in the bisection process. The local bisec-
tion refinement of simplicial grids was also studied by Maubach (1995). Alternatively, a local
refinement of tetrahedral meshes was proposed in which a finite number of classes of simi-
lar tetrahedra were created in the refinement such that the quality of the tetrahedral mesh
was guaranteed (Liu and Joe 1995). A year later, a local refinement of eight-tetrahedron
subdivision was formally presented in which a finite number of sub-classes of similar tet-
rahedra could be created with guaranteed quality. The procedure could be extended to the
neighbouring tetrahedral elements to maintain a conforming mesh (Liu and Joe 1996).
Lee and Lo (1997a,b) presented an adaptive analysis by refining T4 and T10 tetrahedral
meshes according to the error of the FE solution. Lo (1998a) introduced an edge-sorting
scheme for 3D mesh refinement in compliance with a specified node spacing function. A 3D
anisotropic mesh refinement method in compliance with a general metric specification was
also presented (Lo 2001). Lohner and Cebral (2000) generated non-isotropic meshes based
on directional refinement. Arnold et al. (2000) proposed a bisection algorithm, which was
compared with those of Bansch (1991), Liu and Joe (1995) and Maubach (1995). Mesh
conformity of the bisection procedure was also rigorously verified. Baker (2002) proposed
a mesh-enhancing scheme in which coarsening and enrichment were combined with an
r-refinement to produce a flexible approach for mesh adaptation of time-evolving domains.
Plaza et al. (2004) showed that in the repeated partition process of tetrahedra by the eight-
tetrahedron subdivision and the LE bisection, only three dissimilar types are produced.
Hence, the quality of the resulting mesh can be guaranteed. Plaza et al. (2005) discussed
the non-degeneracy property of the eight-tetrahedra LE partition and gave an estimate
on the asymptotic value of the refined elements based on numerical experiments. Li et
al. (2005) presented mesh optimisation and adaptation involving refinement, coarsening,
projecting boundary vertices, shape correction and other techniques according to the given
metric field. Gruau and Coupez (2005) proposed a mesh refinement scheme based on an
anisotropic metric by specifying the number of layers across the thickness direction and
subdividing elements within a topological neighbourhood around a node. Remacle et al.
(2005) proposed a series of local modifications to an FE mesh in compliance with the pre-
scribed anisotropic metric field. Dai and Schmidt (2005) presented a refinement scheme
of triangular meshes on surfaces for large deformation problems. Si and Gaertner (2005)
presented a semi-constrained DT in which tetrahedral mesh for a solid object bounded by
a discretised surface is created by introducing Steiner points at strategic positions on the
boundary edges.
Alauzet et al. (2006) presented a mesh-coarsening and refinement scheme with shape
optimisation for the fluid flow problem. The problem domain was also decomposed for par-
allel processing for which the load balancing and the inter-partition communication issues
were addressed. Wessner et al. (2006) discussed the anisotropic mesh refinement issues for
semiconductor manufacturing processes. A refinement tree-partitioning method related to
Octree and space-filling curves for adaptive parallel processing was proposed by Mitchell
(2007). An algorithm was presented to generate surface and volume meshes for modelling
molecules of arbitrary sizes and shapes by a series of surface modifications and enhance-
ment techniques (Yu et al. 2008a). Yu et al. (2008b) put forward a geometric model and MG
with adaptation targeted to biomedical systems by means of mesh refinement and coarsen-
ing with feature preserving. Loseille and Alauzet (2009) discussed in detail an anisotropic
mesh adaptation for 3D-steady Euler equations based on the optimisation of a functional.
Dey et al. (2012) discussed a restricted Delaunay refinement to generate triangular meshes
at the interface surfaces of objects obtained by labelling images from various modalities.
