A Parallel Local Reconnection Approach for Tetrahedral Mesh Improvement

AbstractA multi-threaded parallel local reconnection algorithm is proposed for tetrahedral meshes. It defines a feature point within the region involved in each operation, and sorts the features points along a Hilbert curve. The decomposition of this Hilbert curve results in a load-balanced distribution of local operations. Meanwhile, the regions of concurrently executed local operations are separated far away, such that the possibility of interference is reduced to a very low level. Finally, a parallel mesh improver is developed by combining the proposed algorithm with a parallel mesh smoothing algorithm, and its effectiveness and efficiency is verified in various numerical experiments

An improved local remeshing algorithm for moving boundary problems

© 2016 The Author(s). Three issues are tackled in this study to improve the robustness of local remeshing techniques. Firstly, the local remeshing region (hereafter referred to as ‘hole’) is initialized by removing low-quality elements and then continuously expanded until a certain element quality is reached after remeshing. The effect of the number of the expansion cycle on the hole size and element quality after remeshing is experimentally analyzed. Secondly, the grid sources for element size control are attached to moving bodies and will move along with their host bodies to ensure reasonable grid resolution inside the hole. Thirdly, the boundary recovery procedure of a Delaunay grid generation approach is enhanced by a new grid topology transformation technique (namely shell transformation) so that the new grid created inside the hole is therefore free of elements of extremely deformed/skewed shape, whilst also respecting the hole boundary. The proposed local remeshing algorithm has been integrated with an in-house unstructured grid-based simulation system for solving moving boundary problems. The robustness and accuracy of the developed local remeshing technique are successfully demonstrated via industry-scale applications for complex flow simulations

Scalable generation of large-scale unstructured meshes by a novel domain decomposition approach

© 2018 Elsevier Ltd A parallel algorithm is proposed for scalable generation of large-scale tetrahedral meshes. The key innovation is the use of a mesh-simplification based domain decomposition approach. This approach works on a background mesh with both its surface and its interior elements much larger than the final elements desired, and decomposes the domain into subdomains containing no undesirable geometric features in the inter-domain interfaces. In this way, the most time-consuming part of domain decomposition can be efficiently parallelized, and other sequential parts consume reasonably limited computing time since they treat a very coarse background mesh. Meanwhile, the subsequent parallel procedures of mesh generation and improvement are most efficient because they can treat individual subdomains without compromising element quality. Compared with published state-of-the-art parallel algorithms, the developed parallel algorithm can reduce the clock time required by the creation of one billion elements on 512 computer cores from roughly half an hour to less than 4 minutes

Exact conversion from Bézier tetrahedra to Bézier hexahedra

International audienceModeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeo-metric analysis. In this paper, we propose two kinds of exact conversion approaches from Bézier tetrahedra to Bézier hexahedra with the same degree by reparametrization technique. In the first method, a Bézier tetrahedron is converted into a degenerate Bézier hexahedron, and in the second approach, a non-degenerate Bézier tetrahedron is converted into four non-degenerate Bézier hexahedra. For the proposed methods, explicit formulas are given to compute the control points of the resulting tensor-product Bézier hexahedra. Furthermore, in the second method, we prove that tetrahedral spline solids with C k-continuity can be converted into a set of tensor-product Bézier volumes with G k-continuity. The proposed methods can be used for the volumetric data exchange problems between different trivariate spline representations in CAD/CAE. Several experimental results are presented to show the effectiveness of the proposed methods

Tetrahedral mesh improvement by shell transformation

Existing flips for tetrahedral meshes simply make a selection from a few possible configurations within a single shell (i.e., a polyhedron that can be filled up with a mesh composed of a set of elements that meet each other at one edge), and their effectiveness is usually confined. A new topological operation for tetrahedral meshes named shell transformation is proposed. Its recursive callings execute a sequence of shell transformations on neighboring shells, acting like composite edge removal transformations. Such topological transformations are able to perform on a much larger element set than that of a single flip, thereby leading the way towards a better local optimum solution. Hence, a new mesh improvement algorithm is developed by combining this recursive scheme with other schemes, including smoothing, point insertion and point suppression. Numerical experiments reveal that the proposed algorithm can well balance some stringent and yet sometimes even conflict requirements of mesh improvement, i.e., resulting in high-quality meshes and reducing computing time at the same time. Therefore, it can be used for mesh quality improvement tasks involving millions of elements, in which it is essential not only to generate high-quality meshes, but also to reduce total computational time for mesh improvement