Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Algorithm 872: Parallel 2D constrained Delaunay mesh generation
ACM Transactions on Mathematical Software (TOMS)
A template for developing next generation parallel Delaunay refinement methods
Finite Elements in Analysis and Design
High quality real-time image-to-mesh conversion for finite element simulations
Proceedings of the 27th international ACM conference on International conference on supercomputing
High quality real-time Image-to-Mesh conversion for finite element simulations
Journal of Parallel and Distributed Computing
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Delaunay refinement has been established as an effective and efficient technique to generate high quality meshes for arbitrary domains. Starting from a constrained Delaunay triangulation of the input of points and line segments, Delaunay refinement adds carefully chosen Steiner points to the mesh while maintaining the constrained Delaunay property. This strategy results in theoretically sound algorithms that generate quality meshes of optimal small size. Sequential implementations of such algorithms are available and work very well in practice. As the meshing problem is time and memory intense large-scale problems call for the use of parallel computers. This thesis presents a parallel Delaunay refinement algorithm to solve the two-dimensional meshing problem on distributed memory computers. In contrast to other work, no assumptions on the size or the regularity of the input are made. Parallelizing Delaunay refinement is difficult as the underlying theory is intrinsically sequential. To approve a Steiner point for insertion a consistent view of the current state of the mesh in the neighborhood of the new point is needed. Inserting a Steiner point changes the mesh only locally but in an unstructured way, which makes it hard to maintain a partition of the mesh based upon mesh entities. The presented algorithm partitions the mesh based upon certain mesh properties and maintains this partition while the mesh is generated and refined. At first, the input is distributed over the parallel machine by means of projection-based dividers. Then local meshes are generated and refined in parallel. Properties of the projection-based dividers are exploited to achieve a very high level of asynchronicity. This thesis first reviews sequential Delaunay refinement algorithms and extends them to work on constrained Delaunay meshes. In the second part the parallel Delaunay refinement algorithm is introduced and described in detail. Correctness and optimality of the new algorithm are proved before illustrative examples are given.