A fast algorithm for particle simulations
Journal of Computational Physics
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Developing a practical projection-based parallel Delaunay algorithm
Proceedings of the twelfth annual symposium on Computational geometry
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Sink-insertion for mesh improvement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Generating well-shaped d-dimensional Delaunay meshes
Theoretical Computer Science - Computing and combinatorics
Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation
Proceedings of the nineteenth annual symposium on Computational geometry
Computing the medial axis of a polyhedron reliably and efficiently
Computing the medial axis of a polyhedron reliably and efficiently
A Load Balancing Framework for Adaptive and Asynchronous Applications
IEEE Transactions on Parallel and Distributed Systems
A time efficient Delaunay refinement algorithm
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 18th annual international conference on Supercomputing
Time complexity of practical parallel steiner point insertion algorithms
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Guaranteed-quality parallel Delaunay refinement for restricted polyhedral domains
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometrySoCG2002
Parallel delaunay refinement mesh generation
Parallel delaunay refinement mesh generation
Flow Past a Stationary and Moving Cylinder: DNS at Re=10,000
DOD_UGC '04 Proceedings of the 2004 Users Group Conference
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Proceedings of the 19th annual international conference on Supercomputing
Delaunay Decoupling Method for Parallel Guaranteed Quality Planar Mesh Refinement
SIAM Journal on Scientific Computing
Streaming computation of Delaunay triangulations
ACM SIGGRAPH 2006 Papers
Numerical Solution of Partial Differential Equations on Parallel Computers (Lecture Notes in Computational Science and Engineering)
Parallel Guaranteed Quality Delaunay Uniform Mesh Refinement
SIAM Journal on Scientific Computing
Algorithm 870: A static geometric Medial Axis domain decomposition in 2D Euclidean space
ACM Transactions on Mathematical Software (TOMS)
Three-dimensional delaunay refinement for multi-core processors
Proceedings of the 22nd annual international conference on Supercomputing
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Parallel Delaunay triangulation-Application to two dimensions
Finite Elements in Analysis and Design
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We describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for general two-dimensional geometries. We generalize the existing sequential point placement strategies for guaranteed quality mesh refinement: instead of a specific position for a new point, we derive two types of two-dimensional regions which we call selection disks. Both types of selection disks are inside the circumdisk of a poor quality triangle, with the Type I disk always inside the Type II disk. We prove that any point placement algorithm which inserts Steiner points inside selection disks of Type I terminates, and any algorithm which inserts Steiner points inside selection disks of Type II produces an asymptotically size-optimal mesh. In the area of parallel Delaunay mesh refinement, we develop a new theoretical framework for the construction of graded meshes on parallel architectures, i.e., for parallel mesh generation with element size controlled by a user-defined criterion. Our sufficient conditions of point Delaunay-independence allow to select points for concurrent insertion in such a way that the standard sequential guaranteed quality Delaunay refinement procedures can be applied in parallel to attain the required element quality constraints. Finally, we present a novel parallel algorithm which can be used in conjunction with any sequential point placement strategy that chooses points within the selection disks. We implemented our algorithm for shared memory multi-core architectures and present the experimental results. Our data show that even on workstations with a few cores, which are now in common use, our implementation is significantly faster than the best sequential counterpart.