G. Blelloch, J. Hardwick, G. L. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica, 24(3/4):243-269, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....boundary and led to independent grid generation. There must exist grid points in the interdomain boundary between sub domains. The parallel implementation of incremental construction algorithm was presented by P. Cignoni [1] The strategy marriage before conquest was used. G. E. Blelloch [8] was the similar strategy as Cignoni. This algorithm found the median line between sub domains by convex hull algorithm, then triangulated sub domain by the divide and conquer algorithm. Its parallel efficiency of 128k points is 48 90 on IBM SP2 with 8 nodes. Details of the divide and conquer ....

G. E. BLELLOCH, J. C. HARDWICK, G. L. MILLER, AND D. TALMOR, Design and implementation of a practical parallel Delaunay algorithm, Algorithmica, 24(1999), pp. 243--269.

....do not necessarily imply a straightforward parallel insertion scheme at each iteration. There are several existing pa allel Delaunay triangulation algorithms that we can employ at each iteration. For example, in 2D we can use the divide and conquer parallel algorithm devel oped by Blelloch et al. [4] for Delaunay triangulation. Their algorithm uses O(nlog n) work and O(log 3 n) paallel time. We can alternatively use the random ized parallel algorithms of Reif and Sen [28] or by Amaro et al. 1] in both two and three dimensions. Both of these randomized parallel Delaunay triangulation ....

G. E. Blelloch, J. C. Hardwick, G. L. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica 24(3):243-269, 1999.

.... parallel evaluation of the finite element shape functions is trivial; the sparse matrix triple product is difficult to implement efficiently though is a straight forward algorithm [1] Efficient 3D parallel Delaunay meshing is, however, an open problem though the 2D problem has been addressed [5]. We are, however, able to avoid computing a complete 3D Delaunay mesh for the coarse grids, as each processor has copies of ghost vertices that surround all vertices, that a processor is responsible for. We are able to mesh only the local subdomain problem and thus construct the restriction ....

G. Blelloch, G.L. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. To appear in Algorithmica, 1998.

....into the existing mesh. The algorithm invariant is that the mesh remain a valid Delaunay mesh after each vertex insertion. The method is not highly optimal nor parallelizable but it is simple to implement, moreover we do not need a parallel Delaunay, the the design of which is an open problem [12]. Additionally Delaunay is only well defined on vertex sets with no nontrivial coplanar or cospherical point sets most algorithms work on these non general position point sets although exact arithmetic is required for robustness. Delaunay methods in 3D require the evaluation of a 5 by 5 ....

....non global coarse grids meshes (x5.4) lead to restriction operators that are not computed with one valid global finite element mesh, and the random selection of facets in our face identification algorithm (x5.3.3) is probably not optimal. These issues require a parallel Delaunay mesh generator [12], and that we use a more rational selection of initial facets with some global view of the problems the design of such an algorithm that is both effective and has acceptable parallel characteristics is a subject of future research. Figure 9.3 shows the efficiency of the data in Figure 9.2; we ....

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Guy Blelloch, Gary L Miller, and Dafna Talmor. Design and implementation of a practical parallel Delaunay algorithm. To appear in Algorithmica, 1998.

....useful to a more general finite element community we need to extend the algorithm and its features. Some areas are: investigate more sophisticated face identification algorithms, to increase robustness of solver on arbitrary complex domains; incorporate a parallel Delaunay tessellation algorithm [5] so as to develop more robust and globally consistent implementations; extend the implementation for more element types: shells, beams, trusses, etc. accommodate higher order elements such as, supporting higher dof per vertex for p adaptive methods and multi physics problems. To extend the depth ....

Guy Blelloch, Gary L Miller, and Dafna Talmor. Design and implementation of a practical parallel Delaunay algorithm. To appear in Algorithmica, 1998.

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G. Blelloch, J. Hardwick, G. L. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica, 24(3/4):243-269, 1999.

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G. Blelloch, J. Hardwick, G. L. Miller, and D. Talmor. Design and implementation of a practical parallel delaunay algorithm. Algorithmica, 24(3/4):243--269, 1999.

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G. Blelloch, J. Hardwick, G. L. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica, 24(3/4):243-269, 1999.

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Guy E. Blelloch, Jonathan C. Hardwick, Gary L. Miller, and Dafna Talmor. Design and implementation of a practical parallel Delaunay algorithm. Submitted for journal publication.

.... triangulation of the dynamically evolving grid points at each time step.Thekeyto such an aggressive approach to meshing is our recent development of a parallel Delaunay triangulation algorithm that is theoretically optimal in work, requires polylogarithmic depth, and is very efficient in practice [5]. Given an arbitrary set of grid points, distributed across the processors, the algorithm returns a Delaunay triangulation of the points and at the same time partitions them for load balance and minimal communication across the processor boundaries. Our 2D results show that frequent triangulation ....

....does not appear to be practical. The problem is that although the sewing step can be parallelized, the parallel version is very much more complicated than the sequential version, and has large overheads. To remedy this problem our parallel Delaunay algorithm uses a somewhat different approach [5]. We still use divide and conquer, but instead of doing most of the work when the recursive calls return we do most of the work at the divide step. This makes our joining step trivial: we just append the list of triangles returned by the recursive calls. This can be seen as similar to the ....

G. BLELLOCH,J.HARDWICK,G.L.MILLER, AND D. TALMOR,Design and implementation of a practical parallel Delaunay algorithm, Algorithmica, 24 (1999), pp. 243--269.

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Blelloch, G. E., Miller, G. L., Hardwick, J. C., and Talmor, D. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica 24, 3 (1999), 243--269.

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Guy Blelloch, Gary L Miller, and Dafna Talmor. Design and implementation of a practical parallel Delaunay algorithm. To appear in Algorithmica, 1998.

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G. E. Blelloch, J. C. Hardwick, G. L. Miller and D. Talmor. Design and Implementation of a Practical Parallel Delaunay Algorithm. Algorithmica 24 (1999). 11

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Blelloch, G. E., Miller, G. L., Hardwick, J. C., and Talmor, D. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica 24, 3 (1999), 243--269.

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Blelloch, G. E., Miller, G. L., Hardwick, J. C., and Talmor, D. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica 24, 3 (1999), 243--269.

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G. Blelloch, J. Hardwick, G. Miller, and D. Talmor. Design and implementation of a practical parallel Delaunay algorithm. Algorithmica, 24:243--269, 1999.

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