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28
Mesh Generation And Optimal Triangulation
, 1992
"... We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some cri ..."
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Cited by 214 (7 self)
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We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.
Parallel Algorithms for the Adaptive Refinement and Partitioning of Unstructured Meshes,”
 Proceedings of IEEE Scalable High Performance Computing Conference,
, 1994
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A Parallel Algorithm for Mesh Smoothing
"... Maintaining good mesh quality during the generation and refinement of unstructured meshes in finiteelement applications is an important aspect in obtaining accurate discretizations and wellconditioned linear systems. In this article, we present a meshsmoothing algorithm based on nonsmooth optimiz ..."
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Cited by 29 (7 self)
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Maintaining good mesh quality during the generation and refinement of unstructured meshes in finiteelement applications is an important aspect in obtaining accurate discretizations and wellconditioned linear systems. In this article, we present a meshsmoothing algorithm based on nonsmooth optimization techniques and a scalable implementation of this algorithm. We report mesh improvement results for twodimensional simplicial meshes that demonstrate the effectiveness of this approach for a number of different test cases. We also show the scalability of the parallel algorithm on the IBM SP supercomputer and an ATMconnected network of SPARC Ultras. 1 Introduction Unstructured meshes have proven to be an essential tool in the numerical solution of largescale scientific and engineering applications on complex computational domains. A problem with such meshes is that the shape of the elements in the mesh can vary significantly, and this variation can affect the accuracy of the numerical ...
A Cost/Benefit Analysis of Simplicial Mesh Improvement Techniques as Measured by Solution Efficiency
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Parallel Adaptive Subspace Correction Schemes with Applications to Elasticity
 Comput. Methods Appl. Mech. Engrg
, 1999
"... : In this paper, we give a survey on the three main aspects of the efficient treatment of PDEs, i.e. adaptive discretization, multilevel solution and parallelization. We emphasize the abstract approach of subspace correction schemes and summarize its convergence theory. Then, we give the main featur ..."
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Cited by 11 (4 self)
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: In this paper, we give a survey on the three main aspects of the efficient treatment of PDEs, i.e. adaptive discretization, multilevel solution and parallelization. We emphasize the abstract approach of subspace correction schemes and summarize its convergence theory. Then, we give the main features of each of the three distinct topics and treat the historical background and modern developments. Furthermore, we demonstrate how all three ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic PDEs and especially of linear elasticity problems. We report on numerical experiments for the adaptive parallel multilevel solution of some test problems, namely the Poisson equation and Lam'e's equation. Here, we emphasize the parallel efficiency of the adaptive code even for simple test problems with little work to distribute, which is achieved through hash storage techniques and spacefilling curves. Keywords: subspace correction, iter...
The RefinementTree Partition for Parallel Solution of Partial Differential Equations
 NIST Journal of Research
, 1998
"... The numerical solution of partial differential equations (PDEs) is the most computationally intense part of solving mathematical models with many important applications. For this reason, much research has been performed ..."
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Cited by 8 (4 self)
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The numerical solution of partial differential equations (PDEs) is the most computationally intense part of solving mathematical models with many important applications. For this reason, much research has been performed
Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing
"... The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edgebased adaptation scheme, called 3D TAG, using message passing. Results show excell ..."
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Cited by 7 (2 self)
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The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edgebased adaptation scheme, called 3D TAG, using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However, performance deteriorates when the mesh is re#ned using a solutionbased error indicator since mesh adaptation for practical problems occurs in a localized region, creating a severe load imbalance. To address this problem, wehave developed PLUM, a global dynamic load balancing framework for adaptivenumerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D...
Combinatorial scientific computing: The enabling power of discrete algorithms in computational science
 In 7th Intl. Mtg. High Perf. Comput. for Computational Sci. (VECPAR’06), Lecture Notes in Computer Science
, 2006
"... Abstract. Combinatorial algorithms have long played a crucial, albeit underrecognized role in scientific computing. This impact ranges well beyond the familiar applications of graph algorithms in sparse matrices to include mesh generation, optimization, computational biology and chemistry, data ana ..."
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Cited by 7 (1 self)
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Abstract. Combinatorial algorithms have long played a crucial, albeit underrecognized role in scientific computing. This impact ranges well beyond the familiar applications of graph algorithms in sparse matrices to include mesh generation, optimization, computational biology and chemistry, data analysis and parallelization. Trends in science and in computing suggest strongly that the importance of discrete algorithms in computational science will continue to grow. This paper reviews some of these many past successes and highlights emerging areas of promise and opportunity. 1
The Full Domain Partition Approach To Parallel Adaptive Refinement
 in Grid Generation and Adaptive Algorithms, IMA Volumes in Mathematics and it Applications 113 SpringerVerlag
, 1998
"... . The combination of adaptive refinement, multigrid and parallel computing for solving partial differential equations is considered. In the full domain partition approach, each processor contains a partition of the grid plus the minimum number of additional coarse elements required to cover the whol ..."
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Cited by 6 (3 self)
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. The combination of adaptive refinement, multigrid and parallel computing for solving partial differential equations is considered. In the full domain partition approach, each processor contains a partition of the grid plus the minimum number of additional coarse elements required to cover the whole domain. A parallel adaptive refinement algorithm using the full domain partition is presented. The method is a small modification of a sequential adaptive refinement algorithm, and uses no interprocessor communication during the refinement process. The only communication is one global reduction before refinement and three alltoall communication steps for synchronization after the refinement is completed. Numerical computations on a network of up to 4 workstations show that parallel efficiency rates of 85% to near 100% can be obtained. Key words. adaptive refinement, finite elements, parallel algorithms, partial differential equations. AMS(MOS) subject classifications. 35J25, 65N30, 65N5...
Propagation Path Properties In Iterative LongestEdge Refinement
 PROC. 12TH INTERNAT. MESHING ROUNDTABLE
, 2003
"... In this work we investigate the refinement propagation process in longestedge based local refinement algorithms for unstructured meshes of triangles. The conformity neighborhood of a triangle, the set of additional triangles that is needed to be refined to ensure mesh conformity is introduced to de ..."
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Cited by 6 (2 self)
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In this work we investigate the refinement propagation process in longestedge based local refinement algorithms for unstructured meshes of triangles. The conformity neighborhood of a triangle, the set of additional triangles that is needed to be refined to ensure mesh conformity is introduced to define the propagation path. We prove that asymptotically the propagation path extends on average to a few neighbor adjacent triangles. We also include numerical evidence which is in complete agreement with the theoretical study reported.