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The Full Domain Partition Approach To Parallel Adaptive Refinement
- in Grid Generation and Adaptive Algorithms, IMA Volumes in Mathematics and it Applications 113 Springer-Verlag
, 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 all-to-all 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...
A Refinement-tree Based Partitioning Method for Dynamic Load Balancing with Adaptively Refined Grids
, 2006
"... The partitioning of an adaptive grid for distribution over parallel processors is considered in the context of adaptive multilevel methods for solving partial differential equations. A partitioning method based on the refinement-tree is presented. This method applies to most types of grids in two an ..."
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The partitioning of an adaptive grid for distribution over parallel processors is considered in the context of adaptive multilevel methods for solving partial differential equations. A partitioning method based on the refinement-tree is presented. This method applies to most types of grids in two and three dimensions. For triangular and tetrahedral grids, it is guaranteed to produce connected partitions; no other partitioning method makes this guarantee. The method is related to the OC-TREE method and space filling curves. Numerical results comparing it with several popular partitioning methods show that it computes partitions in an amount of time similar to fast load balancing methods like recursive coordinate bisection, and with mesh quality similar to slower, more optimal methods like the multilevel diffusive method in ParMETIS.
A Locality Preserving Graph Ordering Approach for Implicit Partitioning: Graph-Filling Curves
"... Linear orderings defined through space-filling curves are often applied to quickly partition graphs arising in finite element simulations. In applications with constant meshes but a rapidly changing load per element, an ordering has to be determined only once and all subsequent partitionings can be ..."
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Linear orderings defined through space-filling curves are often applied to quickly partition graphs arising in finite element simulations. In applications with constant meshes but a rapidly changing load per element, an ordering has to be determined only once and all subsequent partitionings can be computed very quickly through a simple interval splitting. However, partitionings based on space-filling curves have known drawbacks. Especially when applied to deeply refined meshes or discretizations that contain holes, a high edge-cut is produced. In this paper we present a new linear ordering approach called graph-filling curves. In contrast to space-filling curves, we determine a node ordering based on the graph’s structure rather than on its geometric information. Our experimental evaluation shows that such orderings involving the graphs connectivity information lead to clearly superior implicit partitionings.
Copyright © 2005 Inderscience Enterprises Ltd. Tinkertoy parallel programming: a case study with
"... Abstract: As the need for complex parallel simulation software grows, better strategies for efficient and effective software development become important. We advocate a toolkit- or ‘tinkertoy’-approach to parallel application development. By providing efficient implementations of basic services comm ..."
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Abstract: As the need for complex parallel simulation software grows, better strategies for efficient and effective software development become important. We advocate a toolkit- or ‘tinkertoy’-approach to parallel application development. By providing efficient implementations of basic services commonly needed by applications, toolkits allow application developers to benefit from others ’ research, compare algorithms and save time for their own development. Unlike large frameworks, toolkits provide these services with light-weight interfaces and little or no restriction on application data structures, making them easy to use in both new and existing applications. In this paper, we describe features of effective toolkit design, using the Zoltan parallel, dynamic data management toolkit as an example.
Dynamic Load Balancing with the Refinement-Tree Partition for Adaptive Multilevel Methods
, 1998
"... Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on networks of workstations or PCs. An approach that periodically repartitions the grid is taken. A partitioning algorithm based on the refinement tree of the adaptive grid is presen ..."
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Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on networks of workstations or PCs. An approach that periodically repartitions the grid is taken. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of the most important properties of grid partitioners. 1 Introduction Adaptive multilevel methods, which combine adaptive mesh refinement with multigrid solution techniques, have been shown to be very efficient methods for the numerical solution of partial differential equations (PDEs) on sequential computers [1, 6, 10]. The use of these methods on parallel computers is currently a research topic [8, 11]. Among the barriers to efficient parallel implementation of these methods is the balancing of the computational load among the processors in an environment where the grid is dynamically changing through adaptive mesh refinement. This paper presents a dynamic load b...
A Comparison of Three Fast Repartition Methods for Adaptive Grids
, 1999
"... We examine three parallel algorithms for repartitioning adaptive finite element grids in the context of dynamic load balancing for adaptive multigrid methods. The first is a recursive bisection method based on the refinement tree of the adaptive refinement process. The second is a k-way version of t ..."
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We examine three parallel algorithms for repartitioning adaptive finite element grids in the context of dynamic load balancing for adaptive multigrid methods. The first is a recursive bisection method based on the refinement tree of the adaptive refinement process. The second is a k-way version of the refinement tree partitioning method. The third is a multilevel repartitioning algorithm from ParMETIS. The methods are compared numerically via execution time of the partitioner and quality metrics of the partition.
