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Accelerating Shape Optimizing Load Balancing for Parallel FEM Simulations by Algebraic Multigrid
"... We propose a load balancing heuristic for parallel adaptive finite element method (FEM) simulations. In contrast to most existing approaches, the heuristic focuses on good partition shapes rather than on minimizing the classical edgecut metric. By applying Algebraic Multigrid (AMG), we are able to ..."
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Cited by 4 (4 self)
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We propose a load balancing heuristic for parallel adaptive finite element method (FEM) simulations. In contrast to most existing approaches, the heuristic focuses on good partition shapes rather than on minimizing the classical edgecut metric. By applying Algebraic Multigrid (AMG), we are able to speed up the two most time consuming calculations of the approach while maintaining its large amount of natural parallelism.
Graph partitioning and disturbed diffusion
 Parallel Computing
, 2009
"... The N Phard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph’s vertex set into P equally sized subsets such that some objective function is optimized. Stateoftheart libraries addressing this problem show several ..."
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Cited by 3 (2 self)
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The N Phard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph’s vertex set into P equally sized subsets such that some objective function is optimized. Stateoftheart libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edgecuts instead of few boundary vertices, and often produce disconnected partitions. This work introduces our novel graph partitioning and repartitioning heuristic BubbleFOS/C. In contrast to other libraries, BubbleFOS/C does not try to minimize the edgecut explicitly, but focuses instead implicitly on good partition shapes. The shapes are optimized by diffusion processes that are embedded into an iterative framework. This approach incorporates a high degree of parallelism. Besides describing the evolution process that led to the new diffusion scheme FOS/C used by BubbleFOS/C, we reveal some of FOS/C’s properties and propose a number of enhancements for a fast and reliable implementation. Our experiments, in which we compare sequential and parallel BubbleFOS/C implementations to the stateoftheart libraries Metis and Jostle, reveal that our new heuristic generates highquality solutions.
A3: On Balancing of Dynamic Networks
"... Load balancing is an important prerequisite to efficiently execute dynamic computations on parallel computers. In this context, this project has focussed on two topics: balancing dynamically generated work load cost efficiently in a network and partitioning graphs to equally distribute connected tas ..."
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Load balancing is an important prerequisite to efficiently execute dynamic computations on parallel computers. In this context, this project has focussed on two topics: balancing dynamically generated work load cost efficiently in a network and partitioning graphs to equally distribute connected tasks on the processing nodes while reducing the communication overhead. We summarize new insights and results in these areas.
A Locality Preserving Graph Ordering Approach for Implicit Partitioning: GraphFilling Curves
"... Linear orderings defined through spacefilling 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 spacefilling 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 spacefilling curves have known drawbacks. Especially when applied to deeply refined meshes or discretizations that contain holes, a high edgecut is produced. In this paper we present a new linear ordering approach called graphfilling curves. In contrast to spacefilling 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.
GraphOrder Dithering
"... This paper presents a generalization of disperseddot dithering. While existing methods such as Bayer’s assume that color dots are arranged in a square matrix, this method works with arbitrarilyplaced color points. To create a good dither pattern for arbitrarilyplaced points, they must be ordered ..."
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This paper presents a generalization of disperseddot dithering. While existing methods such as Bayer’s assume that color dots are arranged in a square matrix, this method works with arbitrarilyplaced color points. To create a good dither pattern for arbitrarilyplaced points, they must be ordered so that consecutive pairs are maximally separated. In this papre, the ordering is obtained by hierarchically coloring the vertices of the points’ adjacency graph. Each level in the coloring hierarchy adds a color digit to each graph vertex’s label, and sorting the resulting multidigit labels produces the desired consecutivepoint separation. The method can reproduce Bayer’s disperseddot dither matrices, but can also produce many similar matrices. Multiple matrices can be used to minimize repetitive artifacts that plague Bayer dither, while retaining its parallelizability. The method can also be applied to artistic dithering: given a repeatable motif image, its pixels can be grouped into subsets, one for each gray level, and each subset ordered. Concatenating the subsets yields a dither matrix that reproduces a motif while displaying an overall image. Unlike in previous artistic dither methods, the motif image can be arbitrary, and need not be specially constructed.
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"... On domain decomposition with space filling curves for the parallel solution of the coupled Maxwell/Vlasov equations ..."
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On domain decomposition with space filling curves for the parallel solution of the coupled Maxwell/Vlasov equations