D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meth. Appl. Mech. Engrg., 133:25--45, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of iterations of the global CG. Both are at least partially determined by the shape of the subdomains. Whilst an algorithm such as the multigridmethod as the solver on the subdomains is relatively robust against shape, the number of global iterations are heavily influenced by the AR of subdomains, [17]. Essentially, the subdomains can be viewed as elements of the interface problem, 7, 8] and just as with the normal finite element method, where the condition of the matrix system is determined by the AR of elements, the condition of the preconditioning matrix is here dependent on the AR of ....

D. Vanderstraeten,C. Farhat, P. S. Chen, R. Keunings,andO. Zone. A Retrofit BasedMethodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meth. Appl. Mech. Engrg., 133:25--45, 1996.

....solution. However the paradigm does not preclude the use of more complex techniques and there is no reason (other than execution time) why it should not be a more sophisticated scheme. Indeed, in the case of graph partitioning, examples of multilevel implementations exist for simulated annealing, [34], tabu search, 2, 34] and even genetic algorithms, 21] The refinement algorithm must also be able to cope with any additional restrictions placed on it by using a coarsened problem (e.g. in graph partitioning the coarser graphs are always weighted whether or not the original is) If such a ....

....the paradigm does not preclude the use of more complex techniques and there is no reason (other than execution time) why it should not be a more sophisticated scheme. Indeed, in the case of graph partitioning, examples of multilevel implementations exist for simulated annealing, 34] tabu search, [2, 34], and even genetic algorithms, 21] The refinement algorithm must also be able to cope with any additional restrictions placed on it by using a coarsened problem (e.g. in graph partitioning the coarser graphs are always weighted whether or not the original is) If such a refinement algorithm ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

.... complexity improvements (e.g. bucket sorting of vertices) due to Fiduccia Mattheyses, 15] We outline the KL refinement algorithm to illustrate the process, however in principle any iterative refinement scheme can be used and examples of multilevel implementations exist for simulated annealing, [57], tabu search, 4, 57] and even genetic algorithms, 33] A typical KL algorithm will have inner and outer iterative loops with the outer loop terminating when no vertex transfers take place during an inner loop. It is initialised by calculating the gain the potential improvement in the cost ....

.... (e.g. bucket sorting of vertices) due to Fiduccia Mattheyses, 15] We outline the KL refinement algorithm to illustrate the process, however in principle any iterative refinement scheme can be used and examples of multilevel implementations exist for simulated annealing, 57] tabu search, [4, 57], and even genetic algorithms, 33] A typical KL algorithm will have inner and outer iterative loops with the outer loop terminating when no vertex transfers take place during an inner loop. It is initialised by calculating the gain the potential improvement in the cost function (the ....

[Article contains additional citation context not shown here]

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

.... sorting of vertices) introduced to partitioning by Fiduccia Mattheyses, 9] However, although the KL algorithm is perhaps the most commonly used refinement scheme, in principle any iterative refinement scheme can be used and examples of multilevel implementations exist for simulated annealing, [31], tabu search, 4, 31] genetic algorithms, 20] cooperative search, 30] and even ant colony optimisation, 22] Before exploring the hierarchy of landscapes produced by the multilevel coarsening we had to make a number of decisions about what to test and how to test it. Firstly, since we are ....

.... introduced to partitioning by Fiduccia Mattheyses, 9] However, although the KL algorithm is perhaps the most commonly used refinement scheme, in principle any iterative refinement scheme can be used and examples of multilevel implementations exist for simulated annealing, 31] tabu search, [4, 31], genetic algorithms, 20] cooperative search, 30] and even ant colony optimisation, 22] Before exploring the hierarchy of landscapes produced by the multilevel coarsening we had to make a number of decisions about what to test and how to test it. Firstly, since we are interested in the ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

.... for certain classes of solution algorithm, the convergence of the solver is actually heavily influenced by the shape or aspect ratio (AR) of the subdomains and in this case the overall solution time can be more dependent on the number of iterations than on the parallel communications overhead, [23]. In this paper therefore, we modify the multilevel algorithms (the matching and local optimisation) in order to optimise a cost function based on AR. We also abstract the process of modification in order to suggest how the multilevel strategy can be modified into a generic technique which can ....

....of the global CG. Both are at least partially determined by the shape 1 of the subdomains. Whilst an algorithm such as the multigrid method as the solver on the subdomains is relatively robust against shape, the number of global iterations are heavily influenced by the AR of subdomains, [23]. Essentially, the subdomains can be viewed as elements of the interface problem, 10, 11] and just as with the normal finite element method, where the condition of the matrix system is determined by the AR of elements, the condition of the preconditioning matrix is here dependent on the AR of ....

[Article contains additional citation context not shown here]

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meth. Appl. Mech. Engrg., 133:25--45, 1996.

....Depending on the characteristics of the target parallel machine, minimizing the number of neighbors of each subdomain (and therefore the number of messages sent) can be as important as minimizing the total number of shared nodes. In this paper we quantify the conditions for which this is true. In [20], Vanderstraeten et al. presented a two step partitioning paradigm for refining the results of any partitioning scheme to tailor them to specific applications. The first step involves generating a partition using any of the aforementioned decomposition methods. The second (application specific) ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. University of Colorado at Boulder, College of Engineering Technical Report CU-CAS-94-18 (1994). 24

.... that for certain classes of solution algorithm, the convergence of the solver is actually heavily influenced by the shape or aspect ratio (AR) of the subdomains and in this case the overall solution time can be more dependent on the number of iterations than on the parallel communications overhead (Vanderstraeten et al. 1996). In this paper therefore, we modify the multilevel algorithms (the matching and local optimisation) in order to optimise a cost function based on AR. We also abstract the process of modification in order to suggest how the multilevel strategy can be modified into a generic technique which can ....

....of iterations of the global CG. Both are at least partially determined by the shape of the subdomains. Whilst an algorithm such as the multigrid method as the solver on the subdomains is relatively robust against shape, the number of global iterations are heavily influenced by the AR of subdomains (Vanderstraeten et al. 1996). Essentially, the subdomains can be viewed as elements of the interface problem (Farhat et al. 1995; Farhat et al. 1994) and just as with the normal finite element method, where the condition of the matrix system is determined by the AR of elements, the condition of the preconditioning matrix ....

[Article contains additional citation context not shown here]

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. 1996. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45.

.... differential equations on parallel computers are described in [20, 105] The parallel solution of Euler equations and other CFD problems are described in [28, 59, 95, 102] A survey of parallel computing in CFD has been provided in [93] Applications in structural mechanics have been considered in [58, 82, 100]. A comparative study of partitioners in domain decomposition has been provided in [24] Dynamic load balancing for time dependent partial differential equations has been considered in [57, 101, 103] 8.2 Spectral Nested Dissection Nested dissection is a divide and conquer scheme for ordering ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone, A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions, Tech. Report CAS94 -18, Center for Aerospace Structures, University of Colorado, Boulder, 1994.

....size in an attempt to minimize the application s communication costs. In some applications, however, criteria other than subdomain interface size become important. For domain decomposition linear solvers, for example, the aspect ratio of the subdomains affects the convergence of the solvers. In [12, 53], the cost function to be minimized is a weighted combination of the load imbalance and the subdomain aspect ratio. Thus, objects whose coordinates are farthest from the average coordinates of all the processor s objects are selected for migration. While this criterion is specific to a particular ....

D. Vanderstraeten, C. Farhat, P. Chen, R. Keunings, and O. Ozone, A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyond the minimum interface size criterion, Comput. Methods Appl. Mech. Engrg., 133 (1996), pp. 25--45.

....loop of adaptive flow calculations, due to the potentially high partitioning and data movement cost. Some dynamic load balancing techniques reuse the original partition by only considering the transfer of those elements located on the subdomains boundaries. In the work of Vanderstraeten et al. [69] a decomposed domain undergoes one level of adaptive refinement resulting in an unbalanced load. A comparison is then made between retrofitting the original decomposition along its boundaries (using SA) and performing the decomposition from scratch (using the Greedy technique of Farhat [57] ....

D. Vanderstraeten, C. Farhat, P. Chen, R. Keunings, and O. Zone, A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyons the minimum interface size criterion. University of Colorado, Technical Report, CU-CAS-94-18, 1994.

....annealing [12] and greedy methods [8, 13] These methods attempt to balance the computational load assigned to the processors in such a way that the total interprocessor communication remains small. However, their primary focus is on balancing the computational load assigned to each processor. In [20], Vanderstraeten et al. present a two step partitioning paradigm for refining the results of a partitioning scheme to tailor it to specific applications. The first step involves generating a partition of the domain using any of the aforementioned decomposition methods. The second ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: Beyond the minimum interface size criterion. Technical Report CU-CAS-94-18, University of Colorado at Boulder, College of Engineering, 1994.

....bisection [5] simulated annealing [6] and greedy methods [7, 8] These methods attempt to balance the load assigned to the processors in such a way that the total interprocessor communication remains small. Hence their primary focus is on balancing the load assigned to the processors. In [9], Vanderstraeten et al. present a two step partitioning paradigm for refining the results of a partitioning scheme to tailor it to specific applications. The first step involves generating a partition using any of the aforementioned decomposition methods. The second (applicationspecific) step ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. "A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: Beyond the minimum interface size criterion. " Technical Report CU-CAS-94-18, University of Colorado at Boulder, College of Engineering,1994.

....iterations of the global CG. Both are at least partially determined by the shape of the subdomains. Whilst an algorithm such as the multigrid method as the solver on the subdomains is relatively robust against shape, the number of global iterations are heavily influenced by the AR of subdomains, [18]. Essentially, the subdomains can be viewed as elements of the interface problem, 7, 8] and just as with the normal finite element method, where the condition of the matrix system is determined by the AR of elements, the condition of the preconditioning matrix is here dependent on the AR of ....

.... Related work The idea of optimising AR in order to maintain scalability in the solver was first developed by Farhat et al. 7, 8] This was backed up by Vanderstraeten et al. who showed that partitioning for cut edge weight was not necessarily the most appropriate optimisation for every solver [18, 19]. However the field of mesh partitioning has changed somewhat since this work was carried out and although other more recent work exists which takes AR into account, e.g. 5, 6, 17] our aim in this paper is to extend the ideas in the light of recent developments in mesh partitioning technology ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meth. Appl. Mech. Engrg., 133:25--45, 1996.

....Partitioning for Efficient Use of Distributed Systems Jian Chen Valerie E. Taylor Department of Electrical and Computer Engineering Northwestern University Evanston, IL 60208 fjchen, taylorg ece.nwu.edu Abstract Mesh partitioning for homogeneous systems has been studied extensively [2, 4, 14, 31, 36, 37, 41]; however, mesh partitioning for distributed systems is a relatively new area of research. To ensure efficient execution on a distributed system, the heterogeneities in the processor and network performance must be taken into consideration in the partitioning process; equal size subdomains and ....

....the problem domain. Execution of a mesh based application on a parallel or distributed system involves partitioning the mesh into subdomains that are assigned to individual processors in the parallel or distributed system. Mesh partitioning for homogeneous systems has been studied extensively [2, 4, 14, 31, 36, 37, 41]; however, mesh partitioning for distributed systems is a relatively new area of research brought about by the recent availability of such systems. To ensure efficient execution on a distributed system, the heterogeneities in the processor and network performance must be taken into consideration ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: Beyond the minimum interface size criterion. Technical report, Center for Aerospace Structures, University of Colorado, September 1994. 34

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meths. Appl. Mech. Engrg., (to appear).

....when network performance is considered. The result from the irregular problem indicate a 21 increase in efficiency when processor and network performance are considered as compared to even partitioning. 1 Introduction Mesh partitioning for homogeneous systems has been studied extensively [1, 2, 5, 15, 17, 18, 24]; however, mesh partitioning for distributed systems is a relatively new area of research. To ensure efficient execution on a distributed system, the heterogeneities in the processor and network performance must be taken into consideration in the partitioning process; equal size subdomains and ....

D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: Beyond the minimum interface size criterion. Technical report, Center for Aerospace Structures, University of Colorado, September 1994.

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comp. Meth. Appl. Mech. Engrg., 133:25--45, 1996.

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

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D. Vanderstraeten, C. Farhat, P. S. Chen, R. Keunings, and O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions: Beyond the Minimum Interface Size Criterion. Comput. Methods Appl. Mech. Engrg., 133:25--45, 1996.

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