J. Flower, S. Otto, and M. Salana. Optimal mapping of irregular finite element domains to parallel processors. Parallel Computers and Their Impact on Mechanics, 86:239--250, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....approaches for the solution of the optimization problem (2.0) The first approach is based on the approximation of the objective function (2. 0) by another function which is smoother, more robust and suitable for the existing deterministic and stochastic (physical) optimization methods [Fox86a] FOS88] Wil90] and [Man92] The second approach is based on the splitting of the optimization problem into two distinct phases corresponding to the partitioning and allocation of the mesh [CHENHR89] CHH90] Chr92] and [Sim90] In the partitioning phase we decompose the mesh (or grid) in a ....

....where P is the number of available processors. The sorting of geometric data like the coordinates of node points, the coordinates of the sector origin of the elements, and the coordinates of the centroid of the elements of a mesh have been considered by many researchers (see [Bok81] SE87] FOS88] LF90] and [PAF90] This idea is referred in the literature under different names, some of them are : one dimensional (1D) strip partitioning, two dimensional (2D) strip partitioning, multilevel load balanced method, median splitting, and sector splitting. Throughout this paper, we refer to ....

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J. Flower, S. Otto, and M. Salana. Optimal mapping of irregular finite element domains to parallel processors. Parallel Computers and Their Impact on Mechanics, 86:239--250, 1988.

....phases the synchronization term in equation (2.0) is included in W (m(D i ) One approach to solve the optimization problem (2.0) is to approximate its of the objective function (2. 0) by another function which is smoother, more robust and suitable for the existing optimization methods [Fox86a] FOS88] Wil90] and [Man92] A second approach is to split the optimization problem into two distinct phases corresponding to the partitioning and allocation of the mesh [CHENHR89] CHH90] Chr92] and [Sim90] In the partitioning phase we decompose the mesh (or grid) in a prespecified number (usually ....

....where P is the number of available processors. The sorting of geometric data like the coordinates of node points, the coordinates of the sector origin of the elements, and the coordinates of the centroid of the elements of a mesh have been considered by many researchers (see [Bok81] SE87] FOS88] LF90] and [PAF90] This idea is referred in the literature under different names, some of them are : one dimensional (1D) strip partitioning, two dimensional (2D) strip partitioning, multilevel load balanced method, median splitting, and sector splitting. Throughout this paper, we refer to ....

[Article contains additional citation context not shown here]

J. Flower, S. Otto, and M. Salana. Optimal mapping of irregular finite element domains to parallel processors. Parallel Computers and Their Impact on Mechanics, 86:239--250, 1988.

....algorithms that try to achieve load balancing and minimum communication are as different as the number of researchers working on the problem. However, recently published mesh decomposition algorithms can be grouped into three categories: engineering, optimization, and graph theory based heuristics [2 9]. Deciding which specific algorithm or category of algorithms is best is as difficult as defining what exactly constitutes an efficient partition. The answers to both questions are mesh, problem, and machine dependent. The main idea behind designing TOP DOMDEC is to let each analyst decide ....

J. Flower, S. Otto and M. Salama, Optimal mapping of irregular finite element domains to parallel processors, in A. K. Noor, ed., Parallel Computations and Their Impact on Mechanics, The American Society of Mechanical Engineers, AMD-Vol. 86, (1987) 239-252.

....minimized in order to to minimize interprocess communication. I refer to the process of partitioning the elements (cells) of a computational mesh into subdomains that can each be processed in parallel as the domain decomposition problem. A number of solutions to this problem have been proposed [6, 14, 28, 29, 30, 46, 67, 75, 90]. Sadayappan and Ercal [90] summarize a number of categories of approaches to the domain decomposition problem, including graph based approaches, mathematical programming based formulations, queuing theory based models and heuristic approaches such as scattered decomposition [67] simulated ....

.... and Ercal [90] summarize a number of categories of approaches to the domain decomposition problem, including graph based approaches, mathematical programming based formulations, queuing theory based models and heuristic approaches such as scattered decomposition [67] simulated annealing [30] and a graph based recursive bisection model [32] It has been found that the MPVO Algorithm may be a candidate for domain decomposition of unstructured finite element meshes. While the resulting partitioning may not be optimal, it has the property of coherence. The simulated annealing process ....

[Article contains additional citation context not shown here]

FLOWER, J., OTTO,S. and SALAMA, M. Optimal Mapping of Irregular Finite Element Domains to Parallel Processors. in Parallel Computations and Their Impact on Machines, A. Noor, ed., Am. Soc. Mech. Engin., New York (1987), 239--250.

....surely afford to lose another 10 to load imbalance. The problem of distributing a computation onto a parallel machine in an efficient manner can therefore be fruitfully attacked using simulated annealing [41] and other physical optimization methods such as neural networks and genetic algorithms [11, 25, 27, 13, 55, 22, 45]. The physical analogy described above makes this plausible, since these methods are highly appropriate minimization techniques for Equation 14. For example, simulated annealing is a standard Monte Carlo technique that was originally devised to find the ground states of spin models of magnetism ....

....to use time consuming optimization techniques such as simulated annealing to obtain good data distribution. Scattered decomposition has proven to be very effective for problems such as adaptive mesh finite element simulations, where the grid is much finer in regions that are changing more rapidly [49, 11]; growing a cluster in spin models of magnetism [2] and certain matrix problems [30] For a dynamic problem, the Hamiltonian of Equation 16 will vary with (computer) time, and so will its minimum value (the optimal domain decomposition) The operating system will need to redistribute the data ....

Flower, J., Otto, S. & Salama, M. (1987). Optimal mapping of irregular finite element domains to parallel processors. In Proc. Symposium on Parallel Computations and Their Impact on Mechanics, ASME Winter Meeting, Boston, Mass.

.... T solver ; examples are Kernighan Lin algorithm [35] and geometry graph partitioning [4] Yet, another class of mapping algorithms are based on physical optimization that employs techniques from natural sciences [18] examples are neural networks, simulated annealing, and genetic algorithms [30] [16], 17] 38] 58] Although a good deal of work has been published on data mapping, only few attempts have been made at comparing some algorithms using aggregate or a limited number of performance measures [4] 11] 52] 39] 58] 27] In this paper, we use several measures to evaluate and ....

....and (6) a genetic algorithm. The last three algorithms use the first formulation for the data mapping problem while the first three algorithms adopt the second approach. 3. 1 P ThetaQ Partitioning Algorithm A simple and attractive mapping method considered by many researchers (see [2] 49] [16], 45] and [10] is the so called data strip or block partitioning heuristic. This heuristic is referred under different names, some of them are : one dimensional (1D) strip partitioning, two dimensional (2D) strip partitioning, multilevel load balanced method, median splitting, sector splitting, ....

J. Flower, S. Otto, and M. Salana. Optimal mapping of irregular finite element domains to parallel processors. Parallel Computers and Their Impact on Mechanics, 86:239--250, 1988.

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