Partitioning Of Grids Research Articles

Evaluation of the influence of spatial treatments on catch-per-unit-effort standardization: A fishery application and simulation study of Pacific saury in the Northwestern Pacific Ocean

Fishery-dependent catch-per-unit-effort (CPUE) data often exhibit spatial heterogeneity over space and time, which means that the spatial treatment in statistical models used to standardize CPUE is critically important. We evaluated several spatial treatments to standardize CPUE data using Generalized Linear Mixed Models (GLMMs). Results include a real-world application and a simulation based on the Taiwanese stick-held dip net fishery for Pacific saury in the Northwestern Pacific Ocean. We compared the performance of three spatially stratified approaches in GLMMs, (i) Ad hoc; (ii) Binary (binary recursive area partitioning based on model selection criteria); and (iii) Spatial clustering (partitioning of grids into discrete strata based on the spatial proximity and average CPUE in each grid), to a spatio-temporal GLMM (VAST). An influence analysis was constructed to quantify discrepancies between unstandardized and standardized indices that assisted in identifying the annual influence of explanatory variables in GLMMs. We developed a simulation to corroborate the results from the case study and evaluated the four spatial treatments using data generated from two contrasted, random and preferential, sampling scenarios. Results from the real-world application indicated that VAST was statistically superior to the other approaches, based on conditional deviance explained, conditional Akaike Information Criterion, and five-fold cross-validations. The influence analysis indicated that the interaction of year and spatial effect or spatio-temporal variable had a major influence on the standardized CPUE. Both simulation scenarios showed that VAST performed the best, with the lowest model error (measured by root mean square error) and bias, for estimating relative abundance indices. Although the spatial clustering approach created a flexible shape for the area strata, the simulation results under preferential samplings showed that clustering with a stronger emphasis placed on average CPUE could lead to bias in estimated abundance indices. However, spatial clustering that balanced average CPUE with spatial proximity could be a reasonable alternative if it is not possible to apply a spatio-temporal approach. The importance of conducting influence analysis and the greater performance of a spatio-temporal approach are highlighted.

Understanding Communities From a New Functional Perspective in Power Grids

The contributions of this article include a new concept, a new question, and a new method. This article proposes the concept of functional community, which is different from conventional topological community. Functional community is defined with two meanings: (1) tighter internal coupling for better efficiency within the same community; (2) more internal transmission from source to sink nodes within the same community. Then a new question about how to detect functional communities in power grids is analyzed, and most existing algorithms are not applicable. Therefore, a new method is put forward. Corresponding to meaning 1, electrical coupling strength (ECS) is defined to replace conventional adjacency matrix; corresponding to meaning 2, power supply strength is defined and integrated with ECS to form the newly defined electrical functional strength. Based on these two changes, we apply the proposed power supply modularity as a benchmark to evaluate any partitioning of power grids. Moreover, the Newman fast algorithm is modified with power supply modularity maximization to detect functional communities in power grids. The capability of the proposed partitioning method is demonstrated via the IEEE-118, IEEE-300 bus systems, and an Italian power grid. We argue that the conventional topological modularity may exaggerate the community characteristics of power grids and is inferior to the power supply modularity in detecting some functional features in communities. The work can also give inspiration to other engineering networks for functional communities.

Partitioning-Based Unified Power Flow Algorithm for Mixed MTDC/AC Power Systems

This paper presents a unified power flow algorithm for large and complex mixed ac/dc power systems based on the partitioning of power grids, a version of the two-level Newton method, and the modified nodal analysis formulation. Partitioning significantly increases numerical efficiency without altering the accuracy of the power flow solution. This approach can be applied to any combination of multiple dc and possibly non-synchronized ac systems. It considers the steady-state interaction of ac and dc systems for a wide range of converter representations and control functions. Simplification of elements within the converter stations is not required. Both dc and ac-side converter losses are adequately accounted for by using a generalized converter loss model. The steady-state converter equations are derived in their most general form, with the ac and/or dc-side power exchange or voltages defined as controlled quantities.

Graph partitioning of power grids considering electricity sharing

Graph partitioning of power grids considering electricity sharing

A multilevel tabu search algorithm for balanced partitioning of unstructured grids

SummaryThis paper presents a multilevel algorithm for balanced partitioning of unstructured grids. The grid is partitioned such that the number of interface elements is minimized and each partition contains an equal number of grid elements. The partition refinement of the proposed multilevel algorithm is based on iterative tabu search procedure. In iterative partition refinement algorithms, tie‐breaking in selection of maximum gain vertices affects the performance considerably. A new tie‐breaking strategy in the iterative tabu search algorithm is proposed that leads to improved partitioning quality. Numerical experiments are carried out on various unstructured grids in order to evaluate the performance of the proposed algorithm. The partition results are compared with those produced by the well‐known partitioning package Metis and k‐means clustering algorithm and shown to be superior in terms of edge cut, partition balance, and partition connectivity. Copyright © 2015 John Wiley & Sons, Ltd.

A discontinuous Galerkin scheme for Chimera overset viscous meshes on curved geometries

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems. The use of structured meshes has enabled engineers to develop a number of high-order schemes, such as the WENO and compact differencing schemes. This paper demonstrates a Discontinuous Galerkin (DG) scheme with a Chimera overset method applied to viscous meshes on curved geometries. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes. The small stencil simplifies the hole cutting and partitioning of grids that contain holes. In addition, because the DG scheme represents the solution as cell local polynomials, it does not require an interpolation scheme with a large stencil to establish the inter-grid communication in overlapping regions. Furthermore, the DG scheme is capable of using curved cells to represent geometric features. The curved cells resolve issues associated with linear non-co-located Chimera viscous meshes used for finite volume and finite difference schemes. The DG-Chimera method is demonstrated on a set of viscous Chimera meshes, which would produce erroneous results for a finite volume or finite difference scheme without corrections to the interpolation.

Partitioning strategies for structured multiblock grids

A framework is presented for partitioning of multiblock grids used in data parallel applications. It includes partitioning strategies found in the literature, as well as new algorithms proposed here. In particular, a multilevel graph-partitioning strategy – specifically designed for structured composite grids – is proposed. Different partitioning strategies are compared in two case studies involving multiblock grids. One of the applications is a profile of a multi-element wing from Airbus A310. The partition properties from the different strategies and algorithms depend very much on the number of subgrids and their sizes as well as on the number of processors. Results demonstrate that existing strategies behave well in some cases while the new multilevel graph-partitioning strategy gives an overall good performance.

Self-avoiding walks over adaptive unstructured grids

In this paper, we present self-avoiding walks as a novel technique to “linearize” a triangular mesh. Unlike space-filling curves which are based on a geometric embedding, our algorithm is combinatorial since it uses the mesh connectivity only. We also show how the concept can be easily modified for adaptive grids that are generated in a hierarchical manner based on a set of simple rules, and made amenable for efficient parallelization. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.

Octree partitioning of hybrid grids for parallel adaptive viscous flow simulations

A parallel finite volume method for the Navier–Stokes equations with adaptive hybrid prismatic/tetrahedral grids is presented and evaluated in terms of parallel performance. A new method of domain partitioning for complex 3D hybrid meshes is also presented. It is based on orthogonal bisection of a special octree corresponding to the hybrid mesh. The octree is generated automatically and can handle any type of 3D geometry and domain connectivity. One important property of the octree-based partitioning that is exploited is the octree's ability to yield load-balanced partitions that follow the shape of the geometry. This biasing of the octree results in a reduced number of grid elements on the interpartition boundaries and thus fewer data to communicate among processors. Furthermore, the octree-based partitioning gives similar quality of partitions for very different geometries, while requiring minimal user interaction and little computational time. The partitioning method is evaluated in terms of quality of the subdomains as well as execution time. Viscous flow simulations for different geometries are employed to examine the effectiveness of the octree-based partitioning and to test the scalability of parallel execution of the Navier–Stokes solver and hybrid grid adapter on two different parallel systems, the Intel Paragon and the IBM SP2. © 1998 John Wiley & Sons, Ltd.

Topologically Rectangular Grids in the Parallel Simulationof Semiconductor Devices

Topologically rectangular grids offer simplicity and efficiency in the design of parallel semiconductor device simulators tailored for mesh connected MIMD platforms. This paper presents several approaches to the generation of topologically rectangular 2D and 3D grids. The effects of the partitioning of such grids on different processor configurations are studied. A simulated annealing algorithm is used to optimise the partitioning of 2D and 3D grids on two dimensional arrays of processors. Problems related to the discretization, parallel matrix generation and solution strategy are discussed. The use of topologically rectangular grids is illustrated through the example of power electronic device simulation.

Decentralized remapping of data parallel applications in distributed memory multiprocessors

SUMMARY In this paper we present a decentralized remapping method for data parallel applications on distributed memory multiprocessors. The method uses a generalized dimension exchange (GDE) algorithm periodically during the execution of an application to balance (remap) the system’s workload. We implemented this remapping method in parallel WaTor simulations and parallel image thinning applications, and found it to be effective in reducing the computation time. The average performance gain is about 20% in the WaTor simulation of a 256 256 ocean grid on 16 processors, and up to 8% in the thinning of a typical image of size 128 128 on eight processors. The performance gains due to remapping in the image thinning case are reasonably substantial given the fact that the application by its very nature does not necessarily favor remapping. We also implemented this remapping method, using up to 32 processors, for partitioning and re-partitioning of grids in computational fluid dynamics. It was found that the GDE-based parallel refinement policy, coupled with simple geometric strategies, produces partitions that are comparable in quality to those from the best serial algorithms. ©1997 John Wiley & Sons, Ltd.

PARTITIONING STRATEGIES FOR COMPOSITE GRIDS*

Two different strategies are discussed, for the partitioning of composite grids, in the context of parallel computers of MIMD type with distributed memory. The two strategies are compared theoretically, with respect to arithmetic load balance and communication overhead. Moreover, the ability to handle dynamically changing grids is considered. Composite, structured grids are the natural choice for finite difference methods on complicated geometries, which can not be covered by a single, structured grid. A composite grid is a union of (in general curvilinear) structured grids. So called multi-block grids, frequently used, e.g., in aerodynamical computations, constitute a special case. The discussion in the present paper is valid also if the blocks are unstructured, and for hybrids such as dragon grids. Composite grids are more complicated to partition than single grids. The present paper points out the difficulties in detail, giving some quantification of the overhead that may result from a naive implementation of composite grid partitioning. These results indicate what are the crucial implementation issues in the present context.

Straightforward partitioning of composite grids for explicit difference methods

A straightforward partitioning strategy is analyzed for the case of explicit difference methods on composite grids. The computer is assumed to be of MIMD type with distributed memory. The amount of computational work at the boundary points is assumed to differ from that at the interior points. Theoretical estimates of the efficiency show that the straightforward strategy will be sufficiently efficient for problems with a relatively small work load at the boundary points, a modest number of processors, and close to square grids. For problems that are far from having these properties, a more sophisticated partitioning strategy is needed.