Results 11  20
of
65
A Hierarchical Partition Model for Adaptive Finite Element Computation
 Comput. Methods Appl. Mech. Engrg
, 1998
"... Introduction The finite element method (FEM) has become a standard analysis tool for solving partial differential equations (PDEs). Computationally demanding threedimensional problems make adaptive methods and parallel computation essential. Adaptive FEMs provide reliability, robustness, and time an ..."
Abstract

Cited by 27 (5 self)
 Add to MetaCart
Introduction The finite element method (FEM) has become a standard analysis tool for solving partial differential equations (PDEs). Computationally demanding threedimensional problems make adaptive methods and parallel computation essential. Adaptive FEMs provide reliability, robustness, and time and space efficiency. In such a method, the computational domain is discretized into a mesh. During the adaptive solution process, portions of the mesh may be refined or coarsened (hrefinement) or moved to follow evolving phenomena (rrefinement). The method order may also be varied (prefinement). Each adaptive process concentrates the computational effort in areas where the solution resolution would otherwise be inadequate [7]. Conventional arraybased data representations, which work well for fixedmesh solutions, are not wellsuited to solutions involving mesh adaptivity [1]. Traversal of the data must be efficient in all cases, but w
Spectral methods for analyzing and visualizing networks: an introduction
 WORKSHOP SUMMARY AND PAPERS
, 2000
"... Network analysis begins with data that describes the set of relationships among the members of a system. The goal of analysis is to obtain from the lowlevel relational data a higherlevel description of the structure of the system which identifies various kinds of patterns in the set of relationshi ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
Network analysis begins with data that describes the set of relationships among the members of a system. The goal of analysis is to obtain from the lowlevel relational data a higherlevel description of the structure of the system which identifies various kinds of patterns in the set of relationships. These patterns will be based on the way individuals are related to other individuals in the network. Some approaches to network analysis look for clusters of individuals who are tightly connected to one another; some look for sets of individuals who have similar patterns of relations to the rest of the network. Other methods don’t “look for ” anything in particular — instead, they construct a continuous multidimensional representation of the network in which the coordinates of the individuals can be further analyzed to obtain a variety of kinds of information about them and their relation to the rest of the network. One approach to this is to choose a set of axes in the multidimensional space occupied by the network and rotate them so that the first axis points in the direction of the greatest variability in the data; the second axis, orthogonal to the first, points in the direction of greatest remaining variability, and so on. This set of axes is a coordinate system that can be used to describe the relative positions
Dynamic LoadBalancing for Parallel Adaptive Unstructured Meshes
, 1997
"... A parallel method for dynamic partitioning of unstructured meshes is described. The method employs a new iterative optimisation technique which both balances the workload and attempts to minimise the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicat ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
A parallel method for dynamic partitioning of unstructured meshes is described. The method employs a new iterative optimisation technique which both balances the workload and attempts to minimise the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more quickly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners. Key words. graphpartitioning, adaptive unstructured meshes, loadbalancing, parallel scientific computation. 1 Introduction The use of unstructured mesh codes on parallel machines can be one of the most efficient ways to solve large Computational Fluid Dynamics (CFD) and Computational Mechanics (CM) problems. Completely general geometries and complex behaviour can be readily modelled an...
Multiphase Mesh Partitioning
 APPL. MATH. MODELLING
, 1999
"... We consider the loadbalancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
We consider the loadbalancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to as the multiphase mesh partitioning strategy to address such issues. The technique is tested on several examples of meshes, both real and artificial, containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where a standard mesh partitioning approach fails.
HashStorage Techniques for Adaptive Multilevel Solvers and Their Domain Decomposition Parallelization
 Domain decomposition methods 10. The 10th int. conf., Boulder, volume 218 of Contemp. Math
, 1998
"... this article remain attractive even for such a code. ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
(Show Context)
this article remain attractive even for such a code.
JOSTLE: Partitioning of Unstructured Meshes for Massively Parallel Machines
 Parallel Computational Fluid Dynamics: New Algorithms and Applications
, 1995
"... this paper we discuss the mesh partitioning problem in the light of the coming generation of massively parallel machines and the resulting implications for such algorithms ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
(Show Context)
this paper we discuss the mesh partitioning problem in the light of the coming generation of massively parallel machines and the resulting implications for such algorithms
A Local Graph Partitioning Heuristic Meeting Bisection Bounds (Extended Abstract)
 8TH SIAM CONF. ON PARALLEL PROCESSING FOR SCIENTIFIC COMPUTING (PP'97
, 1997
"... The problem of graph partitioning is of major importance for a broad range of applications. VLSILayout and parallel programming are only two examples where large graphs have to be cut into pieces. The partitioning of a graph into several clusters is often done by recursive bisection. Bisection heur ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
(Show Context)
The problem of graph partitioning is of major importance for a broad range of applications. VLSILayout and parallel programming are only two examples where large graphs have to be cut into pieces. The partitioning of a graph into several clusters is often done by recursive bisection. Bisection heuristics are usually divided into global and local methods. Popular global methods are inertial or spectral partitioning. For a long time, the KernighanLin algorithm (KL) was the only efficient local heuristic and is still widely used in several applications. Based on the idea of so called Helpful Sets, we recently proposed a new local graph bisection heuristic [3]. Helpful Sets can be used to prove upper bounds on the bisection width of regular graphs. Thus, we are able to give upper bounds on the quality of the bisections found by HS. In this paper, we will present the HSidea, the bisection heuristic, ideas of the proofs of upper bounds, and, finally, discuss the performance of th...
Parallel Adaptive Mesh Refinement and Redistribution on Distributed Memory Computers
 Comput. Methods Appl. Mech. Engrg
, 1993
"... A procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on distributed memory computers is presented. The procedure uses the mesh topological entity hierarchy as the underlying data structures to easily support the required adjacency inform ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
A procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on distributed memory computers is presented. The procedure uses the mesh topological entity hierarchy as the underlying data structures to easily support the required adjacency information. Mesh refinement is done by employing links back to the geometric representation to place new nodes on the boundary of the domain directly on the curved geometry. The refined mesh is then redistributed by an iterative heuristic based on the Leiss/Reddy [9] load balancing criteria. A fast parallel tree edgecoloring algorithm is used to pair processors having adjacent partitions and forming a tree structure as a result of Leiss/Reddy load request criteria. Excess elements are iteratively migrated from heavily loaded to less loaded processors until load balancing is achieved. The system is implemented on a massively parallel MasPar MP2 system with a SIMD style of computation and uses me...
LoadBalancing for Parallel Adaptive Unstructured Grids
, 1998
"... A parallel method for the dynamic partitioning of unstructured meshes is outlined. The method includes diffusive loadbalancing techniques and an iterative optimisation technique known as relative gain optimisation which both balances the workload and attempts to minimise the interprocessor communic ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
A parallel method for the dynamic partitioning of unstructured meshes is outlined. The method includes diffusive loadbalancing techniques and an iterative optimisation technique known as relative gain optimisation which both balances the workload and attempts to minimise the interprocessor communications overhead. It can also optionally include a multilevel strategy. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners. Key words. graphpartitioning, adaptive unstructured meshes, loadbalancing, parallel computing. 1 Introduction The need for mesh partitioning arises naturally in many finite element (FE) and finite volume (FV) applications. Meshes composed of elements such a...
The Full Domain Partition Approach to Distributing Adaptive Grids
 Appl. Numer. Math
, 1998
"... Adaptive refinement has been shown to be an effective means of speeding up the solution of partial differential equations. Adaptive multilevel methods combine multigrid iteration with adaptive refinement to produce fast O(N) solutions on sequential computers. However, many problems of interest requi ..."
Abstract

Cited by 16 (8 self)
 Add to MetaCart
(Show Context)
Adaptive refinement has been shown to be an effective means of speeding up the solution of partial differential equations. Adaptive multilevel methods combine multigrid iteration with adaptive refinement to produce fast O(N) solutions on sequential computers. However, many problems of interest require parallel computers. While adaptive refinement, multigrid and parallel computers are individually achieving wide spread use in applications, the combination of all three is still a research topic. In this paper we describe the full domain partition (FuDoP) distribution of adaptively refined grids over a distributed memory parallel computer. In the FuDoP approach, each processor has a compatible grid that covers the full domain, but with refinement confined to the processor's partition of the total grid. Outside the partition area, refinement is limited to that required for compatibility and leads to a small number of extra grid elements. With the FuDoP distribution, a parallel multigrid me...