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Adaptive Local Refinement with Octree LoadBalancing for the Parallel Solution of ThreeDimensional Conservation Laws
 J. Parallel Distrib. Comput
, 1997
"... Conservation laws ae solved by a local Gaerkin finite element procedure with adapfive spacetime mesh refinement ad explicit time integration. The Courat stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to method ..."
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Cited by 68 (17 self)
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Conservation laws ae solved by a local Gaerkin finite element procedure with adapfive spacetime mesh refinement ad explicit time integration. The Courat stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. Processor load imbalaces, introduced at adaptive enrichment steps, are corrected by using traversals of an octtee representing a spatial decomposition of the domain. To accommodate the variable time steps, octtee partitioning is extended to use weights derived from element size. Partition boundary smoothing reduces the communications volume of partitioning procedures for a modest cost. Computational results comparing parallel octtee ad inertial partitioning procedures ae presented for the threedimensional Euler equations of compressible flow solved on an IBM SP2 computer.
Dynamic Load Balancing in Computational Mechanics
 Computer Methods in Applied Mechanics and Engineering
"... . In many important computational mechanics applications, the computation adapts dynamically during the simulation. Examples include adaptive mesh refinement, particle simulations and transient dynamics calculations. When running these kinds of simulations on a parallel computer, the work must be a ..."
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Cited by 40 (2 self)
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. In many important computational mechanics applications, the computation adapts dynamically during the simulation. Examples include adaptive mesh refinement, particle simulations and transient dynamics calculations. When running these kinds of simulations on a parallel computer, the work must be assigned to processors in a dynamic fashion to keep the computational load balanced. A number of approaches have been proposed for this dynamic load balancing problem. This paper reviews the major classes of algorithms, and discusses their relative merits on problems from computational mechanics. Shortcomings in the stateoftheart are identified and suggestions are made for future research directions. Key words. dynamic load balancing, parallel computer, adaptive mesh refinement 1. Introduction. The efficient use of a parallel computer requires two, often competing, objectives to be achieved. First, the processors must be kept busy doing useful work. And second, the amount of interprocess...
Parallel Structures and Dynamic Load Balancing for Adaptive Finite Element Computation
 Applied Numerical Mathematics
, 1996
"... this paper, we have focused on describing and comparing several load balancing schemes. Comparisons by timing are difficult, since times vary between runs having the same parameters. The highspeed switch of the IBM SP2 computer is a shared resource that affects run times. More subtle effects can re ..."
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this paper, we have focused on describing and comparing several load balancing schemes. Comparisons by timing are difficult, since times vary between runs having the same parameters. The highspeed switch of the IBM SP2 computer is a shared resource that affects run times. More subtle effects can result from differences in the order in which messages used for migration are processed. Changes in the order in which those messages are received and integrated into the local MDB result in different traversal orders of the mesh entities. These differences cause small changes in load balancings and coarsenings. While such differences in meshes and partitionings do not affect the solution accuracy, they can cause sufficient changes in efficiency to make precise timings difficult. Qualitatively, PSIRB produced the best partitions (measured as a function of total analysis time). Octreegenerated partitions were comparable but resulted in slightly longer solution times. In both cases, one or two iterations of partition boundary smoothing led to a quality improvement. ITB by itself resulted in poorer partition quality, but is useful when mesh changes are small between computational stages. Predictive enrichment provided su21 perior performance to our current enrichment process with transient problems where there are frequent enrichment and balancing steps. Enhancements to the existing load balancing procedures and the implementation of new ones are under investigation. Improvements in the slicebyslice technique used by ITB for migration are necessary. Experiments with geometrical methods that use the spatial location of elements relative to the centroids of sending and receiving processors showed promise at reducing the number of processor interconnections. Vidwans et al. [39] pr...
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 ..."
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Cited by 16 (1 self)
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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...
Multithreaded model for dynamic load balancing parallel adaptive PDE computations
, 1995
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Dynamic Load Balancing for Parallel Finite Element Methods with Adaptive
 In Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing
, 1995
"... We describe a dynamic loadbalancing strategy for parallel finite element methods with adaptive mesh (h) and order (p) refinement. The loadbalancing algorithm is based on the tiling loadbalancing system, where global balance is achieved by performing local balancing within overlapping neighbo ..."
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Cited by 7 (0 self)
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We describe a dynamic loadbalancing strategy for parallel finite element methods with adaptive mesh (h) and order (p) refinement. The loadbalancing algorithm is based on the tiling loadbalancing system, where global balance is achieved by performing local balancing within overlapping neighborhoods of processors. Tiling is applied to each mesh level created by the adaptive hrefinement. Weights are used in the migration routines to reflect the nonuniform elemental work loads caused by adaptive prefinement. The combination of adaptive refinement and tiling significantly reduces total execution time relative to fixedmesh, fixedorder methods yielding comparable accuracy, as we demonstrate with experiments on an nCUBE/2. 1. Introduction Adaptive numerical methods, such as mesh refinement and order enrichment, provide greater efficiency than traditional numerical methods by concentrating computational effort in regions of the problem domain where the solution is difficult to...
Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of ThreeDimensional Conservation Laws
 in Grid Generation and Adaptive Algorithms
, 1999
"... Conservation laws are solved by a local Galerkin finite element procedure with adaptive spacetime mesh refinement and explicit time integration. A distributed octree structure representing a spatial decomposition of the domain is used for mesh generation, and later may be used to correct for pr ..."
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Cited by 5 (3 self)
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Conservation laws are solved by a local Galerkin finite element procedure with adaptive spacetime mesh refinement and explicit time integration. A distributed octree structure representing a spatial decomposition of the domain is used for mesh generation, and later may be used to correct for processor load imbalances introduced at adaptive enrichment steps. A Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Computational results are presented for the threedimensional Euler equations of compressible flow solved on an IBM SP2 computer. The problem examined is the flow inside a perforated shock tube. 1 Introduction Adaptive finite element methods that automatically refine or coarsen meshes (hrefinement) and/or vary the ...
Parallel Paving: An Algorithm for Generating Distributed, Adaptive, Allquadrilateral Meshes on Parallel Computers
 APPENDIX A: CGM CLASS DIAGRAMS
, 1997
"... Paving [1] is an automated mesh generation algorithm which produces allquadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial ..."
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Cited by 2 (2 self)
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Paving [1] is an automated mesh generation algorithm which produces allquadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving's meshing capabilities for hremap remeshing. A significantly modified version of the CUBIT [2] mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm perf...
Vertex Separators for Partitioning a Graph
 Sensors
, 2008
"... Finite Element Method (FEM) is a well known technique extensively studied for spatial and temporal modeling of environmental processes, weather prediction computations, and intelligent signal processing for wireless sensors. The need for huge computational power arising in such applications to simu ..."
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Cited by 1 (0 self)
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Finite Element Method (FEM) is a well known technique extensively studied for spatial and temporal modeling of environmental processes, weather prediction computations, and intelligent signal processing for wireless sensors. The need for huge computational power arising in such applications to simulate physical phenomenon correctly mandates the use of massively parallel computers to distribute the workload evenly. In this study, a novel heuristic algorithm called Line Graph Bisection which partitions a graph via vertex separators so as to balance the workload amongst the processors and to minimize the communication overhead is proposed. The proposed algorithm is proved to be computationally feasible and makes costeffective parallel implementations possible to speed up the solution process.
Techniques for Parallel Adaptivity
 Parallel and Distributed Processing for Computational Mechanics II. SaxeCoburg Publications
, 1998
"... : This paper considers the main algorithmic issues associated with developing parallel mesh adaptivity software for use with tetrahedralbased parallel finite element or finite volume solvers for transient computational mechanics problems in three space dimensions. Issues that are addressed include ..."
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: This paper considers the main algorithmic issues associated with developing parallel mesh adaptivity software for use with tetrahedralbased parallel finite element or finite volume solvers for transient computational mechanics problems in three space dimensions. Issues that are addressed include the use of different parallel data structures, the modification of these data structures when adaptivity occurs and the dynamic maintenance of loadbalance in the parallel solver. 1 Introduction Adaptive algorithms are an important feature of almost all stateoftheart software for computational mechanics and scientific computation. These algorithms can take many forms, the most common being hrefinement (e.g. [25, 33]), prefinement (e.g. [2, 42]) or rrefinement (e.g. [26, 27]), with various combinations of these also possible (e.g. [3, 10, 11]). The overall aim of any adaptive algorithm is to allow a balance to be obtained between accuracy and computational efficiency. In those regions ...