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A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection
- Numerical Mathematics: Theory, Methods and Applications
"... Local mesh refinement is one of the key steps in implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. The algorithm is part of PHG, Parallel Hierarch ..."
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Local mesh refinement is one of the key steps in implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. The algorithm is part of PHG, Parallel Hierarchical Grid, a toolbox under development for parallel adaptive multigrid solution of PDEs. The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Some general properties on local refinement of conforming tetrahedral meshes using bisec-tion are also discussed which are useful in analysing and validating the parallel refinement algorithm as well as in simplifying the implementation.
Experiences from Integrating Algorithmic and Systemic Load Balancing Strategies
, 1998
"... Load balancing increases the efficient usage of existing resources for parallel and distributed applications. At a coarse level of granularity, advances in runtime systems for parallel programs have been proposed in order to control available resources as efficiently as possible by utilizing idle ..."
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Cited by 1 (1 self)
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Load balancing increases the efficient usage of existing resources for parallel and distributed applications. At a coarse level of granularity, advances in runtime systems for parallel programs have been proposed in order to control available resources as efficiently as possible by utilizing idle resources and using task migration. Simultaneous- ly, at a finer granularity level, advances in algorithmic strategies for dynamically balancing computational loads by data redistribution have been proposed in order to respond to variations in processor performance during the execution of a given parallel application. Combining strategies from each level of granularity can result in a system which delivers ad- vantages of both. The resulting integration is systemic in nature and transfers the responsibility of efficient resource uti- lization from the application programmer to the runtime system. This paper reports on recent experimental results of running a computationally intensive sc...
Worst Case Complexity of Parallel Triangular Mesh Refinement by Longest Edge Bisection
, 1996
"... We present a logarithmic algorithm for performing parallel refi#12;nement of triangular meshes by the widely used longest edge bisection procedure. We show that the refi#12;nement propagation forms a data dependency which can be expressed as a forest of directed trees. We solve a parallel Euler Tour ..."
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Cited by 1 (0 self)
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We present a logarithmic algorithm for performing parallel refi#12;nement of triangular meshes by the widely used longest edge bisection procedure. We show that the refi#12;nement propagation forms a data dependency which can be expressed as a forest of directed trees. We solve a parallel Euler Tour problem on the trees to propagate the refi#12;nement. After propagation, we apply re#12;nement templates. Our algorithm improves earlier reported results which had linear worst case complexity.
Computing and Visualization in Science manuscript No. (will be inserted by the editor) Some Variants of the Bank-Holst Parallel Adaptive Meshing Paradigm
, 2004
"... Abstract. The Bank-Holst adaptive meshing paradigm is an efficient approach for parallel adaptive meshing of elliptic partial differential equations. It is designed to keep communication costs low and to take advantage of existing sequential adaptive software. While in principle the procedure could ..."
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Abstract. The Bank-Holst adaptive meshing paradigm is an efficient approach for parallel adaptive meshing of elliptic partial differential equations. It is designed to keep communication costs low and to take advantage of existing sequential adaptive software. While in principle the procedure could be used in any parallel environment, it was mainly conceived for use on small Beowulf clusters with a relatively small number of processors and a slow communication network. A typical calculation on such a machine might involve, say p = 32 processors, an adaptive fine mesh with a few million vertices, and use 2–3 minutes of computational time. In this work we, discuss a variant of the original scheme that could be used in situations where a much larger number of processors, say p> 100 is available. In this case the problem size could be much larger, say 10–100 million, with still a low to moderate computation time. Key words Bank–Holst algorithm, parallel adaptive grid generation.
INTERNATIONAL JOURNAL OF COMPUTATIONAL SCIENCE AND ENGINEERING 1 Incremental Subdivision for Triangle Meshes
"... subdivision of the same mesh produces a smooth surface, but with fewer faces. Abstract — We introduce incremental subdivision as a new adaptive subdivision method for triangle meshes. While regular (global) subdivisions produce a smooth surface from a given polygon mesh by refining all of its faces, ..."
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subdivision of the same mesh produces a smooth surface, but with fewer faces. Abstract — We introduce incremental subdivision as a new adaptive subdivision method for triangle meshes. While regular (global) subdivisions produce a smooth surface from a given polygon mesh by refining all of its faces, adaptive subdivision produces a surface by refining only some selected areas of the mesh. Consequently, the selected area becomes fine and high resolution while the rest of mesh is coarse. Incremental subdivision produces a surface whose subdivided area is identical to when the entire mesh is subdivided regularly. In addition, as a good effect, the resolution of the produced surface gradually increases from coarse to fine. The incremental subdivision method expands the specified area to create a buffer region that is subdivided along with it. This method is efficient and easy to implement. We apply the incremental method to Loop and Butterfly subdivision schemes, and we compare it with other adaptive subdivision methods. We discuss some applications of incremental subdivision.
Dynamic loadbalancing in a lightweight adaptive parallel multigrid PDE solver.
"... A parallel version of an adaptive multigrid solver for partial differential equations is considered. The main emphasis is put on the load balancing algorithm to distribute the adaptive grids at runtime. The background and some applications of space-filling curves are discussed, which are later on us ..."
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A parallel version of an adaptive multigrid solver for partial differential equations is considered. The main emphasis is put on the load balancing algorithm to distribute the adaptive grids at runtime. The background and some applications of space-filling curves are discussed, which are later on used as the basic principle of the load-balancing heuristic. A tight integration of space-filling curves as a memory addressing scheme into the numerical algorithm is proposed. Some experiments on a cluster of PCs demonstrates the parallel efficiency and scalability of the approach. 1 An adaptive multigrid solver Our goal is to solve a partial differential equation as fast as possible. We consider a multigrid solver, adaptive grid refinement and their efficient parallelization. We have to develop a parallel multigrid code that is almost identical to the sequential implementation. The computational workload has to be distributed into similar sized partitions and, at the same time, the communic...
Dynamic Load Balancing with the Refinement-Tree Partition for Adaptive Multilevel Methods
, 1998
"... Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on networks of workstations or PCs. An approach that periodically repartitions the grid is taken. A partitioning algorithm based on the refinement tree of the adaptive grid is presen ..."
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Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on networks of workstations or PCs. An approach that periodically repartitions the grid is taken. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of the most important properties of grid partitioners. 1 Introduction Adaptive multilevel methods, which combine adaptive mesh refinement with multigrid solution techniques, have been shown to be very efficient methods for the numerical solution of partial differential equations (PDEs) on sequential computers [1, 6, 10]. The use of these methods on parallel computers is currently a research topic [8, 11]. Among the barriers to efficient parallel implementation of these methods is the balancing of the computational load among the processors in an environment where the grid is dynamically changing through adaptive mesh refinement. This paper presents a dynamic load b...
Mesh Component Design and Software Integration within SUMAA3d
"... The requirements of distributed-memory applications that use mesh management software tools are diverse, and building software that meets these requirements represents a considerable challenge. In this paper we discuss design requirements for a general, component approach for mesh management for use ..."
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The requirements of distributed-memory applications that use mesh management software tools are diverse, and building software that meets these requirements represents a considerable challenge. In this paper we discuss design requirements for a general, component approach for mesh management for use within the context of solving PDE applications on parallel computers. We describe recent efforts with the SUMAA3d package motivated by a component-based approach and show how these efforts have considerably improved both the flexibility and the usability of this software. 1 Introduction Numerical solution of a PDE-based application typically requires that the computational domain be discretized into a collection of vertices, edges, faces, and/or cells. This discretization can take a number of different forms ranging from logically rectangular and multiblock structured grids to unstructured meshes consisting of simple geometric entities such as triangles or tetrahedra. Each approach has its...
