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A New Paradigm for Parallel Adaptive Meshing Algorithms
 SIAM J. Sci. Comput
, 2003
"... We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to ru ..."
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Cited by 46 (9 self)
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We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to run in a parallel environment without a large investment in recoding. In this new approach, the load balancing problem is reduced to the numerical solution of a small elliptic problem on a single processor, using a sequential adaptive solver, without requiring any modifications to the sequential solver. The small elliptic problem is used to produce a posteriori error estimates to predict future element densities in the mesh, which are then used in a weighted recursive spectral bisection of the initial mesh. The bulk of the calculation then takes place independently on each processor, with no communication, using possibly the same sequential adaptive solver. Each processor adapts its region of the mesh independently, and a nearly loadbalanced mesh distribution is usually obtained as a result of the initial weighted spectral bisection. Only the initial fanout of the mesh decomposition to the processors requires communication. Two additional steps requiring boundary exchange communication may be employed after the individual processors reach an adapted solution, namely, the construction of a global conforming mesh from the independent subproblems, followed by a final smoothing phase using the subdomain solutions as an initial guess. We present a series of convincing numerical experiments that illustrate the e#ectiveness of this approach. The justification of the initial refinement prediction step, as well as the justification of skipping the two communicationintensive steps, ...
The RefinementTree Partition for Parallel Solution of Partial Differential Equations
 NIST Journal of Research
, 1998
"... The numerical solution of partial differential equations (PDEs) is the most computationally intense part of solving mathematical models with many important applications. For this reason, much research has been performed ..."
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Cited by 8 (4 self)
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The numerical solution of partial differential equations (PDEs) is the most computationally intense part of solving mathematical models with many important applications. For this reason, much research has been performed
Computing and Visualization in Science manuscript No. (will be inserted by the editor) Some Variants of the BankHolst Parallel Adaptive Meshing Paradigm
, 2004
"... Abstract. The BankHolst 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 BankHolst 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.
ANAC header will be provided by the publisher Parallel Adaptive Multilevel Methods with Full Domain Partitions
, 2003
"... Adaptive multilevel methods are methods for solving partial differential equations that combine adaptive grid refinement with multigrid solution techniques. These methods have been shown to be very effective on sequential computers. Recently, a technique for parallelizing these methods for cluster c ..."
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Adaptive multilevel methods are methods for solving partial differential equations that combine adaptive grid refinement with multigrid solution techniques. These methods have been shown to be very effective on sequential computers. Recently, a technique for parallelizing these methods for cluster computers has been developed. This paper presents an overview of a particular adaptive multilevel method and the parallelization of that method via the full domain partition. 1
The Design of a Parallel Adaptive Multilevel
 in: Proc. 2002 Internatl. Conf. on Computational Science
, 2002
"... Software for the solution of partial dierential equations using adaptive re nement, multilevel solvers and parallel processing is complicated and requires careful design. This paper describes the design of such a code, PHAML. PHAML is written in Fortran 90 and makes extensive use of advanced F ..."
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Software for the solution of partial dierential equations using adaptive re nement, multilevel solvers and parallel processing is complicated and requires careful design. This paper describes the design of such a code, PHAML. PHAML is written in Fortran 90 and makes extensive use of advanced Fortran 90 features, such as modules, optional arguments and dynamic memory, to provide a clean objectoriented design with a simple user interface.
Convergence Analysis of a Domain Decomposition Paradigm
, 2008
"... on the occasion of his 60th birthday ..."
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