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Hash Based Adaptive Parallel Multilevel Methods with SpaceFilling Curves
 NIC Series
, 2002
"... this paper a parallelisable and cheap method based on spacefilling curves is proposed. The partitioning is embedded into the parallel solution algorithm using multilevel iterative solvers and adaptive grid refinement. Numerical experiments on two massively parallel computers prove the efficienc ..."
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Cited by 11 (0 self)
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this paper a parallelisable and cheap method based on spacefilling curves is proposed. The partitioning is embedded into the parallel solution algorithm using multilevel iterative solvers and adaptive grid refinement. Numerical experiments on two massively parallel computers prove the efficiency of this approach
Parallel Adaptive Subspace Correction Schemes with Applications to Elasticity
 Comput. Methods Appl. Mech. Engrg
, 1999
"... : In this paper, we give a survey on the three main aspects of the efficient treatment of PDEs, i.e. adaptive discretization, multilevel solution and parallelization. We emphasize the abstract approach of subspace correction schemes and summarize its convergence theory. Then, we give the main featur ..."
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: In this paper, we give a survey on the three main aspects of the efficient treatment of PDEs, i.e. adaptive discretization, multilevel solution and parallelization. We emphasize the abstract approach of subspace correction schemes and summarize its convergence theory. Then, we give the main features of each of the three distinct topics and treat the historical background and modern developments. Furthermore, we demonstrate how all three ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic PDEs and especially of linear elasticity problems. We report on numerical experiments for the adaptive parallel multilevel solution of some test problems, namely the Poisson equation and Lam'e's equation. Here, we emphasize the parallel efficiency of the adaptive code even for simple test problems with little work to distribute, which is achieved through hash storage techniques and spacefilling curves. Keywords: subspace correction, iter...
A Parallel Adaptive Multigrid Method
"... A parallel version of an adaptive multigrid solver for elliptic partial differential equations is described. It operates on a finite difference discretization on quadtree and octtree meshes, which are obtained by adaptive mesh refinement. A fast parallel load balancing strategy for the parallel mu ..."
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A parallel version of an adaptive multigrid solver for elliptic partial differential equations is described. It operates on a finite difference discretization on quadtree and octtree meshes, which are obtained by adaptive mesh refinement. A fast parallel load balancing strategy for the parallel multigrid equation solver is proposed that is defined by a spacefilling Hilbert curve and is applicable to arbitrary shaped domains. Some numerical experiments demonstrate the parallel efficiency and scalability of the approach.
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 spacefilling 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 spacefilling curves are discussed, which are later on used as the basic principle of the loadbalancing heuristic. A tight integration of spacefilling 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...