
A TwoLevel Preconditioned HelmholtzJacobiDavidson Method for the Maxwell Eigenvalue Problem
In this paper, based on a domain decomposition (DD) method, we shall pro...
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Spacefilling Curves for Highperformance Data Mining
Spacefilling curves like the Hilbertcurve, Peanocurve and Zorder map...
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pAdic scaled space filling curve indices for high dimensional data
Space filling curves are widely used in Computer Science. In particular ...
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GenEO coarse spaces for heterogeneous indefinite elliptic problems
Motivated by recent work on coarse spaces for Helmholtz problems, we pro...
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Hinged Trouchet tiling fractals
This article describes a new method of producing space filling fractal d...
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A Study of Energy and Locality Effects using Spacefilling Curves
The cost of energy is becoming an increasingly important driver for the ...
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DataDriven SpaceFilling Curves
We propose a datadriven spacefilling curve method for 2D and 3D visual...
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A faulttolerant domain decomposition method based on spacefilling curves
We propose a simple domain decomposition method for ddimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a spacefilling curve to create equally sized subproblems and to determine a certain overlap based on the onedimensional ordering of the spacefilling curve. Furthermore we employ agglomeration and a purely algebraic Galerkin discretization in the construction of the coarse problem. This way, the use of ddimensional geometric information is avoided. The subproblems are dealt with in an additive, parallel way, which gives rise to a subspace correction type linear iteration and a preconditioner for the conjugate gradient method. To make the algorithm faulttolerant we store on each processor, besides the data of the associated subproblem, a copy of the coarse problem and also the data of a fixed amount of neighboring subproblems with respect to the onedimensional ordering of the subproblems induced by the spacefilling curve. This redundancy then allows to restore the necessary data if processors fail during the computation. Theory supports that the convergence rate of such a linear iteration method stays the same in expectation, and only its order constant deteriorates slightly due to the faults. We observe this in numerical experiments for the preconditioned conjugate gradient method in slightly weaker form as well. Altogether, we obtain a faulttolerant, parallel and efficient domain decomposition method based on spacefilling curves which is especially suited for higherdimensional elliptic problems.
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