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439
9 SpringerVerlag 1986 On the MultiLevel Splitting of Finite Element Spaces
"... Summary. In this paper we analyze the condition number of the stiffness matrices arising in the discretization of selfadjoint and positive definite plane elliptic boundary value problems of second order by finite element methods when using hierarchical bases of the finite element spaces instead of t ..."
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Summary. In this paper we analyze the condition number of the stiffness matrices arising in the discretization of selfadjoint and positive definite plane elliptic boundary value problems of second order by finite element methods when using hierarchical bases of the finite element spaces instead of the usual nodal bases. We show that the condition number of such a stiffness matrix behaves like O((log ~c) 2) where ~ is the condition number of the stiffness matrix with respect to a nodal basis. In the case of a triangulation with uniform mesh size h this means that the stiffness matrix with respect to a hierarchical basis of the finite element space has a condition number behaving like O log ~ instead of O for a nodal basis. The proofs of our theorems do not need any regularity properties of neither the continuous problem nor its discretization. Especially we do not need the quasiuniformity of the employed triangulations. As the representation of a finite element function with respect to a hierarchical basis can be converted very easily and quickly to its representation with respect to a nodal basis, our results mean that the method of conjugate gradients needs only O(logn) steps and O(nlogn) computer operations to reduce the energy norm of the error by a given factor if one uses hierarchical bases or related preconditioning procedures. Here n denotes the dimension of the finite element space and of the discrete linear problem to be solved.
A GPUbased Multilevel Subspace Decomposition Scheme for Hierarchical Tensor Product Bases
, 2013
"... I would never have been able to finish my thesis without the guidance of my scientific advisor, help from friends and support from my family. I would like to express my deepest gratitude to my advisor, Dipl.Inf. Gerrit Buse, for his excellent guidance, patience, and providing me perfect background ..."
MULTILEVEL DECOMPOSITION OF PROBABILISTIC RELATIONS
"... Two methods of decomposition of probabilistic relations are presented. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way as to minimize a cost function which depends on the size and structure of the result. The de ..."
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Cited by 1 (1 self)
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Two methods of decomposition of probabilistic relations are presented. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way as to minimize a cost function which depends on the size and structure of the result
A New Solution to the Coherence Problems in Multicache Systems
 IEEE Transactions on Computers
, 1987
"... AbstractA memory hierarchy has coherence problems as sooncontents of the main memoryis copied in thecache. One as one of its levels is split in several independent unitswhich are not says that such a datumis present in the cache. If a processor p^ilarl adonauMla frnw factor lnwale nr nrd%d ..."
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Cited by 256 (1 self)
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AbstractA memory hierarchy has coherence problems as sooncontents of the main memoryis copied in thecache. One as one of its levels is split in several independent unitswhich are not says that such a datumis present in the cache. If a processor p^ilarl adonauMla frnw factor lnwale nr nrd
Splitting Sequential Monte Carlo for Efficient Unreliability Estimation of Highly Reliable Networks
"... Assessing the reliability of complex technological systems such as communication networks, transportation grids, and bridge networks is a difficult task. From a mathematical point of view, the problem of estimating network reliability belongs to the #P complexity class. As a consequence, no analyt ..."
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under some mild conditions, it is known to be inadequate for stable estimation of network reliability in a rareevent setting. To overcome this obstacle, we suggest a quite general combination of Sequential Monte Carlo and multilevel splitting. The proposed method is shown to bring a significant
On the length of onedimensional reactive paths
 ALEA, Lat. Am. J. Probab. Math. Stat
"... Abstract. Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simple setting, namely paths generated by a onedimensional overdamped Langevin equation for a double well potential. More precisely, we are interested in socalled rea ..."
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Cited by 4 (0 self)
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Carlo method, namely the multilevel splitting approach [6]. 1. Introduction and
A Formal Semantics for Multilevel Staged Configuration
, 2009
"... Multilevel staged configuration (MLSC) of feature diagrams has been proposed as a means to facilitate configuration in software product line engineering. Based on the observation that configuration often is a lengthy undertaking with many participants, MLSC splits it up into different levels that c ..."
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Cited by 19 (6 self)
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Multilevel staged configuration (MLSC) of feature diagrams has been proposed as a means to facilitate configuration in software product line engineering. Based on the observation that configuration often is a lengthy undertaking with many participants, MLSC splits it up into different levels
ALEA,Lat. Am. J.Probab. Math. Stat.10(1),359–389(2013) On the length of onedimensional reactive paths
"... Abstract. Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simple setting, namely paths generated by a onedimensional overdamped Langevin equation for a double well potential. Specifically, we are interested in socalled reacti ..."
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Carlo method, namely the multilevel splitting approach (see Cérou et al. (2011)). 1. Introduction and
Parallel multilevel solvers for spectral element methods
"... Efficient solution of the NavierStokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In ..."
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Cited by 12 (10 self)
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. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed
Results 1  10
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439