1,721,328 research outputs found
A reduced order model-based preconditioner for the efficient solution of transient diffusion equations
Full text linkThis paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive-definite linear systems arising from the numerical discretization of transient parabolic and selfadjoint partial differential equations. The preconditioners are obtained by nesting appropriate projections of reduced-order models into the classical iteration of the preconditioned conjugate gradient (PCG). The main idea is to employ the reduced-order solver to project the residual associated with the conjugate gradient iterations onto the space spanned by the reduced bases. This approach is particularly appealing for transient systems where the full-model solution has to be computed at each time step. In these cases, the natural reduced space is the one generated by full-model solutions at previous time steps. When increasing the size of the projection space, the proposed methodology highly reduces the system conditioning number and the number of PCG iterations at every time step. The cost of the application of the preconditioner linearly increases with the size of the projection basis, and a trade-off must be found to effectively reduce the PCG computational cost. The quality and efficiency of the proposed approach is finally tested in the solution of groundwater flow models. (C) 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd
Effective anisotropy tensor for the numerical solution of flow problems in heterogeneous porous media
No full textThe numerical solution of porous media flow equations often requires the computationof discrete interfacial average fluxes. Standard methods, such as Integrated Finite Differences(IFD) or Finite Volumes (FV), rely on the definition of average gradients of thesolution, and calculate the interface fluxes by means of appropriate averages of the conductivitytensor K. The question of how to choose a correct average for the conductivityin the anisotropic case is however still open. We derive a procedure based on conservationof flux and energy, which is particularly suited for non-asymptotical regimes, at afixed mesh (size). The resulting effective tensor provides standard arithmetic-harmonicmeans of tensor coefficients with respect to tangential and normal components of thegradient in simple cases. Moreover, this tensor is shown to coincide with a matrix arisingfrom homogenization theory, even though it has been obtained for different purposes,and following a different approach. The effectiveness of the proposed method is verifiednumerically.http://proceedings.cmwr-xvi.or
Nodal domain count for the generalized graph p-Laplacian
Full text linkInspired by the linear Schrödinger operator, we consider a generalized p-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this operator with particular attention to the nodal domain count of its eigenfunctions. Just like the one-dimensional continuous p-Laplacian, we prove that the variational spectrum of the discrete generalized p-Laplacian on forests is the entire spectrum. Moreover, we show how to transfer Weyl's inequalities for the Laplacian operator to the nonlinear case and prove new upper and lower bounds on the number of nodal domains of every eigenfunction of the generalized p-Laplacian on generic graphs, including variational eigenpairs. In particular, when applied to the linear case p=2, in addition to recovering well-known features, the new results provide novel properties of the linear Schrödinger operator
Branching structures emerging from a continuous optimal transport model
Full text linkRecently a Dynamic-Monge-Kantorovich formulation of the PDE-based [Formula presented]-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that evolves proportionally to the transported flux. In this paper we present an extension of this model that considers a time derivative of the conductivity that grows as a power-law of the transport flux with exponent β>0. A sub-linear growth (01) favors flux intensity and promotes concentrated transport, leading to the emergence of steady-state “singular” and “fractal-like” configurations that resemble those of Branched Transport Problems. We derive a numerical discretization of the proposed model that is accurate, efficient, and robust for a wide range of scenarios. For β>1 the numerical model is able to reproduce highly irregular and fractal-like formations without any a-priory structural assumption
GRAPH p-LAPLACIAN EIGENPAIRS AS SADDLE POINTS OF A FAMILY OF SPECTRAL ENERGY FUNCTIONS
No full textWe address the problem of computing the graph p-Laplacian eigenpairs for p \in (2, \infty). We propose a reformulation of the graph p-Laplacian eigenvalue problem in terms of a constrained weighted Laplacian eigenvalue problem and discuss theoretical and computational advantages. We provide a correspondence between p-Laplacian eigenpairs and linear eigenpairs of a constrained generalized weighted Laplacian eigenvalue problem. As a result, we can assign an index to any p-Laplacian eigenpair that matches the Morse index of the p-Rayleigh quotient evaluated at the eigenfunction. In the second part of the paper, we introduce a class of spectral energy functions that depend on edge and node weights. We prove that differentiable saddle points of the kth energy function correspond to p-Laplacian eigenpairs having index equal to k. Moreover, the first energy function is proved to possess a unique saddle point which corresponds to the unique first p-Laplacian eigenpair. Finally, we develop novel gradient-based numerical methods suited to compute p-Laplacian eigenpairs for any p \in (2, \infty) and present some experiments
The High-Order Mixed Mimetic Finite Difference Method for Time-Dependent Diffusion Problems
Full text linkEssential thrombocythaemia in children: is a treatment needed?
No full textThe myeloproliferative disorder, essential thrombocythaemia (ET), is extremely rare in children. In adults, thrombosis is the most common complication whereas a low number of children develop thrombosis and/or haemorrhages. Diagnosis of ET is often difficult, but identifying ET from other causes of thrombocytosis is essential, otherwise therapy may be ineffective as the wrong disease will be treated. Only anecdotal experiences have been published with regard to the treatment of paediatric ET. A watch-and-wait strategy seems appropriate in asymptomatic cases and low-dose aspirin should be used to reduce microvascular disturbances. Anagrelide or IFNs may be considered as first-line, and hydroxyurea as second-line therapy. Anagrelide may become the treatment of choice for ET in children if a lack of leukaemogenic potential is confirmed
Multicommodity routing optimization for engineering networks
Full text linkOptimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions—quantities determining the interaction between passengers—in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers’ fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra’s algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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