WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12469/4465

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Browsing WoS İndeksli Yayınlar Koleksiyonu by browse.metadata.publisher "Academic Press inc Elsevier Science"

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    Article
    Extended Hybridizable Discontinuous Galerkin (x-Hdg) Method for Linear Convection-Diffusion Equations on Unfitted Domains
    (Academic Press inc Elsevier Science, 2024) Ahmad, Haroon; Gurkan, Ceren
    In this work, we propose a novel strategy for the numerical solution of linear convection diffusion equation (CDE) over unfitted domains. In the proposed numerical scheme, strategies from high order Hybridized Discontinuous Galerkin method and eXtended Finite Element method are combined with the level set definition of the boundaries. The proposed scheme and hence, is named as eXtended Hybridizable Discontinuous Galerkin (XHDG) method. In this regard, the Hybridizable Discontinuous Galerkin (HDG) method is eXtended to the unfitted domains; i.e., the computational mesh does not need to fit to the domain boundary; instead, the boundary is defined by a level set function and cuts through the background mesh arbitrarily. The original unknown structure of HDG and its hybrid nature ensuring the local conservation of fluxes is kept, while developing a modified bilinear form for the elements cut by the boundary. At every cut element, an auxiliary nodal trace variable on the boundary is introduced, which is eliminated afterwards while imposing the boundary conditions. Both stationary and time dependent CDEs are studied over a range of flow regimes from diffusion to convection dominated; using high order (p <= 4) XHDG through benchmark numerical examples over arbitrary unfitted domains. Results proved that XHDG inherits optimal (p + 1) and super (p + 2) convergence properties of HDG while removing the fitting mesh restriction.
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    On minimum vertex bisection of random d-regular graphs
    (Academic Press inc Elsevier Science, 2024) Diaz, Josep; Diner, Oznur Yasar; Serna, Maria; Serra, Oriol
    Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random d -regular graphs, for constant values of d . Our approach is based on analyzing a greedy algorithm by using the differential equation method. In this way, we obtain the first known non -trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald (2014) [30]. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).