Institute of Mathematics AS CR, v. v. i.
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On multipoint constraints in FETI methods
No full textsummary:FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners' variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI
Corrigendum to “Braided coproduct, antipode and adjoint action for ” [Arch. Math. (Brno) 60(5) (2024), 365–376, DOI: 10.5817/AM2024-5-365]
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Non-finitely generated bigraded local cohomology modules
No full textsummary:Let be a field, and let denote a standard bigraded polynomial ring over . Consider , a finitely generated bigraded -module, and set . Assume that there exists such that . We demonstrate that is not finitely generated. Furthermore, we explore a more general version of this result
Stochastic queue core problem with an efficient length on a tree network
No full textsummary:In this paper, we consider a stochastic queue core () problem on a tree network, aiming to identify a path , called the core, in an environment system. Let be a tree network, the problem on involves finding a core , with an optimal length, that minimizes the total weighted travel time from all vertices to the core as well as the average response time to the customer demands. We assume that a mobile server traverses the core to provide services to customers, while customers move to their nearest vertex on the core to receive service. Some general properties of the problem on the tree network are represented. Then a polynomial time algorithm is proposed to solve this problem
Weakly -2-absorbing ideals
No full textsummary:Let be a commutative ring with identity. The notion of --absorbing ideal was introduced by G. Ulucak, Ü. Tekir, S. Koç (2020) as a generalization of -absorbing ideal. We introduce weaker version of 2-absorbing ideals by defining the concept of weakly--2-absorbing ideal. Let be a multiplicatively closed subset of . A proper ideal of disjoint with is called a weakly -2-absorbing ideal of if whenever for then there exists such that or or . We investigate many properties and characterizations of weakly -2-absorbing ideals
Stable computation of Laplacian eigenfunctions corresponding to clustered eigenvalues
No full textsummary:The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. Using the shape difference quotient of eigenvalues, we propose a stable computation method for the eigenfunctions of clustered eigenvalues caused by domain perturbation
Conformal quasi-hemi-slant -Riemannian submersions from Sasakian manifolds
No full textsummary:We introduce some geometric properties of a horizontally conformal quasi-hemi-slant Riemannian submersion from a Sasakian manifold, normal to the characteristic vector field, supported by an example. Under some conditions, we obtain geometric configurations of fibres and the base manifold of such submersions. We also give a characterization theorem for the proper horizontal conformal quasi-hemi-slant Riemannian submersions with totally umbilical fibres