Summary In this paper, we consider efficient algorithms for solving the algebraic equation , 0< α <1, where is a properly scaled symmetric and positive definite matrix obtained from finite difference or element approximations of second‐order elliptic problems in d =1,2,3. This solution then written as with β integer. The approximate method propose study based on best uniform rational approximation function t − ≤1 assumption that one has at hand an (e.g., multigrid, multilevel, other...

This paper proves a new approach for rapid prototyping of radio antennas through 3D printing and chemical metallization. For this purpose, standard metal pyramidal horn prototype is compared with its printed replica. Three different polymer printers are tested. The samples assessed nondestructively by an X-ray Industrial Computed Tomography (CT) scanner, then metalized via deposition chemical-electrochemical deposition. Copper two layer thicknesses nickel materials deployed verified as...

Data from the World Health Organization indicate that Bulgaria has second-highest COVID-19 mortality rate in world and lowest vaccination European Union. In this context, to find crucial epidemiological parameters characterize ongoing pandemic Bulgaria, we introduce an extended SEIRS model with time-dependent coefficients. addition this, vital dynamics are included model. We construct appropriate Cauchy problem for a system of nonlinear ordinary differential equations prove its unique...

In this paper we propose and analyze a preconditioner for system arising from mixed finite element approximation of second-order elliptic problems describing processes in highly heterogeneous media. Our approach uses the technique multilevel methods (see, e.g., [P. Vassilevski, Multilevel Block Factorization Preconditioners: Matrix-Based Analysis Algorithms Solving Finite Element Equations, Springer, New York, 2008]) recently proposed based on additive Schur complement by J. Kraus [SIAM Sci....

Geometrically nonlinear vibrations of three-dimensional elastic structures, due to harmonic external excitations, are investigated in the frequency domain. The material structure is assumed be linearly elastic. equation motion derived by conservation linear momentum Lagrangian coordinate system and it discretized into a ordinary differential equations finite element method. shooting method used, obtain periodic solutions. A procedure which transforms initial value problem two point boundary...

Summary Mathematical models with fractional‐order differential operators are computationally expensive due to the non‐local nature of these operators. In this work, we construct and investigate parallel solvers for problems described by fractional powers elliptic operators, like diffusion. Three state‐of‐the‐art approaches used transform problem into local partial equation formulated in a space higher dimension. Numerical schemes algorithms developed all three approaches. The resulting have...

Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Svetozar Margenov, Nedyu Popivanov, Iva Ugrinova, Stanislav Harizanov, Tsvetan Hristov; Mathematical computer modeling of COVID-19 transmission dynamics in Bulgaria by time-depended inverse SEIR model. AIP Conf. Proc. 8 March 2021; 2333 (1): 090024. https://doi.org/10.1063/5.0041868 Download citation file: Ris...

In this paper the recently proposed algebraic multilevel iteration method for iterative solution of elliptic boundary value problems with anisotropy and discontinuous coefficients is studied. Based on a special approximation blocks corresponding to new nodes at every discretization level, an optimal order preconditioner respect arithmetic cost independent both discontinuity constructed. The advantages algorithms are illustrated by numerical tests.

Abstract Preconditioners based on various multilevel extensions of two‐level finite element methods (FEM) lead to iterative which have an optimal order computational complexity with respect the size system. Such were first presented in Axelsson and Padiy ( SIAM. J. Sci. Stat. Comp . 1990; 20 :1807) Vassilevski Numer. Math 1989; 56 :157), are (recursive) splittings space. The key role derivation convergence rate estimates is played by constant γ so‐called Cauchy–Bunyakowski–Schwarz (CBS)...

Abstract In this paper we discuss robust two-level domain decomposition preconditioners for highly anisotropic heterogeneous multiscale problems. We present a construction of several coarse spaces that employ standard finite element and basis functions techniques to reduce the dimensions without sacrificing robustness. experimentally study performance preconditioner on variety two-dimensional test problems with channels high anisotropy. The numerical tests confirm robustness perconditioner...