Vol 37, No 5 (2016)
- Year: 2016
- Articles: 10
- URL: https://journals.rcsi.science/1995-0802/issue/view/12390
Article
Hermitian finite element complementing the Bogner–Fox–Schmit rectangle near curvilinear boundary
Abstract
We discuss the Hermitian finite elements of high-order accuracy for solving boundary value problems for partial differential equations in domains with curvilinear boundaries. New elements are constructed in such a way that they can be used in conjunction with the Bogner–Fox–Schmit rectangular elements.
A new functional a posteriori error estimate for problems of bending of Timoshenko beams
Abstract
In this paper a new functional a posteriori error estimate is obtained for problems of bending of curvilinear Timoshenko beams. For sake of simplicity clamped beams under the action of traverse and axial forces and bending moment are considered. The derived estimate is reliable, is applicable to any conforming approximation and can be used both for global accuracy control and for local error indication for subsequent mesh adaptation. Its theoretical properties are confirmed by results of numerical experiments.
Mathematical modeling of blood flow alteration in microcirculatory network due to angiogenesis
Monotonicity in RT0 and PWCF methods on triangular and tetrahedral meshes
Abstract
In this paper we derive the monotonicity conditions for condensed-algebraic systems obtained by the discretization of the Poisson’s problem by the classical lowest order Raviart–Thomas (RT0) and the piece-wise constant fluxes (PWCF) MFE methods on triangular and tetrahedral meshes. We also establish the correspondence between the condensed system matrices resulting from application of these two methods.
Preconditioned Uzawa-type method for a state constrained parabolic optimal control problem with boundary control
Abstract
Iterative solution method for mesh approximation of an optimal control problem of a system governed by a linear parabolic equation is constructed and investigated. Control functions of the problem are in the right-hand side of the equation and in Neumann boundary condition, observation is in a part of the domain. Constraints on the control functions, state function and its time derivative are imposed. A mesh saddle point problem is constructed and preconditioned Uzawa-type method is applied to its solution. The main advantage of the iterative method is its effective implementation: every iteration step consists of the pointwise projections onto the segments and solving the linear mesh parabolic equations.
Nonlinear finite volume method with discrete maximum principle for the two-phase flow model
Abstract
The discrete maximum principle is a meaningful requirement for numerical schemes used in multiphase flow models. It eliminates numerical pressure overshoots and undershoots, which may cause unnatural Darcy velocities and wrong numerical saturations. In this paper we study the application of the nonlinear finite volume method with discrete maximum principle [1] to the two-phase flow model. The method satisfies the discrete maximum principle for numerical pressures of incompressible fluids with neglected capillary pressure. For non-zero capillary pressure and constant phase viscosities the discrete maximum principle holds for numerical global pressure.
Numerical integration over implicitly defined domains for higher order unfitted finite element methods
Abstract
The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment–fitting, local quasi-parametrization and Monte-Carlo techniques. As an application of these techniques, the paper addresses numerical solution of elliptic PDEs posed on domains and manifolds defined implicitly. A higher order unfitted finite element method (FEM) is assumed for the discretization. In such a method the underlying mesh is not fitted to the geometry, and hence the errors of numerical integration over curvilinear elements affect the accuracy of the finite element solution together with approximation errors. The paper studies the numerical complexity of the integration procedures and the performance of unfitted FEMs which employ these tools.
Eigenvibrations of a beam with elastically attached load
Abstract
The nonlinear eigenvalue problem describing eigenvibrations of a beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. The problem is approximated by the finite element method with Hermite finite elements of arbitrary order. The convergence and accuracy of approximate eigenvalues and eigenfunctions are investigated.
Error estimates for a Galerkin method with perturbations for spectral problems of the theory of dielectric waveguides
Abstract
We obtain error estimates for a Galerkin method with perturbations for approximating eigenvalues and eigenfunctions of one class of abstract spectral problems. Using these results, we get the justification of applying the method for spectral problems of the theory of dielectric waveguides.
Application of the conditional gradient method to resource allocation in wireless networks
Abstract
We propose a new two-level iterative method for solution of a general problem of optimal allocation of a homogeneous resource (bandwidth) in a wireless communication network. It is divided into service zones (clusters) and the network manager can buy external volumes of this resource. This approach leads to a convex optimization problem, which is solved with a dual Lagrangian method, where calculation of the cost function value decomposes into a system of independent zonal optimization problems. Each of them is treated as a market equilibrium problem. This optimization problem is solved with conditional gradient method for different information exchange schemes for participants. Besides, we suggest several ways to adjust the basic problemto the case of moving nodes. We give some results of numerical experiments on the proposed method which confirm its preference over the previous ones.