Easily implementable iterative methods for variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution

© 2015, walter de gruyter gmbh. All rights reserved. New iterative solution methods are proposed for the finite element approximation of a class of variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution. Implementation of every iteration of these methods reduces to the solution of a system of linear equations and a set of two-dimensional minimization problems. Convergence is proved by the application of a general result on the convergence of the iterative methods for a nonlinear constrained saddle point problem

Iterative solution methods for variational inequalities with nonlinear main operator and constraints to gradient of solution

Convergence of the preconditioned Uzawa-type and Arrow-Hurwitz-type iterative methods for nonlinear finite dimensional constrained saddle point problems is investigated. The general results are applied to the finite element approximation of a variational inequality with nonlinear main operator and constraints to gradient of solution. © 2012 Pleiades Publishing, Ltd

Explicit algorithms to solve a class of state constrained parabolic optimal control problems

© 2015 by Walter de Gruyter Berlin/Boston. We consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the finite difference approximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulae. Computational experiments confirm the theoretical results

Non-overlapping domain decomposition method for a variational inequality with gradient constraints

© Published under licence by IOP Publishing Ltd.Non-overlapping domain decomposition method is applied to a variational inequality with nonlinear diffusion-convection operator and gradient constraints. The method is based on the initial approximation of the problem and its subsequent splitting into subproblems. For the resulting constrained saddle point problem block relaxation-Uzawa iterative solution method is applied

Preconditioned Uzawa-type method for a state constrained parabolic optimal control problem with boundary control

© 2016, Pleiades Publishing, Ltd.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

Development of an automated prototype of THz filter based on magnetic fluids

Many new investigation approaches or techniques that rely on THz radiation are emerging today. It requires the development of devices for controlling THz radiation characteristics intensity, polarization, spectral properties, etc. One of the promising approaches to the implementation of such devices is the use of ferromagnetic fluids. Earlier, the efficient operation of polarizers and non selective THz attenuators based on ferromagnetic liquids was demonstrated. The liquids used consisted of 5BDSR alloy particles obtained by the mechanical synthesis in a planetary mill or Fe particles obtained by the electric explosion, dispersed in synthetic engine oil. Magnetic fluids were controlled using an external magnetic field generated by Helmholtz coils. In this study, we propose a prototype of a THz filter based on previously developed ferromagnetic fluids. Filter consists of a quartz or polymer cuvette with a magnetic fluid, several Helmholtz coils and a control circuit. This device allows one to orient the magnetic particles and to create ordered structures in the form of extended clusters. As a result, physical properties of electromagnets were optimized for effective controlling of particle clusters; the control process itself was automated. Spectral properties in the THz range are studied for various filter states. For reliable continuous operations, the device was supplemented with a homogenization system, based on mechanical mixing or sonication. The developed device can be used as a polarizer or an attenuator for polarized radiation in the range of 0.3-3 THz

戴帽式・祝辞

Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied: convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analysed in the case when both operators are linear, self-adjoint and positive definite. The results are applied for the mesh variational inequalities which are solved using a non-overlapping domain decomposition method and the splitting iterative procedure. Parallel solution of a mesh scheme for continuous casting problem is presented and the dependence of the calculation time on the number of processors is discussed