A. Lapin - Academia.edu (original) (raw)

Uploads

Papers by A. Lapin

Research paper thumbnail of Non-overlapping domain decomposition method for a variational inequality with gradient constraints

IOP Conference Series: Materials Science and Engineering, 2016

Research paper thumbnail of Some mesh schemes for quasi-linear elliptic equations

USSR Computational Mathematics and Mathematical Physics, 1980

Research paper thumbnail of A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients

Computational Methods in Applied Sciences, 2008

Research paper thumbnail of Preconditioned Uzawa-type methods for finite-dimensional constrained saddle point problems

Lobachevskii Journal of Mathematics, 2010

A new approach for the constructing and investigating the algorithms to solve a class of finite d... more A new approach for the constructing and investigating the algorithms to solve a class of finite dimensional constrained saddle point problems is suggested. General convergence theorem for the preconditioned Uzawa-type iterative method is proved and applied to the finite element approximations of variational inequalities and optimal control problems.

Research paper thumbnail of A penalty approach to the numerical simulation of a constrained wave motion

Journal of Numerical Mathematics, 2003

The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.

Research paper thumbnail of Iterative methods and parallel solution of the dam problem

Computer Methods in Applied Mechanics and Engineering, 2001

A free boundary problem of fluid flow in the porous medium is considered. A finite difference sch... more A free boundary problem of fluid flow in the porous medium is considered. A finite difference scheme is constructed and written in the form of the inclusion for the sum of several multi-valued operators. The study of this mesh scheme and iterative algorithms of its numerical solution is performed. Solution of the mesh problem by Gauss–Seidel and by Schwarz alternating

Research paper thumbnail of On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems

Computational Methods in Applied Mathematics, 2000

The main goal of this article is to investigate the capability of fictitious domain methods to si... more The main goal of this article is to investigate the capability of fictitious domain methods to simulate the scattering of linear waves by an obstacle whose shape does not fit the mesh. The space-time discretization relies on a combination of a mixed finite element methodà la Raviart-Thomas with a fairly standard finite difference scheme for the time discretization. The numerical results described in the article point to a good performance of the numerical method investigated here.

Research paper thumbnail of IP Gavrilyuk (Germany), VL Makarov (Ukraine), V. Vasylyk (Ukraine)

Research paper thumbnail of On 3D dynamic control of secondary cooling in continuous casting process

Lobachevskii Journal …, 2003

In this paper a 3D-model for simulation and dynamic control of the continuous casting process is ... more In this paper a 3D-model for simulation and dynamic control of the continuous casting process is presented. The diffusion convection equation with multiphase transition is used as a simulation model. The developed model is discretized by finite element method and the algebraic equations are solved using pointwise relaxation method. Two different type of methods are used to control the secondary cooling, namely PID and optimal control method. The numerical results are presented and analyzed.

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

Lobachevskii Journal of Mathematics, 2012

Convergence of the preconditioned Uzawa-type and Arrow-Hurwitz-type iterative methods for nonline... more 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.

Research paper thumbnail of Non-overlapping domain decomposition method for a variational inequality with gradient constraints

IOP Conference Series: Materials Science and Engineering, 2016

Research paper thumbnail of Some mesh schemes for quasi-linear elliptic equations

USSR Computational Mathematics and Mathematical Physics, 1980

Research paper thumbnail of A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients

Computational Methods in Applied Sciences, 2008

Research paper thumbnail of Preconditioned Uzawa-type methods for finite-dimensional constrained saddle point problems

Lobachevskii Journal of Mathematics, 2010

A new approach for the constructing and investigating the algorithms to solve a class of finite d... more A new approach for the constructing and investigating the algorithms to solve a class of finite dimensional constrained saddle point problems is suggested. General convergence theorem for the preconditioned Uzawa-type iterative method is proved and applied to the finite element approximations of variational inequalities and optimal control problems.

Research paper thumbnail of A penalty approach to the numerical simulation of a constrained wave motion

Journal of Numerical Mathematics, 2003

The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.

Research paper thumbnail of Iterative methods and parallel solution of the dam problem

Computer Methods in Applied Mechanics and Engineering, 2001

A free boundary problem of fluid flow in the porous medium is considered. A finite difference sch... more A free boundary problem of fluid flow in the porous medium is considered. A finite difference scheme is constructed and written in the form of the inclusion for the sum of several multi-valued operators. The study of this mesh scheme and iterative algorithms of its numerical solution is performed. Solution of the mesh problem by Gauss–Seidel and by Schwarz alternating

Research paper thumbnail of On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems

Computational Methods in Applied Mathematics, 2000

The main goal of this article is to investigate the capability of fictitious domain methods to si... more The main goal of this article is to investigate the capability of fictitious domain methods to simulate the scattering of linear waves by an obstacle whose shape does not fit the mesh. The space-time discretization relies on a combination of a mixed finite element methodà la Raviart-Thomas with a fairly standard finite difference scheme for the time discretization. The numerical results described in the article point to a good performance of the numerical method investigated here.

Research paper thumbnail of IP Gavrilyuk (Germany), VL Makarov (Ukraine), V. Vasylyk (Ukraine)

Research paper thumbnail of On 3D dynamic control of secondary cooling in continuous casting process

Lobachevskii Journal …, 2003

In this paper a 3D-model for simulation and dynamic control of the continuous casting process is ... more In this paper a 3D-model for simulation and dynamic control of the continuous casting process is presented. The diffusion convection equation with multiphase transition is used as a simulation model. The developed model is discretized by finite element method and the algebraic equations are solved using pointwise relaxation method. Two different type of methods are used to control the secondary cooling, namely PID and optimal control method. The numerical results are presented and analyzed.

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

Lobachevskii Journal of Mathematics, 2012

Convergence of the preconditioned Uzawa-type and Arrow-Hurwitz-type iterative methods for nonline... more 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.

Log In