I am working in area of applied mathematics, optimiztions, numerical algebra, and solving problems of solid and fluid mechnics with nonlinear boundary conditions describen fricition or stick-slip effect.
The semi-smooth Newton method for solving discretized contact problems with Tresca friction in th... more The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).
This paper deals with the formulation, discretization and implementation of the Stokes system inv... more This paper deals with the formulation, discretization and implementation of the Stokes system involving Coulomb’s type slip boundary conditions. The computational strategy is based on a fixed-point formulation of the problem and the method of successive approximations. Numerical experiments confirm the usability of this approach.
Mathematics and Computers in Simulation, Nov 1, 2021
Abstract The paper deals with the numerical realization of the 3D Stokes flow subject to threshol... more Abstract The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity–pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.
where |x1| = |x2| = |x3| = m, n = 3m, A ∈ Rn×n is the symmetric, positive definite Hessian matrix... more where |x1| = |x2| = |x3| = m, n = 3m, A ∈ Rn×n is the symmetric, positive definite Hessian matrix, b ∈ R, and l, g ∈ R. This problem arises, e.g., in duality based methods for the solution of 3D contact problems of linear elasticity with Tresca friction. As a widely used approach of contact problems with (more realistic) Coulomb friction is based on a sequence of Tresca friction problems [2], an efficient solver for (1) is of crucial importance. In this contribution we shall test algorithms based on an ”interior point” idea.
ABSTRACT The paper deals with a mixed finite element approximation of Signorini problem with a gi... more ABSTRACT The paper deals with a mixed finite element approximation of Signorini problem with a given friction, which is based on the so-called reciprocal variational formulation. Two types of finite element approximations of Lagrange multipliers are studied: piecewise constant and continuous piecewise linear ones. Numerical results are compared with the classical algebraic Lagrange multiplier approach.
2008 15th IEEE International Conference on Image Processing, 2008
... 190 199, 2008. ... Vrochidis S, Mezaris V, Kompatsiaris I, Spyrou E, Avrithis Y, Morzinger ... more ... 190 199, 2008. ... Vrochidis S, Mezaris V, Kompatsiaris I, Spyrou E, Avrithis Y, Morzinger R, Schallauer P, Bailer W, Piatrik T, Chandramouli K, Izquierdo E, Haller M, Goldmann L, Samour A, Cobet A, Sikora T, and Praks P, K-space at trevid 2007, in TRECVid 2007 - Text ...
The semi-smooth Newton method for solving discretized contact problems with Tresca friction in th... more The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).
This paper deals with the formulation, discretization and implementation of the Stokes system inv... more This paper deals with the formulation, discretization and implementation of the Stokes system involving Coulomb’s type slip boundary conditions. The computational strategy is based on a fixed-point formulation of the problem and the method of successive approximations. Numerical experiments confirm the usability of this approach.
Mathematics and Computers in Simulation, Nov 1, 2021
Abstract The paper deals with the numerical realization of the 3D Stokes flow subject to threshol... more Abstract The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity–pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.
where |x1| = |x2| = |x3| = m, n = 3m, A ∈ Rn×n is the symmetric, positive definite Hessian matrix... more where |x1| = |x2| = |x3| = m, n = 3m, A ∈ Rn×n is the symmetric, positive definite Hessian matrix, b ∈ R, and l, g ∈ R. This problem arises, e.g., in duality based methods for the solution of 3D contact problems of linear elasticity with Tresca friction. As a widely used approach of contact problems with (more realistic) Coulomb friction is based on a sequence of Tresca friction problems [2], an efficient solver for (1) is of crucial importance. In this contribution we shall test algorithms based on an ”interior point” idea.
ABSTRACT The paper deals with a mixed finite element approximation of Signorini problem with a gi... more ABSTRACT The paper deals with a mixed finite element approximation of Signorini problem with a given friction, which is based on the so-called reciprocal variational formulation. Two types of finite element approximations of Lagrange multipliers are studied: piecewise constant and continuous piecewise linear ones. Numerical results are compared with the classical algebraic Lagrange multiplier approach.
2008 15th IEEE International Conference on Image Processing, 2008
... 190 199, 2008. ... Vrochidis S, Mezaris V, Kompatsiaris I, Spyrou E, Avrithis Y, Morzinger ... more ... 190 199, 2008. ... Vrochidis S, Mezaris V, Kompatsiaris I, Spyrou E, Avrithis Y, Morzinger R, Schallauer P, Bailer W, Piatrik T, Chandramouli K, Izquierdo E, Haller M, Goldmann L, Samour A, Cobet A, Sikora T, and Praks P, K-space at trevid 2007, in TRECVid 2007 - Text ...
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