References of "Netuzhylov, H"
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See detailMeshfree collocation method for implicit time integration of ODEs
Netuzhylov, H.; Zilian, Andreas UL

in International Journal of Computational Methods (2011), 8(1), 119-137

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular ... [more ▼]

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method. © 2011 World Scientific Publishing Company. [less ▲]

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See detailHybridized enriched space-time finite element method for analysis of thin-walled structures immersed in generalized Newtonian fluids
Zilian, Andreas UL; Netuzhylov, H.

in Computers & Structures (2010), 88(21-22), 1265-1277

The paper addresses the numerical treatment of a specific class of fluid-structure interaction problems: flow-immersed thin structures undergoing considerable motion and deformation. The simultaneous ... [more ▼]

The paper addresses the numerical treatment of a specific class of fluid-structure interaction problems: flow-immersed thin structures undergoing considerable motion and deformation. The simultaneous solution procedure uses a mixed-hybrid velocity-based formulation of both fluid and structure discretized by a stabilized time-discontinuous space-time finite element method. The continuity at the interface is ensured by a localized mixed-hybrid interface method avoiding Lagrange multipliers and penalty approaches. The XFEM is utilized for enrichment of the approximation space of the fluid variables in order to represent non-smooth (discontinuous) solution features resulting from immersing a thin structure in a fluid. © 2010 Elsevier Ltd. All rights reserved. [less ▲]

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See detailSpace-time meshfree collocation method: Methodology and application to initial-boundary value problems
Netuzhylov, H.; Zilian, Andreas UL

in International Journal for Numerical Methods in Engineering (2009), 80(3), 355-380

A novel space-time meshfree collocation method (STMCM) for solving systems of non-linear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an ... [more ▼]

A novel space-time meshfree collocation method (STMCM) for solving systems of non-linear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh-based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods that do not have any underlying mesh, but work on a set of nodes only without any a priori node-to-node connectivity. Instead, the neighbouring information is established on-the-fly. The STMCM is constructed using the Interpolating Moving Least-squares technique, which allows a simplified implementation of boundary conditions due to fulfillment of the Kronecker delta property by the kernel functions, which is not the case for the major part of other meshfree methods. The method is validated by several examples ranging from interpolation problems to the solution of PDEs, whereas the STMCM solutions are compared with either analytical or reference ones. © 2009 John Wiley & Sons, Ltd. [less ▲]

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