• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.119-133
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• 2011

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1831-1844
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• 2016

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter ${\theta}$. This value is adapted with the value of proximity function ${\delta}$ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter ${\theta}$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that ${\theta}$ takes a default fixed value.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.65-72
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• 2001

This paper demonstrates an explicit-implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for an existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory. Darcy's law is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full Newton-Raphson method is used for solving the nonlinear governing equations.

• Journal of the Korean Society of Safety
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• v.11 no.4
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• pp.143-150
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• 1996

This is an explicit-Implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE ) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for and existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The Ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory Darcy's law Is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full newton-Raphson method is used for solving the nonlinear governing equations.