• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
• /
• v.3 no.1
• /
• pp.33-41
• /
• 1992

In this paper the propagation problems of waves nomally incident upon an anisotropic medium with arbitrary permittivity tensors are analyzed through the variational finite element method. First, a variational equation is derived from the new approach basd on the induction theorm, reactions, and reciprocity. Next, by using the finite element method, the propagation problems are solved from the obtained functional. Specially, the reflection and transmission coefficient and axis ratio are obtained on the case of normally incident upon a homogeneous and inhomogeneous anisotropic medium such as cold mgnetoplasma slab and showed agreement with those of the previous method.

• Nuclear Engineering and Technology
• /
• v.55 no.6
• /
• pp.2172-2194
• /
• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.131-164
• /
• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• The Pure and Applied Mathematics
• /
• v.9 no.1
• /
• pp.47-55
• /
• 2002

In this pope., we consider a Minty's lemma for ($\theta ,\eta$)-pseudomonotone-type set-valued mappings in real Banach spaces and then we show the existence of solutions to variational-type inequality problems for ($\theta ,\eta$)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces.

• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1179-1194
• /
• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

• Journal of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.845-860
• /
• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Structural Engineering and Mechanics
• /
• v.23 no.4
• /
• pp.431-447
• /
• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Journal of the korean society of oceanography
• /
• v.35 no.2
• /
• pp.78-88
• /
• 2000

A weakly viscous wave and an approximate variational principle in viscous fluids are introduced, with which we can interpret the fundamentals such as how viscosity dissipation occurs with time elapse, and how the free surface boundary layer exists at the wavy surface in weakly viscous fluids. As an application, responses of a spherical buoy on the weakly viscous capillary gravity wave are investigated to show the viscosity effects. At the end, surfactant problems are briefly reviewed with the view of short viscous waves as expected future applications.

• Structural Engineering and Mechanics
• /
• v.65 no.4
• /
• pp.409-413
• /
• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.89-106
• /
• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.