• Journal of computational fluids engineering
• /
• v.9 no.3
• /
• pp.26-38
• /
• 2004

A study has been made for the investigation of the robustness and convergence of various implicit operators of the LU-SGS scheme using linear stability analysis. It is shown that the behavior of the implicit operator is not determined by its own characteristics, but is determined relatively depending on the dissipative property of the explicit operator. It is also shown that, as the dissipation level of the implicit operator increases, the robustness of the scheme increases, but the convergence rate can be deteriorated due to the excessive dissipation. The numerical results demonstrate that the dissipation level of the impliict operator needs to be higher than that of the explicit operator for computing stiff problems.

• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.37-47
• /
• 2012

In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

• Kyungpook Mathematical Journal
• /
• v.46 no.3
• /
• pp.345-356
• /
• 2006

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a new class of parametric generalized nonlinear implicit quasi-variational inclusion problem in $L_p(p{\geq}2)$ spaces. The results presented in this paper are new and generalize many known results in this field.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.889-902
• /
• 2007

An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.73-77
• /
• 2004

In the present study, an efficient and robust implicit operator for the LU-SGS method is proposed. Numerical experiments for supersonic flow are performed to demonstrate the performance of the proposed method.

• Honam Mathematical Journal
• /
• v.26 no.4
• /
• pp.391-399
• /
• 2004

In this paper, we develop an iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities in Hilbert spaces. The resolvent operator technique is used to establish the equivalence between variational inequalities and fixed point problems. This equivalence is used to study the existence of a solution of nonlinear mixed implicit variational inequalities and to suggest an iterative algorithm for solving variational inequalities. In our results, we do not assume that the mapping is strongly monotone.

• Communications of the Korean Mathematical Society
• /
• v.25 no.1
• /
• pp.129-137
• /
• 2010

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

• Communications of the Korean Mathematical Society
• /
• v.20 no.2
• /
• pp.311-319
• /
• 2005

In this paper we introduce a new class of parametric nonlinear implicit quasivariational inclusions and obtain some results about the existence and sensitivity analysis of solutions for this kind of quasivariational inclusions.

• Korean Journal of Computational Design and Engineering
• /
• v.13 no.3
• /
• pp.187-199
• /
• 2008

This paper describes a C++ class hierarchy of implicit objects for geometry modeling and processing. This class structure provides a software kernel for integrating many various models and methods found in current implicit modeling areas. The software kernel includes primitive objects playing a role of unit element in creating a complex shape, and operator objects used to construct more complex shape of implicit object formed with the primitive objects and other operators. In this paper, class descriptions of these objects are provided to better understand the details of the algorithm or implementation, and its instance examples to show the capabilities of the object classes for constructive shape geometry. In addition, solid modeling system shown as an application example demonstrates that the proposed implicit object classes allow us to carry out modern solid modeling techniques, which means they have the capabilities to extend to various applications.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.34 no.3
• /
• pp.151-157
• /
• 2021

This paper is devoted to a convergence study of the nonlocal integral operator in peridynamics. The implicit formulation can be an efficient approach to obtain the static/quasi-static solution of crack propagation problems. Implicit methods require constly large-matrix operations. Therefore, convergence is important for improving computational efficiency. When the radial influence function is utilized in the nonlocal integral equation, the fractional Laplacian integral equation is obtained. It has been mathematically proved that the condition number of the system matrix is affected by the order of the radial influence function and nonlocal horizon size. We formulate the static crack problem with peridynamics and utilize Newton-Raphson methods with a preconditioned conjugate gradient scheme to solve this nonlinear stationary system. The convergence behavior and the computational time for solving the implicit algebraic system have been studied with respect to the order of the radial influence function and nonlocal horizon size.