• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.33-34
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• 2003

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.153-159
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• 1998

The Newton-Krylov method on the unstructured grid flow solver using the cell-centered spatial discretization oi compressible Euler equations is presented. This flow solver uses the reconstructed primitive variables to get the higher order solutions. To get the quadratic convergence of Newton method with this solver, the careful linearization of face flux is performed with the reconstructed flow variables. The GMRES method is used to solve large sparse matrix and to improve the performance ILU preconditioner is adopted and vectorized with level scheduling algorithm. To get the quadratic convergence with the higher order schemes and to reduce the memory storage. the matrix-free implementation and Barth's matrix-vector method are implemented and compared with the traditional matrix-vector method. The convergence and computing times are compared with each other.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.7
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• pp.683-687
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• 2007

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.479-483
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• 2006

Indoor positioning is recently highlighted and various kinds of indoor positioning systems are under developments. Since positioning systems have their own characteristics, proper positioning scheme should be chosen according to the required specifications. Positioning methods are often classified into time-based and angle-based one, and this paper presents the error analysis of these location methods. Because measurement equations of these methods are nonlinear, linearization is usually needed to get the position estimate. In this paper, Gauss-Newton method is used in the linearization. To analyze the position error, we investigate the error ellipse parameters that include eccentricity, rotation angle, and the size of ellipse. Simulation results show that the major axes of error ellipses of TOA and AOA method lie in different quadrants at most region of workspace, especially where the geometry is poor. When the TOA/AOA hybrid scheme is employed, it is found that the error ellipse is reduced to the intersection of ellipses of TOA and AOA method.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.10
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• pp.962-967
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• 2006

Indoor positioning is highlighted recently, and various kinds of indoor positioning systems are under developments. Since positioning systems have their own characteristics, proper positioning scheme should be chosen according to the required specifications. Positioning methods are classified into time-based and angle-based one. This paper presents the error analysis of time-based and angle-based location methods. Because measurements of these methods are nonlinear, linearizations are needed in both cases to estimate the user position. In the linearization, Gauss-Newton method is used in both cases. To analyze the position error, we investigate the error ellipse parameters that include eccentricity, rotation angle, and the size of ellipse. Simulation results show that the major axes of TOA and AOA method lie in different quadrants at most region of workspace, especially where the geometry is poor. When the TOA/AOA hybrid is employed, it is found that the error ellipse is reduced to the intersection of ellipses of TOA and AOA.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.485-489
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• 2006

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and closed-form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a self-tuning weighted least square AOA algorithm that is a modified version of the conventional closed-form solution. In order to estimate the error covariance matrix as a weight, two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.3
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• pp.1-10
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• 1988

A higher order plate bending finite element using cubic in-plane displacement profiles is proposed for geometrically nonlinear analysis of thin and thick plates. The higher order plate bending element has been derived from the three dimensional plate-like continuum by discretization of the equations of motion by Galerkin weighted residual method, together with enforcing higher order plate assumptions. Total Lagrangian formulation has been used for geometrically nonlinear analysis of plates and consistent linearization by Newton-Raphson method has been performed to solve the nonlinear equations. The element characteristics have been computed by, selective reduced integration technique using Gauss quadrature to avoid shear locking phenomenon in case of extremely thin plates. Several numerical examples were solved with FEAP macro program to demonstrate versatility and accuracy of the present higher order plate bending element.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.