• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.471-506
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• 2018

In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.645-658
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• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

• The Transactions of the Korean Institute of Power Electronics
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• v.23 no.1
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• pp.66-71
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• 2018

We propose an online parameter estimation method for surface-mounted permanent-magnet synchronous motor (SPMSM) using an affine projection algorithm (APA). The proposed method estimates parameters with two APAs based on the discrete-time model equation of SPMSM during motor operation. The first APA is designed to estimate inductance, and the second APA is designed to estimate resistance and flux linkage. However, in case when the d-axis current is controlled to 0A, the second APA cannot estimate resistance and flux linkage simultaneously because the matrix rank in APA becomes deficient. To overcome this problem, we temporarily inject a negative reference current input to the d-axis control loop, and the matrix in the APA then becomes full rank, which enables the simultaneous estimation of resistance and flux linkage. The proposed method is verified by PSIM simulation and an actual experiment, and the results reveal that SPMSM parameters can be estimated online during motor operation.

• Journal of Korea Multimedia Society
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• v.18 no.4
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• pp.443-451
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• 2015

In this paper we suggest a new two-wheelers detection algorithm using uniform local binary pattern weighting value for projection vectors. The first, we calculate feature vectors using projection method which has robustness for rotation invariant and reducing dimensionality for each cell from origin image. The second, we applied new weighting values which are calculated by the modified local binary pattern showing the fast compute and simple to implement. This paper applied the Adaboost algorithm to make a strong classification from weak classification. In this experiment, we can get the result that the detection rate of the proposed method is higher than that of the traditional method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.4
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• pp.295-308
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• 2016

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.3
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• pp.233-251
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• 2011

The Gauge-Uzawa method [GUM] in [9] which is a projection type algorithm to solve evolution Navier-Stokes equations has many advantages and superior performance. But this method has been studied for backward Euler time discrete scheme which is the first order technique, because the classical second order GUM requests rather strong stability condition. Recently, the second order time discrete GUM was modified to be unconditionally stable and estimated errors in [12]. In this paper, we contemplate several GUMs which can be derived by the same manner within [12], and we dig out properties of them for both stability and accuracy. In addition, we evaluate an stability condition for the classical GUM to construct an adaptive GUM for time to make free from strong stability condition of the classical GUM.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.553-568
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• 2022

In this paper, we introduce and study two different iterative hybrid projection algorithms for solving a fixed point problem of nonexpansive mappings. The first algorithm is generated by the combination of the inertial method and the hybrid projection method. On the other hand, the second algorithm is constructed by the convex combination of three updated vectors and the hybrid projection method. The strong convergence of the two proposed algorithms are proved under very mild assumptions on the scalar control. For illustrating the advantages of these two newly invented algorithms, we created some numerical results to compare various numerical performances of our algorithms with the algorithm proposed by Dong and Lu [11].

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.331-334
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• 2000

This paper presents the method for the decision of eye states using the eye blink in video sequences. The entire procedure consists of two steps: in the first step, the accurate eye position is found in the input image by using symmetry information of faces and projection, and in the second step, the eye open/close state is decided by the horizontal and vertical projection. The method in this paper is also used for detecting drivers' fatigue in the drowsiness detection system.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.237-260
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• 2001

The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.