A SEMI-LAGRANGIAN METHOD BASED ON WENO INTERPOLATION

Dokkyun Yi,Hyunsook Kim 충청수학회 2015 충청수학회지 Vol.28 No.4

In this paper, a general Weighted Essentially Non-Oscillatory (WENO) interpolation is proposed and applied to a semi-Lagrangian method. The proposed method is based on the conservation law, and characteristic curves are used to complete the semi-Lagrangian method. Therefore, the proposed method satisfies conservation of mass and is free of the CFL condition which is a necessary condition for convergence.Using a several standard examples, the proposed method is compared with the third order Strong Stability Preserving (SSP) Runge-Kutta method to verify the high-order accuracy.

A mass conservative scheme for solving the Vlasov–Poisson equation using characteristic curve

Yi, Dokkyun,Bu, Sunyoung Koninklijke Vlaamse Ingenieursvereniging 2017 Journal of computational and applied mathematics Vol.324 No.-

<P><B>Abstract</B></P> <P>In this paper, we introduce a mass conservative scheme for solving the Vlasov–Poisson equation. This scheme is based on an Eulerian approach and is constructed using an interpolation scheme with limiters. In order to preserve the mass, the difference in the values for numerical flux functions on each cell is used; for this, the flux functions are constructed by preserving both the solution along a characteristics and the mass in each cell. We mainly investigate the conservation of <SUB> L 1 </SUB> and <SUB> L 2 </SUB> norms of the distribution function, total energy, entropy, and minimum value. In addition, we show that this scheme is bounded on the total variation. To demonstrate the efficiency of the proposed scheme, this scheme is compared with the flux balance scheme, Positive and Flux Conservative scheme, Umeda’s scheme, and fifth order WENO reconstruction finite volume scheme.</P>

A SEMI-LAGRANGIAN METHOD BASED ON WENO INTERPOLATION

Yi, Dokkyun,Kim, Hyunsook Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.4

In this paper, a general Weighted Essentially Non-Oscillatory (WENO) interpolation is proposed and applied to a semi-Lagrangian method. The proposed method is based on the conservation law, and characteristic curves are used to complete the semi-Lagrangian method. Therefore, the proposed method satisfies conservation of mass and is free of the CFL condition which is a necessary condition for convergence. Using a several standard examples, the proposed method is compared with the third order Strong Stability Preserving (SSP) Runge-Kutta method to verify the high-order accuracy.

THE NUMERICAL SOLUTION FOR THE VLASOV EQUATION USING WENO METHODS

Youngsoo Ha,Dokkyun Yi 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5

This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poissons equation for the computation of the self-consistent electric field. The coupled model is non linear. In this report we present a WENO method for the solution of the Vlasov equation using a phase space grid is proposed. WENO(essentially non-oscillatory) schemes have proven to be very useful to compute the discontinuous solutions of hyperbolic conservation laws. The WENO scheme are based on the essentially non-oscillatory (ENO) scheme, which were first introdued by Harten et al: [3] in the form of finite volume schemes and were later improved by Shu and Osher into a more efficient and easy-to-implement finite difference form. The WENO schemes have an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimensionby-dimension.

Characterizing Facial Expressions in Males and Females by Using Branch Length Similarity Entropy

이상희,김은연,Dokkyun Yi 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.58 No.2

Branch length symmetry (BLS) entropy, defined on a simple network consisting of a single node and branches, was used to characterize facial expressions in both males and females. As a component of a larger network, this simple network is referred to as a unit branching network (UBN). We introduced a new variable, γ, which represents the topological property of the network, as a function of entropy in order to topologically characterize a branching network composed of UBNs. We constructed UBNs for images of 70 male and 56 female faces displaying four different expressions (neutral, happy, angry, and screaming) by joining 17 facial landmark points such as the centers of the eyes, the corners of the mouth, and the underside tip of the nose. Based on these expressions, we computed the values of γ for the facial networks and found a statistical difference between the γ values of male and female faces. With the exception of a comparison between the neutral and the angry expressions, which had the same γ values, there was a significant difference in the γ values among different expressions within the same gender. Neutral and angry expressions had equal γ values because the change in the distances between the facial landmark points for these two expressions was negligible. This study is valuable because it demonstrates that BLS entropy can be usefully applied to characterize facial expressions.

Development of semi-Lagrangian gyrokinetic code for full-f turbulence simulation in general tokamak geometry

Kwon, Jae-Min,Yi, Dokkyun,Piao, Xiangfan,Kim, Philsu Elsevier 2015 Journal of computational physics Vol.283 No.-

<P><B>Abstract</B></P> <P>In this work, we report the development of a new gyrokinetic code for full-f simulation of electrostatic turbulence in general tokamak geometry. Backward semi-Lagrangian scheme is employed for noise-free simulation of the gyrokinetic Vlasov equation with finite Larmor radius effects. Grid systems and numerical interpolations are implemented to deal with arbitrary equilibrium information given in a GEQDSK format file. In particular, we introduce an adaptive interpolation technique for fluctuating quantities, which have elongated structures along equilibrium magnetic fields. This field-aligned interpolation can reduce the required number of grid points to represent the fluctuating quantities. Also, it is shown that the new interpolation allows us to choose bigger time sizes with better simulation accuracy. Several benchmark simulation results are presented for comparison with previously known cases. It is demonstrated that the new code can reproduce the well known results of zonal flow and linear ITG instabilities in concentric circular equilibrium. It is also shown that the code can capture the effects of plasma shaping on the zonal flow and ITG instabilities, and the stabilization effects of the shaping result in significant up-shifts of the threshold of ion temperature gradient for ITG in nonlinear simulation.</P>

모바일 센서 네트워크에서 2계층 영역을 이용한 에너지 효율적 클러스터링 기법

김현숙(Hyunsook Kim),이덕균(Dokkyun Yi) 한국정보기술학회 2016 한국정보기술학회논문지 Vol.14 No.2

In MWSNs, the mobility of a cluster head is one of the major causes of topology change and re-clustering. Also it affects the transmission delay and the network lifetime. Therefore, a stable and energy-efficient clustering scheme is needed to reduce the frequent cluster reconstruction. In this paper, we propose a cluster head selection scheme using two-tier zone to increase the energy efficiency and the network throughput. In proposed scheme, a node having stable mobility with a high residual energy is selected as a cluster head without extra exchange messages. In addition, we divided cluster into the two-tier zone and reconstructed a cluster aimed at nodes that enter and/or leave to a virtual zone newly. Also we showed that our proposed scheme produces better performance comparing with M-LEACH and MBC protocols on its network lifetime, drop ratio and throughput.

A second order backward semi-Lagrangian scheme for guiding center problems

Xiang Fan Piao,Jae-Min Kwon,Dokkyun Yi,Sang Dong Kim,Philsu Kim 한국산업응용수학회 2013 한국산업응용수학회 학술대회 논문집 Vol.8 No.1

In this study, we develop a class of backward semi-Lagrangian finite difference methods for solving nonlinear guiding center models. A key problem in the time discretization is to find the starting point of the characteristic curves arriving at each grid point, which is a highly nonlinear problem with a self-consistency imposed by the Poisson equation. The proposed method is based on the error correction method recently developed by the au-thors. For the error correction method, we introduce a modified Euler’s polygon and solve the induced asymptotically linear differential equation with the mid-point quadrature rule to get the error correction term. It is proved that the proposed method is iteration free and has the convergence order 3 in space and 2 in time. In particular, it is shown that the proposed method has a good performance in computational cost together with a superior mass conservation and a similar conservation in the total kinetic energy compared to the conventional second-order iteration methods.