http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Piao, Xiangfan,Kim, Philsu,Kim, Dojin Elsevier 2018 Journal of computational physics Vol.366 No.-
<P><B>Abstract</B></P> <P>We present a backward semi-Lagrangian method with third-order temporal accuracy for solving the guiding center problem. For solving highly nonlinear characteristic curves, we propose an iteration-free L ( α ) -stable method equipped with an error correction technique and a classical collocation method. As a discretization of the Poisson equation, we adopt the fourth-order centered differential scheme and the Shortley–Weller discretization depending on the boundary of the domain, and apply the local cubic interpolation polynomial for the evaluation of the density and the potential at the non-grid foot points of the characteristics. The novelty of the proposed method is its good stability as well as its outstanding computational cost compared to those of the recently developed high-order Adams–Moulton method. Furthermore, based on several numerical tests, we conclude that the proposed method exhibits excellent performance for long-time stable simulations and allows for large temporal step sizes.</P>
Block LU Factorization for the Coupled Stokes Equations by Spectral Element Discretization
Piao, Xiangfan,Kim, Philsu,Kim, Sang Dong Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.4
The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.
An embedded formula of the Chebyshev collocation method for stiff problems
Piao, Xiangfan,Bu, Sunyoung,Kim, Dojin,Kim, Philsu Elsevier 2017 Journal of computational physics Vol.351 No.-
<P><B>Abstract</B></P> <P>In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge–Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.</P>
An iteration free backward semi-Lagrangian scheme for solving incompressible Navier–Stokes equations
Piao, Xiangfan,Bu, Sunyoung,Bak, Soyoon,Kim, Philsu Elsevier 2015 Journal of computational physics Vol.283 No.-
<P><B>Abstract</B></P> <P>A backward semi-Lagrangian method based on the error correction method is designed to solve incompressible Navier–Stokes equations. The time derivative of the Stokes equation is discretized with the second order backward differentiation formula. For the induced steady Stokes equation, a projection method is used to split it into velocity and pressure. Fourth-order finite differences for partial derivatives are used to the boundary value problems for the velocity and the pressure. Also, finite linear systems for Poisson equations and Helmholtz equations are solved with a matrix-diagonalization technique. For characteristic curves satisfying highly nonlinear self-consistent initial value problems, the departure points are solved with an error correction strategy having a temporal convergence of order two. The constructed algorithm turns out to be completely iteration free. In particular, the suggested algorithm possesses a good behavior of the total energy conservation compared to existing methods. To assess the effectiveness of the method, two-dimensional lid-driven cavity problems with large different Reynolds numbers are solved. The doubly periodic shear layer flows are also used to assess the efficiency of the algorithm.</P>
A NOTE ON DEGENERATE LAH-BELL POLYNOMIALS ARISING FROM DERIVATIVES
Xiangfan Piao,Yunjae Kim,Jongkyum Kwon 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.4
Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.
A note on derangement polynomials and degenerate derangement polynomials
장이채,김윤재,Xiangfan Piao,권종겸 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.4
In 1708, Pierre Remonde de Motmort introduced the problem of counting derangement for the first time. A derangement is a permutation that has no fixed points. Recently, many researchers have studied the derangement polynomials and T. Kim introduced the degenerate derangement polynomials and investigated some identities of those polynomials. In, Jang-Kim-Kim-Lee introduced some identities involving derangement polynomials and numbers and moments of gamma random variables. In this paper, we study some identities and properties of the derangement polynomials and degenerate derangement polynomials and investigate the zeros of derangement polynomials. Moreover, we investigate the numerical pattern of the roots of the polynomials Dn,λ(x) varying the degree of polynomials from 1 to 40.
Convergence on error correction methods for solving initial value problems
Kim, Sang Dong,Piao, Xiangfan,Kim, Do Hyung,Kim, Philsu Elsevier 2012 Journal of computational and applied mathematics Vol.236 No.17
<P><B>Abstract</B></P><P>Higher-order semi-explicit one-step error correction methods(ECM) for solving initial value problems are developed. ECM provides the excellent convergence O(<SUP>h2p+2</SUP>) one wants to get without any iteration processes required by most implicit type methods. This is possible if one constructs a local approximation having a residual error O(<SUP>hp</SUP>) on each time step. As a practical example, we construct a local quadratic approximation. Further, it is shown that special choices of parameters for the local quadratic polynomial lead to the known explicit second-order methods which can be improved into a semi-explicit type ECM of the order of accuracy 6. The stability function is also derived and numerical evidences are presented to support theoretical results with several stiff and non-stiff problems. It should be remarked that the ECM approach developed here does not yield explicit methods, but semi-implicit methods of the Rosenbrock type. Both ECM and Rosenbrock’s methods require to solve a few linear systems at each integration step, but the ECM approach involves 2p+2 evaluations of the Jacobian matrix per integration step whereas the Rosenbrock method demands one evaluation only. However, it is much easier to get high order methods by using the ECM approach.</P>
Miao He,Qingjuan Xu,Cui Yang,Xiangfan Piao,Narayanan Kannan,Donghao Li 대한화학회 2014 Bulletin of the Korean Chemical Society Vol.35 No.10
A sensitive concentration method utilising modified gas-purge microsyringe extraction (GP-MSE) was developed. Concentration (reduction in volume) to a microlitre volume was achieved. PAHs were utilised as semivolatile analytes to optimise the various parameters that affect the concentration efficiency. The injection rate and temperature were the key factors that affected the concentration efficiency. An efficient concentration (75.0−96.1%) of PAHs was obtained under the optimised conditions. The method exhibited good reproducibility (RSD values that ranged from 1.5 to 9.0%). The GP-MSE concentration method enhances the volume reduction (concentration factor), leading to a low method detection limit (0.5−15 ng L–1). Furthermore, this method offers the advantage of small-volume sampling, enabling even the detection of diurnal hourly changes in the concentration of PAHs in ambient air. Utilising this method in combination with GC−MS, the diurnal hourly flux of PAHs from the gas phase of ambient air was measured. Indeed, the proposed technique is a simple, fast, low-cost and environmentally friendly.