• Title, Summary, Keyword: Poisson equation

### ANALYSIS OF THE VLASOV-POISSON EQUATION BY USING A VISCOSITY TERM

• Choi, Boo-Yong;Kang, Sun-Bu;Lee, Moon-Shik
• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.501-516
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• 2013
• The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

### Shape Recognition and Classification Based on Poisson Equation- Fourier-Mellin Moment Descriptor

• Zou, Jian-Cheng;Ke, Nan-Nan;Lu, Yan
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• v.8 no.1
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• pp.69-72
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• 2009
• In this paper, we present a new shape descriptor, which is named Poisson equation-Fourier-Mellin moment Descriptor. We solve the Poisson equation in the shape area, and use the solution to get feature function, which are then integrated using Fourier-Mellin moment to represent the shape. This method develops the Poisson equation-geometric moment Descriptor proposed by Lena Gorelick, and keeps both advantages of Poisson equation-geometric moment and Fourier-Mellin moment. It is proved better than Poisson equation-geometric moment Descriptor in shape recognition and classification experiments.

### Analysis of Transport Characteristics for FinFET Using Three Dimension Poisson's Equation

• Jung, Hak-Kee;Han, Ji-Hyeong
• Journal of information and communication convergence engineering
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• v.7 no.3
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• pp.361-365
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• 2009
• This paper has been presented the transport characteristics of FinFET using the analytical potential model based on the Poisson's equation in subthreshold and threshold region. The threshold voltage is the most important factor of device design since threshold voltage decides ON/OFF of transistor. We have investigated the variations of threshold voltage and drain induced barrier lowing according to the variation of geometry such as the length, width and thickness of channel. The analytical potential model derived from the three dimensional Poisson's equation has been used since the channel electrostatics under threshold and subthreshold region is governed by the Poisson's equation. The appropriate boundary conditions for source/drain and gates has been also used to solve analytically the three dimensional Poisson's equation. Since the model is validated by comparing with the three dimensional numerical simulation, the subthreshold current is derived from this potential model. The threshold voltage is obtained from calculating the front gate bias when the drain current is $10^{-6}A$.

### HOMOMORPHISMS BETWEEN POISSON BANACH ALGEBRAS AND POISSON BRACKETS

• PARK, CHUN-GIL;WEE, HEE-JUNG
• Honam Mathematical Journal
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• v.26 no.1
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• pp.61-75
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• 2004
• It is shown that every almost linear mapping $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital Poisson Banach algebra ${\mathcal{A}}$ to a unital Poisson Banach algebra ${\mathcal{B}}$ is a Poisson algebra homomorphism when h(xy) = h(x)h(y) holds for all $x,y{\in}\;{\mathcal{A}}$, and that every almost linear almost multiplicative mapping $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a Poisson algebra homomorphism when h(qx) = qh(x) for all $x\;{\in}\;{\mathcal{A}}$. Here the number q is in the functional equation given in the almost linear almost multiplicative mapping. We prove that every almost Poisson bracket $B:{\mathcal{A}}\;{\times}\;{\mathcal{A}}\;{\rightarrow}\;{\mathcal{A}}$ on a Banach algebra ${\mathcal{A}}$ is a Poisson bracket when B(qx, z) = B(x, qz) = qB(x, z) for all $x,z{\in}\;{\mathcal{A}}$. Here the number q is in the functional equation given in the almost Poisson bracket.

### A discretization method of the three-dimensional poisson's equation with excellent convergence characteristics (우수한 수렴특성을 갖는 3차원 포아송 방정식의 이산화 방법)

• 김태한;이은구;김철성
• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.8
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• pp.15-25
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• 1997
• The integration method of carier concentrations to redcue the discretization error of th box integratio method used in the discretization of the three-dimensional poisson's equation is presented. The carrier concentration is approximated in the closed form as an exponential function of the linearly varying potential in the element. The presented method is implemented in the three-dimensional poisson's equation solver running under the windows 95. The accuracy and the convergence chaacteristics of the three-dimensional poisson's equation solver are compared with those of DAVINCI for the PN junction diode and the n-MOSFET under the thermal equilibrium and the DC reverse bias. The potential distributions of the simulatied devices from the three-dimensional poisson's equation solver, compared with those of DAVINCI, has a relative error within 2.8%. The average number of iterations needed to obtain the solution of the PN junction diode and the n-MOSFET using the presented method are 11.47 and 11.16 while the those of DAVINCI are 21.73 and 23.0 respectively.

### Solution of Poisson Equation using Isogeometric Formulation

• Lee, Sang-Jin
• Architectural research
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• v.13 no.1
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• pp.17-24
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• 2011
• Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

### On the Multivariate Poisson Distribution with Specific Covariance Matrix

• Kim, Dae-Hak;Jeong, Heong-Chul;Jung, Byoung-Cheol
• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.161-171
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• 2006
• In this paper, we consider the random number generation method for multivariate Poisson distribution with specific covariance matrix. Random number generating method for the multivariate Poisson distribution is considered into two part, by first solving the linear equation to determine the univariate Poisson parameter, then convoluting independent univariate Poisson variates with appropriate expectations. We propose a numerical algorithm to solve the linear equation given the specific covariance matrix.

### AN EFFICIENT ALGORITHM FOR INCOMPRESSIBLE FREE SURFACE FLOW ON CARTESIAN MESHES (직교격자상에서 효율적인 비압축성 자유표면유동 해법)

• Go, G.S.;Ahn, H.T.
• Journal of computational fluids engineering
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• v.19 no.4
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• pp.20-28
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• 2014
• An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.

### A Numerical Analysis on the solution of Poisson Equation by Direct Method (직접법을 이용한 Poisson 방정식 수치해법에 관하여)

• Y.S. Shin;K.P. Rhee
• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.62-71
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• 1995
• In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

### Analysis of Threshold Voltage Characteristics for FinFET Using Three Dimension Poisson's Equation (3차원 포아송방정식을 이용한 FinFET의 문턱전압특성분석)

• Jung, Hak-Kee
• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.11
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• pp.2373-2377
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• 2009
• In this paper, the threshold voltage characteristics have been analyzed using three dimensional Poisson's equation for FinFET. The FinFET is extensively been studing since it can reduce the short channel effects as the nano device. We have presented the short channel effects such as subthreshold swing and threshold voltage for PinFET, using the analytical three dimensional Poisson's equation. We have analyzed for channel length, thickness and width to consider the structural characteristics for FinFET. Using this model, the subthreshold swing and threshold voltage have been analyzed for FinFET since the potential and transport model of this analytical three dimensional Poisson's equation is verified as comparing with those of the numerical three dimensional Poisson's equation.