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Poisson equation
"... Part of the Nanoscience and Nanotechnology Commons This document has been made available through Purdue ePubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. ..."
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Part of the Nanoscience and Nanotechnology Commons This document has been made available through Purdue ePubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.
EULERPOISSON EQUATIONS IN R
"... Abstract. We prove the finite time blowup for C 1 solutions of the attractive EulerPoisson equations in R n, n ≥1, with and without background state, for a large set of ’generic ’ initial data. We characterize this supercritical set by tracing the spectral dynamics of the deformation and vorticity ..."
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Abstract. We prove the finite time blowup for C 1 solutions of the attractive EulerPoisson equations in R n, n ≥1, with and without background state, for a large set of ’generic ’ initial data. We characterize this supercritical set by tracing the spectral dynamics of the deformation
Solving the Poisson Equation with Multigrid
, 2005
"... I give a short explanation of how to use multigrid to solve the Poisson equation in cylindrical coordinates for a solid conducting pipe. I also explain how to use a nonuniform grid to optimize the problem. 1 ..."
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I give a short explanation of how to use multigrid to solve the Poisson equation in cylindrical coordinates for a solid conducting pipe. I also explain how to use a nonuniform grid to optimize the problem. 1
Prewavelet Solution to Poisson Equations
, 2008
"... Finite element method is one of powerful numerical methods to solve PDE. Usually, if a finite element solution to a Poisson equation based on a triangulation of the underlying domain is not accurate enough, one will discard the solution and then refine the triangulation uniformly and compute a new f ..."
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Finite element method is one of powerful numerical methods to solve PDE. Usually, if a finite element solution to a Poisson equation based on a triangulation of the underlying domain is not accurate enough, one will discard the solution and then refine the triangulation uniformly and compute a new
SYMETRIZATION OF VLASOVPOISSON EQUATIONS ∗
, 2013
"... Abstract. We detail the spectrum of the linearized VlasovPoisson equation, and construct an original integrodifferential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we ap ..."
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Abstract. We detail the spectrum of the linearized VlasovPoisson equation, and construct an original integrodifferential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we
Critical Thresholds in EulerPoisson Equations
, 2001
"... We present a preliminary study of a new phenomena associated with the EulerPoisson equations  the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1) critica ..."
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Cited by 53 (26 self)
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We present a preliminary study of a new phenomena associated with the EulerPoisson equations  the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1
WIGNERPOISSON EQUATIONS
, 2005
"... This thesis applies modern numerical methods to solve the WignerPoisson equations for simulating quantum mechanical electron transport in nanoscale semiconductor devices, in particular, a resonant tunneling diode (RTD). The goal of this dissertation is to provide engineers with a simulation tool th ..."
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This thesis applies modern numerical methods to solve the WignerPoisson equations for simulating quantum mechanical electron transport in nanoscale semiconductor devices, in particular, a resonant tunneling diode (RTD). The goal of this dissertation is to provide engineers with a simulation tool
On the Poisson equation and diffusion approximation 1
 Ann. Probab
, 2001
"... Dedicated to N. V. Krylov on his sixtieth birthday A Poisson equation in �d for the elliptic operator correspondingto an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established alongwith the bounds for its growth. This result i ..."
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Cited by 8 (2 self)
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Dedicated to N. V. Krylov on his sixtieth birthday A Poisson equation in �d for the elliptic operator correspondingto an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established alongwith the bounds for its growth. This result
Abstract VLASOVPOISSON EQUATIONS
, 2002
"... We consider the applications of a numericalanalytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of VlasovPoisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in highlo ..."
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We consider the applications of a numericalanalytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of VlasovPoisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high
On the solutions of generalized discrete Poisson equation
, 2008
"... The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with squaresummable discrete derivatives are unique up to a constant. The proof uses the Fourier transform as the main tool. Th ..."
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The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with squaresummable discrete derivatives are unique up to a constant. The proof uses the Fourier transform as the main tool
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