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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.
Poisson equation
"... ABSTRACT MEMS (microelectromechanical system) are driven typically by the electrostatic force, and their vibration under atmospheric condition is strongly damped by the fluid viscous force from the surrounding air. Moreover, both of these forces are sensitive to its dynamic behavior. Therefore, t ..."
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ABSTRACT MEMS (microelectromechanical system) are driven typically by the electrostatic force, and their vibration under atmospheric condition is strongly damped by the fluid viscous force from the surrounding air. Moreover, both of these forces are sensitive to its dynamic behavior. Therefore, the interaction of the structure, fluid and electrostatic field or the structurefluidelectrostatic interaction has to be carefully taken into account during the design process in order to predict the vibration characteristics such as the resonance frequency and the damping ratio, which are the key design parameters. In this study, a hierarchal decomposition for the structurefluidelectrostatic interaction is proposed in order to solve it efficiently. The proposed decomposition partitions it into the fluidstructure interaction (FSI) and the electrostatic field, and moreover splits the FSI into the fluid pressure and the fluidstructure velocities using a projection method The proposed decomposition is implemented using a finite element method and is applied for a micro cantilever beam actuated by the electrostatic force in air. It follows from the comparison between the computational and experimental results that the proposed method predicts the vibration characteristics of the micro cantilever beam with the strong interaction accurately. REFERENCES [1] D. Ishihara and S. Yoshimura, "A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure
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
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
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 41 (19 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
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
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
Localization of Multiscale Screened Poisson Equation
, 2012
"... In this paper we investigate a local fine scale problem which arises in various multiscale methods, see e.g. [1]. Local fine scale problems are solved and used to modify coarse scale basis functions. We analyze the decay of these basis functions in the case of localization of the screened Poisson e ..."
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equation, and state a Proposition in which we get a theoretical bound of the decay. Furthermore we present extensive numerical tests which confirms our theoretical results. The screened Poisson equation can be view as a temporal discrete parabolic equation, and can be used to model time
Results 1  10
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