1,703 research outputs found
Asymptotic boundary conditions for dissipative waves: General theory
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed
A compact finite difference scheme for div(Rho grad u) - q2u = 0
A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation
Ion collection from a plasma by a pinhole
Ion focusing by a biased pinhole is studied numerically. Laplace's equation is solved in 3-D for cylindrical symmetry on a constant grid to determine the potential field produced by a biased pinhole in a dielectric material. Focusing factors are studied for ions of uniform incident velocity with a 3-D Maxwellian distribution superimposed. Ion currents to the pinhole are found by particle tracking. The focusing factor of positive ions as a function of initial velocity, temperature, injection radius, and hole size is reported. For a typical Space Station Freedom environment (oxygen ions having a 4.5 eV ram energy, 0.1 eV temperature, and a -140 V biased pinhole), a focusing factor of 13.35 is found for a 1.5 mm radius pinhole
A multi-resolution, probabilistic approach to 2D inverse conductivity problems
Caption title.Bibliography: p. 35-36.Supported, in part, by a grant from the National Science Foundation. ECS-8700903 Supported, in part, by a grant from the Army Research Office. DAAL03-86-K-0171 Supported, in part, by a grant from the Institut de Recherche en Informatique et Systemes Aleatoires, Rennes, France.Kenneth C. Chou, Alan S. Willsky
Asymptotic analysis of dissipative waves with applications to their numerical simulation
Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented
Physical electrostatics of small field emitter arrays/clusters
This paper improves understanding of electrostatic influences on apex field
enhancement factors (AFEFs) for small field emitter arrays. Using the "floating
sphere at emitter-plate potential" (FSEPP) model, it re-examines the
electrostatics and mathematics of three simple systems of identical post-like
emitters. For the isolated emitter, various approaches are noted. On need
consider only the effects of sphere charges and (for separated emitters) image
charges. For the 2-emitter system, formulas are found for "charge-blunting" and
"neighbour-field" effects, for widely spaced and "sufficiently closely spaced"
emitters. Mutual charge-blunting is always dominant, with a related (negative)
fractional AFEF-change {\delta}_two. For sufficiently small emitter spacing c,
|{\delta}_two| varies as 1/c; for large spacing, |{\delta}_two| decreases as
1/c^3. In a 3-emitter linear array, differential charge-blunting and
differential neighbor-field effects occur, but the former are dominant, and
cause the "exposed" outer emitters to have higher AFEF ({\gamma}_0) than the
central emitter ({\gamma}_1). Formulas are found for the exposure ratio
{\Xi}={\gamma}_0/{\gamma}_1, for large and for sufficiently small separations.
The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge
models (LCMs) are an alternative, but an apparent difficulty with recent LCM
models is identified. Better descriptions of array electrostatics may involve
developing good fitting equations for AFEFs derived from accurate numerical
solution of Laplace's equation, perhaps with equation form(s) guided
qualitatively by FSEPP-model results. In existing fitting formulas, the
AFEF-reduction decreases exponentially as c increases, which differs from
FSEPP-model formulas. FSEPP models might provide a useful guide to the
qualitative behaviour of small field emitter clusters larger than those
investigated.Comment: 34 pages, including 3 figures, with an extra 7 pages of Supplementary
Material (giving details of algebraic analysis); v3 is slightly revised
version, submitted after reviewin
On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds
Application of integral operators in the numerical solution of elliptic boundary value problems
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