7,380 research outputs found
Solution of systems of nonlinear equations Final report
Algorithm and computer program of diagonal discrimination method for computing nonlinear and transcendental function
Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional
In the distributed nucleus approximation we represent the singular nucleus as
smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus
allows us to solve the Poisson equation for theoverall electrostatic potential
using a linear scaling multigrid algorithm.This work is done in the context of
minimizing the Kohn-Sham energy functionaldirectly in real space with a
multiscale approach. The efficacy of the approximation is illustrated
bylocating the ground state density of simple one electron atoms and
moleculesand more complicated multiorbital systems.Comment: Submitted to JCP (July 1, 1995 Issue), latex, 27pages, 2figure
A numerical method for oscillatory integrals with coalescing saddle points
The value of a highly oscillatory integral is typically determined
asymptotically by the behaviour of the integrand near a small number of
critical points. These include the endpoints of the integration domain and the
so-called stationary points or saddle points -- roots of the derivative of the
phase of the integrand -- where the integrand is locally non-oscillatory.
Modern methods for highly oscillatory quadrature exhibit numerical issues when
two such saddle points coalesce. On the other hand, integrals with coalescing
saddle points are a classical topic in asymptotic analysis, where they give
rise to uniform asymptotic expansions in terms of the Airy function. In this
paper we construct Gaussian quadrature rules that remain uniformly accurate
when two saddle points coalesce. These rules are based on orthogonal
polynomials in the complex plane. We analyze these polynomials, prove their
existence for even degrees, and describe an accurate and efficient numerical
scheme for the evaluation of oscillatory integrals with coalescing saddle
points
Minimum-fuel Attitude Control of a Rigid Body in Orbit by an Extended Method of Steepest-descent
Minimum fuel control of spacecraft in orbit using extended method of steepest descen
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