14,550 research outputs found
Computerized optimization of elastic booster autopilots. Volume 1: Technical manual
The philosophy and the mathematical basis of the nonlinear programming algorithm underlying the development of the COEBRA program were given. A User's Manual was given in a separate document. The purpose of this work was to convert the COEBRA program from the CDC 6400/6500 digital computer system to the UNIVAC 1108 at the George C. Marshall Space Flight Center and to provide an instruction manual on the use of the program
Convergence Rates for Newton’s Method at Singular Points
If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence
Newton's Method in Three Precisions
We describe a three precision variant of Newton's method for nonlinear
equations. We evaluate the nonlinear residual in double precision, store the
Jacobian matrix in single precision, and solve the equation for the Newton step
with iterative refinement with a factorization in half precision. We analyze
the method as an inexact Newton method. This analysis shows that, except for
very poorly conditioned Jacobians, the number of nonlinear iterations needed is
the same that one would get if one stored and factored the Jacobian in double
precision. In many ill-conditioned cases one can use the low precision
factorization as a preconditioner for a GMRES iteration. That approach can
recover fast convergence of the nonlinear iteration. We present an example to
illustrate the results.Comment: 10 page
Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation
Spatially distributed problems are often approximately modelled in terms of
partial differential equations (PDEs) for appropriate coarse-grained quantities
(e.g. concentrations). The derivation of accurate such PDEs starting from finer
scale, atomistic models, and using suitable averaging, is often a challenging
task; approximate PDEs are typically obtained through mathematical closure
procedures (e.g. mean-field approximations). In this paper, we show how such
approximate macroscopic PDEs can be exploited in constructing preconditioners
to accelerate stochastic simulations for spatially distributed particle-based
process models. We illustrate how such preconditioning can improve the
convergence of equation-free coarse-grained methods based on coarse
timesteppers. Our model problem is a stochastic reaction-diffusion model
capable of exhibiting Turing instabilities.Comment: 8 pages, 6 figures, submitted to Journal of Chemical Physic
Self-steepening of light pulses
Self-steepening of light pulses due to propagation in medium with intensity-dependent index of refractio
Density of bulk trap states in organic semiconductor crystals: discrete levels induced by oxygen in rubrene
The density of trap states in the bandgap of semiconducting organic single
crystals has been measured quantitatively and with high energy resolution by
means of the experimental method of temperature-dependent
space-charge-limited-current spectroscopy (TD-SCLC). This spectroscopy has been
applied to study bulk rubrene single crystals, which are shown by this
technique to be of high chemical and structural quality. A density of deep trap
states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the
exponentially varying shallow trap density near the band edge could be
identified (1 decade in the density of states per ~25 meV). Furthermore, we
have induced and spectroscopically identified an oxygen related sharp hole bulk
trap state at 0.27 eV above the valence band.Comment: published in Phys. Rev. B, high quality figures:
http://www.cpfs.mpg.de/~krellner
Geometry-induced pulse instability in microdesigned catalysts: the effect of boundary curvature
We explore the effect of boundary curvature on the instability of reactive
pulses in the catalytic oxidation of CO on microdesigned Pt catalysts. Using
ring-shaped domains of various radii, we find that the pulses disappear
(decollate from the inert boundary) at a turning point bifurcation, and trace
this boundary in both physical and geometrical parameter space. These
computations corroborate experimental observations of pulse decollation.Comment: submitted to Phys. Rev.
- …