41,429 research outputs found
Composing Scalable Nonlinear Algebraic Solvers
Most efficient linear solvers use composable algorithmic components, with the
most common model being the combination of a Krylov accelerator and one or more
preconditioners. A similar set of concepts may be used for nonlinear algebraic
systems, where nonlinear composition of different nonlinear solvers may
significantly improve the time to solution. We describe the basic concepts of
nonlinear composition and preconditioning and present a number of solvers
applicable to nonlinear partial differential equations. We have developed a
software framework in order to easily explore the possible combinations of
solvers. We show that the performance gains from using composed solvers can be
substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table
Composite Learning Control With Application to Inverted Pendulums
Composite adaptive control (CAC) that integrates direct and indirect adaptive
control techniques can achieve smaller tracking errors and faster parameter
convergence compared with direct and indirect adaptive control techniques.
However, the condition of persistent excitation (PE) still has to be satisfied
to guarantee parameter convergence in CAC. This paper proposes a novel model
reference composite learning control (MRCLC) strategy for a class of affine
nonlinear systems with parametric uncertainties to guarantee parameter
convergence without the PE condition. In the composite learning, an integral
during a moving-time window is utilized to construct a prediction error, a
linear filter is applied to alleviate the derivation of plant states, and both
the tracking error and the prediction error are applied to update parametric
estimates. It is proven that the closed-loop system achieves global
exponential-like stability under interval excitation rather than PE of
regression functions. The effectiveness of the proposed MRCLC has been verified
by the application to an inverted pendulum control problem.Comment: 5 pages, 6 figures, conference submissio
Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics
The effective nonlinear response of films of random composites consisting of
a binary composite with nonlinear particles randomly embedded in a linear host
is theoretically and numerically studied. A theoretical expression for the
effective second harmonic generation susceptibility, incorporating the
thickness of the film, is obtained by combining a modified effective-medium
approximation with the general expression for the effective second harmonic
generation susceptibility in a composite. The validity of the thoretical
results is tested against results obtained by numerical simulations on random
resistor networks. Numerical results are found to be well described by our
theory. The result implies that the effective-medium approximation provides a
convenient way for the estimation of the nonlinear response in films of random
dielectrics.Comment: 9 pages, 2 figures; accepted for publication in Phys. Rev.
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