Search results for "Numerical Analysis"
showing 10 items of 883 documents
Numerical study of an optical regenerator exploiting self-phase modulation and spectral offset filtering at 40 Gbit/s
2008
Topic: Nonlinear optics; International audience; In this work, we numerically investigate the performances of optical regenerators based on self-phase modulation and spectral offset filtering at 40 Gbit/s. We outline the different effects affecting the device performances and explain the choice of the optimal working power. The impact of the regenerator on the output signal is also analysed through a statistical approach. Both single- and double-stage configurations are investigated.
Wave Propagation in a 3-D Optical Waveguide
2003
In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.\cite{MS} The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavio…
Computational methods for optimal shakedown design of FE structures
1998
The paper concerns the optimal shakedown design of structures discretized by elastic perfectly plastic finite elements. The design problem is formulated in four alternative versions, i.e. as the search for the minimum volume design whose shakedown limit load multiplier is assigned or as the search for the maximum shakedown limit load multiplier design whose volume is assigned; both problems are approached on the grounds of the shakedown lower bound and upper bound theorems. Correspondingly four computational methods, one for each original problem, are presented. These methods consist in solving iteratively new problems which are simpler than the original ones, but expressed in such a way th…
Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures
2019
Abstract In this paper the use of the Tuned Mass Damper Inerter (TMDI) to control the response of base isolated structures under stochastic horizontal base acceleration is examined. Notably, the TMDI, recently introduced as a generalization of the classical Tuned Mass Damper, allows to achieve enhanced performance compared to the other passive vibration control devices. Thus, it represents an ideal alternative for reducing displacements of base isolated structures. To this aim, firstly a straightforward numerical approach is developed for the optimal design of this device considering a white noise base excitation. Further, a simplified analytical solution for the optimal design of TMDI para…
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2020
This work is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuska-Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, …
Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
2019
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…
Comparison of Numerical Methods in the Contrast Imaging Problem in NMR
2013
International audience; In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach, and make a first step towards global optimality. Finally, some preliminary results are given in the bi-input case.
Numerische Behandlung von Verzweigungsproblemen bei gew�hnlichen Differentialgleichungen
1979
We present a new method for the numerical solution of bifurcation problems for ordinary differential equations. It is based on a modification of the classical Ljapunov-Schmidt-theory. We transform the problem of determining the nontrivial branch bifurcating from the trivial solution into the problem of solving regular nonlinear boundary value problems, which can be treated numerically by standard methods (multiple shooting, difference methods).
Numerical Analysis of Bearing Capacity of a Ring Footing on Geogrid Reinforced Sand
2021
A ring footing is found to be of practical importance in supporting symmetrical constructions for example silos, oil storage container etc. In the present paper, numerical analysis was carried out with explicit code FLAC3D 7.0 to investigate bearing capacity of a ring footing on geogrid reinforced sand. Effects of the ratio n of its inner/outer diameter (Di/D) of a ring footing, an optimum depth to lay the geogrid layer were examined. It was found that an intersection zone was developed in soil under inner-side (aisle) of ring footing, contributing to its bearing capacity. Substantial increase of bearing capacities could be realized if ratio n of a ring footing was around 0.6. Numerical res…
A note on an overdetermined problem for the capacitary potential
2016
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.