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Displaying 521 –
540 of
604
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
In this paper, we present numerical methods
for the determination of solitons, that consist in spatially localized
stationary states of nonlinear scalar equations or coupled systems
arising in nonlinear optics.
We first use the well-known shooting method in order to find
excited states (characterized by the number k of nodes) for the
classical nonlinear Schrödinger equation. Asymptotics can then
be derived in the limits of either large k are large nonlinear
exponents σ.
In a second part, we compute...
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null...
We consider a special configuration of vorticity that consists of a pair of
externally tangent circular vortex sheets, each having a circularly symmetric core
of bounded vorticity concentric to the sheet, and each core precisely balancing the
vorticity mass of the sheet. This configuration is a stationary weak solution of the
2D incompressible Euler equations. We propose to perform numerical experiments to verify
that certain approximations of this flow configuration converge to a non-stationary...
Two mathematical models of railway track oscillations are compared on the basis of numerical experiments.
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
We study in this paper some numerical schemes for hyperbolic systems
with unilateral constraint. In particular, we deal with the scalar case, the isentropic
gas dynamics system and the full-gas dynamics system.
We prove the convergence of the scheme to an entropy solution
of the isentropic
gas dynamics with unilateral constraint on the density and mass loss.
We also study the non-trivial steady states of the system.
In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we extend the procedure of [D. Gallistl, P. Henning, B. Verfürth, Numerical homogenization for H(curl)-problems,...
These notes give a state of the art of numerical homogenization methods for linear
elliptic equations. The guideline of these notes is analysis. Most of the numerical
homogenization methods can be seen as (more or less different) discretizations of the same
family of continuous approximate problems, which H-converges to the homogenized problem.
Likewise numerical correctors may also be interpreted as approximations of Tartar’s
correctors. Hence the...
In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...
The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach...
In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.
Currently displaying 521 –
540 of
604