Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on $3n$ variables where $n$ stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed many...

This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is much cheaper...

Many problems in quantum
chemistry deal with the computation of fundamental or excited states of
molecules and lead to the resolution of eigenvalue problems. One of the
major difficulties in these computations lies in the very large
dimension of the systems to be solved. Indeed these eigenfunctions depend
on variables where stands for the number of particles
(electrons and/or nucleari) in the molecule. In order to diminish the size
of the systems to be solved, the chemists have proposed many
interesting...

This paper is concerned with the coupling of two models for the
propagation of particles in scattering media. The first model is a
linear transport equation of Boltzmann type posed in the phase space
(position and velocity). It accurately describes the physics but is
very expensive to solve. The second model is a diffusion equation
posed in the physical space. It is only valid in areas of high
scattering, weak absorption, and smooth physical coefficients, but
its numerical solution is...

We study the well-posedness of an unsteady fluid-structure interaction problem.
We consider a viscous incompressible flow, which is modelled by the
Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid
domain depends on time and is defined by the position of the structure, itself resulting
from a stress distribution coming from the fluid. The problem is then
nonlinear and the equations we deal with are coupled. We prove its local
solvability in time through two...

In this article, we provide error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the electronic...

The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...

The paper deals with the application of a non-conforming domain
decomposition method
to the problem of the computation of induced currents in electric engines
with moving conductors.
The is considered as a quasi-static
approximation of Maxwell
equations and we study its two-dimensional formulation with either the
modified magnetic vector potential or the magnetic field as primary variable.
Two discretizations are proposed, the first one based on curved finite
elements
and the second one based...

In this article, we provide error estimates for the spectral and
pseudospectral Fourier (also called planewave) discretizations of the
periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral
discretization of the periodic Kohn-Sham
model, within the local density approximation (LDA). These models
allow to compute approximations of the electronic ground state energy and density
of molecular systems in the condensed phase. The TFW model is strictly
convex with respect to the electronic...

The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators are...

In error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup
stability constants is essential. In [Huynh ,
(2007) 473–478], the authors presented an efficient
method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to
minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters...

Linear Force-free (or Beltrami) fields are three-components
divergence-free fields solutions of the equation =
,
where is a real number.
Such fields appear in many branches of physics like astrophysics,
fluid mechanics, electromagnetics and plasma physics. In this paper,
we deal with some related boundary value problems
in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.

The reduced basis element method is a new approach for approximating
the solution of problems described by partial differential equations.
The method takes its roots in domain decomposition methods and
reduced basis discretizations. The basic idea is to first decompose
the computational domain into a series of subdomains that are deformations
of a few reference domains (or generic computational parts).
Associated with each reference domain are precomputed solutions
corresponding to the same...

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...

In this paper, we extend the reduced-basis approximations developed earlier for elliptic and parabolic partial differential equations with parameter
dependence to problems involving (a) dependence on the
parameter, and (b) dependence on the field variable.
The method replaces the nonaffine and nonlinear terms with a coefficient function approximation which then permits an efficient offline-online computational
decomposition. We first review the coefficient function approximation procedure:...

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