The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive to round-off...

We study a free energy computation procedure, introduced in
[Darve and Pohorille,
(2001) 9169–9183; Hénin and Chipot,
(2004) 2904–2914], which relies on the long-time
behavior of a nonlinear stochastic
differential equation. This nonlinearity comes from a conditional
expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to
this equation has been proved
in [Lelièvre ,
(2008) 1155–1181],...

In this article,
we analyze the stability of various numerical schemes for differential models of viscoelastic fluids.
More precisely, we consider the prototypical Oldroyd-B model,
for which a dissipation holds,
and we show under which assumptions such a dissipation is also satisfied for the numerical scheme.
Among the numerical schemes we analyze,
we consider some discretizations based on the of the Oldroyd-B system proposed
by Fattal and Kupferman in [
(2004) 281–285],...

We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni,...

The Diffusion Monte Carlo method is devoted to the computation of
electronic ground-state energies of molecules. In this paper, we focus on
implementations of this method which consist in exploring the
configuration space with a fixed number of random walkers evolving
according to a stochastic differential equation discretized in time. We
allow stochastic reconfigurations of the walkers to reduce the
discrepancy between the weights that they carry. On a simple
one-dimensional example, we prove...

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