Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
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Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulatio ...
In this work we compare different families of nested quadrature points, i.e. the classic Clenshaw-Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests th ...
The computation of the reachable set of states of a given dynamic system is an important step to verify its safety during operation. There are different methods of computing reachable sets, namely interval integration, capture basin, methods involving the ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
We introduce a new family of explicit integrators for stiff Ito stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from th ...
This paper is concerned with the initial-boundary value problems of scalar transport equations with uncertain transport velocities. It was demonstrated in our earlier works that regularity of the exact solutions in the random spaces (or the parametric spac ...
Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
An efficient and accurate method, based on the weighted averages (WA) extrapolation technique, is presented for the evaluation of semi-infinite range integrals involving products of Bessel functions of arbitrary order. The method requires splitting the int ...
Institute of Electrical and Electronics Engineers2013
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...