相关论文: A Bloch decomposition-based stochastic Galerkin me…

We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…

A space-time Trefftz discontinuous Galerkin method for the Schr\"odinger equation with piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz methods, trial and test spaces are spanned by non-polynomial…

We introduce a space-time finite element method for the linear time-dependent Schr\"odinger equation with Dirichlet conditions in a bounded Lipschitz domain. The proposed discretization scheme is based on a space-time variational…

In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin method for the linear semiconductor Boltzmann equation under diffusive scaling and with random inputs from an anisotropic collision kernel and the…

This paper is devoted to the derivation of a pleasingly parallel Galerkin method for the time-independent $N$-body Schr\"odinger equation, and its time-dependent version modeling molecules subject to an external electric field. In this…

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…

We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time…

We study a numerical reconstruction strategy for the potential in the fractional Calder\'on problem from a single partial exterior measurement. The forward model is the fractional Schr\"odinger equation in a bounded domain, with prescribed…

We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…

We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schr\"odinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete…

We consider the stochastic nonlinear Schroedinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We…

Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…

The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) particle {method} for collisional kinetic models of plasmas under…

In this paper we present a numerical method for the Boltzmann equation. It is a spectral discretization in the velocity and a discontinuous Galerkin discretization in physical space. To obtain uniform approximation properties in the mach…

This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution.…

We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singu- lar nature of the solution, the standard gPC-SG methods may suffer from a poor or…

In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…

In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…

Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…

Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from…