相关论文: Quantitative version of the Kipnis-Varadhan theore…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.
We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…
Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to…
In the present contribution we establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy…
Since its formulation in the late 1940s, the Feynman-Kac formula has proven to be an effective tool for both theoretical reformulations and practical simulations of differential equations. The link it establishes between such equations and…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
General elliptic equations with spatially discontinuous diffusion coefficients may be used as a simplified model for subsurface flow in heterogeneous or fractured porous media. In such a model, data sparsity and measurement errors are often…
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally…
It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic…
We develop a quantitative theory of stochastic homogenization for linear, uniformly parabolic equations with coefficients depending on space and time. Inspired by recent works in the elliptic setting, our analysis is focused on certain…
The aim of this paper is to obtain convergence in mean in the uniform topology of piecewise linear approximations of Stochastic Differential Equations (SDEs) with $C^1$ drift and $C^2$ diffusion coefficients with uniformly bounded…
We present an introduction to periodic and stochastic homogenization of ellip- tic partial differential equations. The first part is concerned with the qualitative theory, which we present for equations with periodic and random coefficients…
This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is built using a method designed to exploit…
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…