A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh re ...
A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...
This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...
We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapid ...
In this paper, we propose a new approach for sampling from probability measures in, possibly, high-dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the invariant measure of t ...
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 simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chains) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this ...
The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients sufer from the so-called resonance error, originating from a mismatch between the tr ...
This paper gives numerical experiments for the Finite Element Heterogeneous Multiscale Method applied to problems in linear elasticity, which has been analyzed in [A. Abdulle, Math. Models Methods Appl. Sci. 16, 2006]. The main results for the FE-HMM a pri ...
We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...
Explicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods to avoid the severe time-step restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper we provide a fully discrete ...
