Zobrazeno 1 - 10
of 375
pro vyhledávání: '"Abdulle, Assyr"'
Optimal explicit stabilized postprocessed $\tau$-leap method for the simulation of chemical kinetics
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In
Externí odkaz:
http://arxiv.org/abs/2106.09339
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of t
Externí odkaz:
http://arxiv.org/abs/2104.10587
Autor:
Abdulle, Assyr, Garegnani, Giacomo
Publikováno v:
Comput. Methods Appl. Mech. Engrg. 384 (2021) 113961
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduc
Externí odkaz:
http://arxiv.org/abs/2103.06204
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully d
Externí odkaz:
http://arxiv.org/abs/2102.03209
Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by very few "fa
Externí odkaz:
http://arxiv.org/abs/2010.15193
Autor:
Abdulle, Assyr, Garegnani, Giacomo, Pavliotis, Grigorios A., Stuart, Andrew M., Zanoni, Andrea
We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift c
Externí odkaz:
http://arxiv.org/abs/2009.13457
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 requires solvi
Externí odkaz:
http://arxiv.org/abs/2007.10828
Stabilized Runge-Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge-Kutta
Externí odkaz:
http://arxiv.org/abs/2006.00744
We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subd
Externí odkaz:
http://arxiv.org/abs/2004.07148
An explicit stabilized additive Runge-Kutta scheme is proposed. The method is based on a splitting of the problem in severely stiff and mildly stiff subproblems, which are then independently solved using a Runge-Kutta-Chebyshev scheme. The number of
Externí odkaz:
http://arxiv.org/abs/2003.03154