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Optimal explicit stabilized postprocessed -leap method for the simulation of chemical kinetics
Assyr Abdulle, Lia Gander, Giacomo Rosilho de Souza
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge…
A probabilistic finite element method based on random meshes: Error estimators and Bayesian inverse problems
Assyr Abdulle, Giacomo Garegnani
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, whic…
Explicit stabilized multirate method for stiff stochastic differential equations
Assyr Abdulle, Giacomo Rosilho de Souza
Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loo…
Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homog…
Instabilities and order reduction phenomenon of an interpolation based multirate Runge-Kutta-Chebyshev method
Assyr Abdulle, Giacomo Rosilho de Souza
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 ind…
An elliptic local problem with exponential decay of the resonance error for numerical homogenization
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the h…