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6 papers
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…
A parabolic local problem with exponential decay of the resonance error for numerical homogenization
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equatio…
Ensemble Kalman filter for multiscale inverse problems
Assyr Abdulle, Giacomo Garegnani, Andrea Zanoni
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on nume…
Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales
Assyr Abdulle, Timothée Pouchon
A family of effective equations for wave propagation in periodic media for arbitrary timescales , where is the period of the tensor…