MATHICSE Technical Report : On heterogeneous coupling of multiscale methods for problems with and without scale separation
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The objective of this work is to develop a numerical framework to perform rapid and reliable simulations for solving parametric problems in domains represented by networks and to extend the classical reduced basis method. Aimed at this scope, we propose tw ...
In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...
An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Par ...
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 ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
In this paper, a mixed numerical-experimental identification procedure for characterising the storage and loss properties in sandwich structures with a relatively stiff core is developed. At the computational level, the proposed method is based upon an ori ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupl ...
Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computat ...
A novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated ...