Fernando A Morales

The Interaction Between PDE and Graphs in Multiscale Modeling

In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in

NOTES ON THE NONLINEAR DEPENDENCE OF A MULTISCALE COUPLED SYSTEM WITH RESPECT TO THE INTERFACE

\mathbb{R}^{2}

The narrow fracture approximation by channeled flow

or

Interface approximation of Darcy flow in a narrow channel

\mathbb{R}^{3}

A Darcy–Brinkman model of fractures in porous media☆

. The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described by partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.

On the generation of bipartite grids with controlled regularity for 2-D and 3-D simply connected domains

This work studies the dependence of the solution with respect to interface geometric perturbations, in a multiscaled coupled Darcy flow system in direct variational formulation. A set of admissible perturbation functions and a sense of convergence is presented, as well as sufficient conditions on the forcing terms, in order to conclude strong convergence statements. For the rate of convergence of the solutions we start solving completely the one dimensional case, using orthogonal decompositions on the appropriate subspaces. Finally, the rate of convergence question is analyzed in a simple multi dimensional setting, by studying the nonlinear operators introduced due to the geometric perturbations.