This project is an ambitious research program which takes into account
fundamental theoretical aspects as well as their interaction with computational methods in two research topics. A comprehensive
list of research topics which we are planning to consider is as follows:
Higher order macro coefficients in periodic structure.
We
propose to contribute to the understanding of higher order macro coefficients in higher dimensions
useful in the study of finer aspects of oscillations for different periodic materials in homogenization
theory. We study new phenomena that appear with the decrease of scale and we search important
properties of them, as for instance, the upper and lower bounds with respect to the microstructure.
We first focus on laminated materials, then on spherical Hashin structures,
finishing with arbitrary periodic micro-geometry. In a
longer term, we want to find some extensions of Bloch
waves theory suitable for study general non-periodic
microstructures.
Numerical analysis in non-linear fluid-structure interactions.
The general objective of the second research field is to
advance in understanding of numerical methods for
simulating the swimming of several aquatic organisms,
where the deformation produced by their muscles changes
the density. We propose to conceive stable and accurate
numerical schemes for different types of bodies immersed
in incompressible viscous fluid for bounded domains. We
start by studying rigid solids of arbitrary shape and we
continue with deformable bodies. In a longer term, we
want to examine the convergence and stability properties
for numerical algorithms modeling the human vascular
system.
