Research
Research Interests
computational modelling and advanced numerical methods for engineering and applied sciences.
Thin-shell flexoelectric metamaterials
Automatic data-driven collective variables identification
Biomechanics and multiscale mechanobiological modeling of cerebral arteries
Cerebral aneurysm morphometry, biomechanics descriptors and rupture risk assessment
Multiscale modeling and simulation of ultrasonic analysis for additive manufacturing enhancement
Previous topics
Maximum entropy approximants [Marino Arroyo, LME beta-Matlab code, CME-Matlab code]
Quantitative analysis of the Euglenoid movement [Movie 1 Movie 2]
Automatic identification of collective variables in biomolecules
Nonlinear model reduction for finite solid dynamics
Point-set manifold processing for computational mechanics
In many applications, one would like to perform calculations on smooth manifolds of small dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. We approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients:
partitioning of the point set into subregions of trivial topology,
the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques,
the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and
patching together the local representations by means of a partition of unity.
