My field of expertise covers various aspects of Applied Mathematics
including Partial Differential Equations (PDE), Numerical Analysis, Control and Data Sciences. These interconnected fields have as goal the modelling, analysis, computer simulation and control and design of natural phenomena and engineering processes arising in several contexts of R+D+i.
- Analysis of Partial Differential Equations (PDE)
- Control of diffusion models arising in Biology and Social Sciences
- Modeling and control of multi-agent systems
- Hyperbolic models arising in traffic flow and energy transport
- Fractional PDE
- Optimal design in Material Sciences
- Micro-macro limit processes
- Machine Learning
- The interplay between discrete and continuous modelling in design and control
- The emergence of turnpike phenomena in long-time horizons
- Inversion and parameter identification
- Development of new computation tools and software
- Waves in heterogeneous media: discrete and continuous
- Optimal placement of sensors and actuators
Interactions with Industry
I had also the opportunity to work and run a numerous research projects in close collaboration with industry:
Aeronautics optimal design
In collaboration with my former PhD student Francisco Palacios (The Boeing Company, Long Beach, CA) I developed an intensive research agenda in aeronautic optimal design and numerical analysis with connections with industry and in particular the Airbus Consortium. This research has lead to the development of the new software Stanford University Unstructured – SU2
I contributed to launch the research group in Computational Fluid Dynamics of Baltogar company.
I was the PI of a joint industrial research project with the Arteche Group to develop computational software for parameter identification of electrical networks from onsite measurements.
Research & Innovation
I had the honour of collaborating with Eibar City Hall in the development of dissemination activities on Research and Innovation.