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Our research group on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)" is composed of:
- Five professors working at UPV/EHU, and
- Four Ph.D. students.
Additionally, we collaborate with over 20 professors at different institutions worldwide.

Our group has three key objectives:

a) To develop research on the numerical simulation of ordinary and partial differential equations as well as optimization problems.
b) To transfer this mathematical knowledge to the industry, and
c) To train new researchers in the area.

Our work is divided mainly into three areas of knowledge:

1) Mathematics, used to develop advanced numerical methods,
2) Scientific Computing, used to implement efficiently those numerical methods, and
3) Engineering, used to understand and solve real-world industry problems.


We focus on the following research areas:

Development of highly accurate and robust numerical methods for solving via computer simulations challenging multiphysics applications. These applications arise in different areas of knowledge, including medicine, bio-technology, nano-technology and a variety of engineering applications such as Petroleum Engineering.
Our main simulation technology is based on a high-order Finite Element method, where we employ self-adaptive goal-oriented grids to obtain superior accuracy and approximate the error in a given (user-prescribed) quantity of interest. Depending upon the application, we also combine the Finite Element method with other numerical techniques, such as a Fourier transform in a non-orthogonal system of coordinates (for borehole simulations in deviated wells), and a discontinuous Petrov-Galerkin method (for minimizing the dispersion error in acoustic applications).

Advanced numerical methods for time integration of differential equations. This line of research seeks to analyze, design, and implement numerical integration methods for time evolution problems governed by differential equations whose solution is cannot be obtained using conventional packages based on multistep methods nor Runge-Kutta schemes. We make an special emphasis on geometric integration methods and, in particular, methods for conservative problems. We are also interested on highly oscillatory problems. Among the application areas, we include classical mechanics, quantum mechanics, astrophysics, and molecular dynamics.

Applied Optimization Problems. The main objective is to carry out projects with companies, making technology transfer in the fields of Optimization, Simulation, Operational Research, and Statistics.
We have participated in projects with companies like CESPA, Metro Bilbao, EuskoTren, LVEF, Eroski, and Vicinay Cadenas. We conducted several projects such as planning and allocation of working hours (EuskoTren), forecasts in electricity consumption (Tecnalia), and improvement of the manufacturing process of mega- and tera- chains (Vicinay).


   Figures: Illustration of a Butt Welding process.