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Mathematical Design, Modeling and Simulations - MATHDES

The work of the group is mainly devoted to the analysis of modern numerical methods (such as the finite element method (FEM) and the finite difference method (FDM)) and their applications to various real-life problems.

We are addressing both classical FEM and FDM issues (convergence, superconvergence, mesh generation, preservation of qualitative properties of solutions, etc. with emphasize on high-dimensional problems and interconnections with discrete and computational geometry) and some recent trends in numerical analysis, such as reliable a posteriori error estimates and efficient mesh adaptivity procedures for stationary and time-dependent problems. In addition, we develop rigorous computational methods to prove existence of stationary solutions, periodic orbits and connecting orbits for system of ODEs like the Lorenz system and PDEs like the Kuramoto-Sivashinsky equation.

In terms of applications and implementation, we are dealing with problems related to heat conduction, wave propagation, modeling of fuel cells, computational fluid dynamics, medical image registration and segmentation, and chaotic dynamical systems.

PIXIL: Pyrenees Imaging eXperience: an InternationaL network

Duration: 01/09/2019 - 30/04/2022


The PIXIL project is a transnational and multidisciplinary scientific and technological cooperation. Its main goal is to develop the most advanced tools to analyze the Earths subsurface, with a special focus on fostering the uptake of geothermal energy in the region. The project will contribute to making the trans-Pyrenean area a technology hub in subsoil characterization within two years. Its success is expected to boost the wealth and creation of jobs related to the generation and management of underground natural resources in the area.

PIXIL has a strong research profile where scientific collaboration between institutions prevails. The project outcomes will result in advances in the three disciplines that make up modern geophysical imaging: Geophysics, Applied Mathematics and Computing.

Specific objectives:

Generate a cross-border R&D exchange network in the field of geophysical imaging for the characterization of the subsoil, allowing the region to establish itself as a world leader in the field. Promote our developments to other communities that use waves to study complex or hidden media. Generate free high-performance computing (HPC) software prototypes for industrial problems in the field of geophysical imaging, with a particular focus on geothermal energy. Such software will be validated by companies in the sector (some of which are associate partners of PIXIL) and will be the seed of future competitive products. Promote the development and cost reduction of geothermal energy in the region, as well as to gather promoters of these technologies and potential public and private clients in dissemination events. Both sides of the border will be targeted in order to expand the use of such technology and expose successful use cases in the region.

FEDER reference
SP: Fondo de Desarrollo Regional (FEDER)
EN: European Regional Development Fund (ERDF)
Link to EU policy


Design, analyze, implement and optimize numerical schemes for mathematical models arising from real-life applications.
PDE models, numerical analysis, reliable numerical modelling, error control, mesh generation and adaptivity, shape analysis, rigorous computations, interval arithmetic.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del País Vasco (UPV/EHU) Ayuntamiento de Bilbao - Bilboko Udala