CENTRE

CIMNE - Centre Internacional de Mètodes Numèrics a l'Enginyeria

ADDRESS

C/ Gran Capità, s/n, Campus Nord UPC, Ed. C1, 08034 Barcelona, Barcelona

AREA OF KNOWLEDGE

Physical Sciences, Mathematics and Engineering Panel

GROUP OF DISCIPLINES

Theoretical and Applied Mathematics, Computer Sciences and IT

GROUP LEADER

Prof. Pedro Díez

pedro.diez@upc.edu

RESEARCH PROJECT/RESEARCH GROUP

Credible high-fidelity data-driven models research group

https://www.lacan.upc.edu/Credible

POSITION DESCRIPTION

-Research Project / Research Group Description:

This project lies in the interface of two research fields with very high impact and strong interdisciplinarity: mathematical modelling and simulation with applications to mechanobiology and tissue engineering.

Architectured materials are particularly well suited to be used as scaffolds for cell cultures, aiming at obtaining in-vitro biological tissues. In this context, predictive tools are required to design the protocols (structural characteristics of the scaffold and loading conditions all along the cell growing process) mimicking the in-vivo physiological environment. More particularly, the optimal design of the unit structural cell characterizing the metamaterial (by periodic repetition) is seen as an inverse problem providing the design parameters that produce the desired mechanical response. Thus, the resulting bulk material that can be eventually manufactured with micro 3D printing technologies, is optimally suited to support cell growth.

An explicit parametric solution of the forward problem is a key factor to easily solve the inverse problem. Nevertheless, the computational complexity of the forward analysis blows up with the number of parametric dimensions. The Proper Generalized Decomposition (PGD) is proposed here in order to overcome this curse of dimensionality. PGD provides explicit solutions of parametric models also named as Computational Vademecums.

Moreover, sensitivities with respect to parameters are easily computable. Thus, the optimal design problem (the inverse problem) is straightforwardly solved as a real-time post-processing of the PGD Computational Vademecum.

When simulating the mechanical response of the scaffolds, one has to face the mathematical challenge of extending the scope of the standard PGD formulation (devised for parametric PDEs) such that it is able to deal with nonlinear algebraic systems of equations.

-Job position description:

This interdisciplinary project lies at the interface of computational engineering, mathematical modeling and material sciences, with application to energy harvesting technologies.

The PhD thesis will be developed within the Credible high-fidelity data-driven models group of Laboratori de Càlcul Numèric (LaCàN) at Universitat Politècnica de Catalunya-CIMNE. This research group is active on different topics related to the development of innovative numerical methods in computational mechanics, computational fluid dynamics and computational electromagnetics, and their application to industrial problems. The candidate will integrate a very dynamic research team of recognized experts under the supervision of Prof. P. Díez and Dr. A. García González. He/she will have access to state-of-the-art research and computing facilities. He/she is expected to develop high-quality research in applied mathematics and computational engineering applied to the thriving field of metamaterials design for bioengineering, to attend advanced training courses, to present the obtained results in international conferences and to contribute to the writing of technical reports and scientific articles for high-impact international journals.

Requirements:

• Strong undergraduate and MS degree (or equivalent) record in mathematics, engineering or related discipline.
• Good written and oral communication skills in English.
• Good knowledge of numerical methods for the approximation of partial differential equations (in particular, the finite element method).
• Knowledge of computational solid mechanics is required.
• Experience in multiscale models is not compulsory but will be considered an advantage.
• Advanced programming skills (Matlab and/or Fortran).
• Curiosity and commitment to develop high-quality research.
• Hard-working and enthusiastic attitude towards research and innovation.
• Flexibility and ability to work in an interdisciplinary team.

FURTHER INFORMATION

Hosts La Caixa Fellowship