'The Transfer Path Method for non-coincident meshes. Applications to interface problems and non-body-fitted grids' is the name of the research project led by Dr. Manuel Solano Palma that is part of the proposals selected for funding in the Regular line of the National Fund for Scientific and Technological Development, Fondecyt.  

With it, the academic of the Department of Mathematical Engineering of the Faculty of Physical and Mathematical Sciences Universidad de Concepción (UdeC) and researcher of the Center for Research in Mathematical Engineering, CI²Ma, of the UdeC seeks to improve certain methods of application of partial differential equations (PDEs) for the modeling of physical phenomena that involve interaction of fluids and solids, also incorporating the time evolution of the geometry.  

"Numerical methods for PDEs", explained the also researcher of the Center for Mathematical Modeling of the Universidad de Chile, "are usually based on a polyhedral discretization of the domain, originating a variational crime due to the approximation of the geometry that restricts the precision of the numerical scheme".  

"In the literature we can find two different approaches to overcome this limitation: adjusted methods and unadjusted methods," he detailed. "In the former, the domain discretization is adapted to the domain, which causes difficulties from the implementation point of view, especially when dealing with complicated structures or evolving domains. On the other hand, unadjusted methods are based on a background mesh in which the domain of interest is immersed, and the main challenge is to incorporate the boundary conditions on the computational boundary, which does not necessarily coincide with the real boundary".  

"During the last decade", Solano deepened, "unadjusted methods have been intensively developed, especially the CutFEM method, the Shifted Boundary Method and the Transfer Path Method, which has been developed by me. The main goal of the project is to extend the applicability of the Transfer Path Method in two contexts: non-coincident triangulations and evolving domains with non-domain-matched meshes. For just over 10 years, I have been leading the development of such numerical methods and training students in the discipline".

Track record of awards 

This is the fourth consecutive project of Dr. Solano, which accesses Fondecyt funding: one Initiation (2013-2014), and three Regular (2016-2019, 2020-2023 and 2024-2027). "In all of them I have been Principal Investigator.  It motivates me that international evaluators recognize the contribution of my work to the discipline", highlighted the researcher and adds that "it is very competitive to award this type of competitions, since there are many people who apply with excellent projects and very good academic background". 

"This recognition of Dr. Solano's trajectory is excellent news for our center, especially knowing how competitive it is to be awarded a Fondecyt project nowadays," said the director of CI²Ma, Dr. Rodolfo Araya Durán. "This award, together with his track record of awards, demonstrates the great academic quality of Dr. Solano. We wish him every success in the development of this new project," he added.