Liliana Camargo collaborates with Professor Manuel Solano in numerical methods for PDEs
Between August 18 and November 14, the Colombian student Liliana Camargo visited the Research Center in Mathematical Engineering, CI²MA, of Universidad de Concepción. She was born in Medellín and obtained a master's degree in Mathematical Sciences at Universidad del Valle, located in Cali. She is currently a thesis student of the Ph.D Program in Mathematical Sciences at Universidad Nacional de Colombia, Medellín campus.
“Numerical solution of partial differential equations is the line of research I am interested in. The research stay was organized by my doctoral thesis advisers, who know the extensive experience of the CI²MA researchers in the topics we are currently working on”, the visiting Ph.D. student says.
Professor Manuel Solano explained that “Liliana’s advisors in Colombia are Mauricio Osorio and Bibiana López. Mauricio has visited CI²MA before. Bibiana was a student of our PhD program in Applied Sciences with a minor in Mathematical Engineering, and Rodolfo Rodríguez was her advisor. I have met Mauricio and Bibiana before in some national conferences. On their last visit to CI²MA, in 2014, they were studying HDG methods, in which I specialized in my doctorate. They asked me about computational aspects of these methods. Later, at the beginning of this year, they asked me to be Liliana's international advisor, since they were interested on applying HDG methods to Maxwell equations that model solar cells. That's why Liliana came to visit me and work on these methods”.
Concerning the expectations she had about her stay in Concepción, Liliana explains that “certainly, the experience during my time at the research center met my expectations. The goals were successfully achieved and we have planned future work to continue with the research”. She specifies that “main objective (of her stay) was to address the first step of the project: to implement the HDG method in 3D applied to Maxwell’s equations in multi-layered domains and validate numerically the order of convergence of the method. Professor Solano emphasizes that “Liliana worked hard and made good progress. In addition to the implementation of the methods, we showed that the scheme is well-posed under certain assumptions and made progress in the error analysis of the method. We are preparing a paper based on this work”.