The "Numerical Linear Algebra of High Performance for Partial Differential Equations" course -dictated the Spanish academic Pep Mulet, at the Center for Research in Mathematical Engineering, CI²MA, of the Universidad de Concepción, during January- was part of the activities of the Summer School 2017 of the UdeC and gathered undergraduate students of advanced courses in the Civil Engineering Mathematics, and postgraduate, both the PhD in Applied Sciences with mention in Mathematical Engineering of that house of studies, and the Master in Mathematics of The Universidad del Bío-Bío.

In terms of the contents of the course, managed by Raimund Bürger -investigator of CI²MA and director of this doctoral program - these covered some numerical linear algebra techniques to solve problems with partial differential equations (PDE) elliptic or convection-diffusion in systems High performance computing. "In the first stage I presented the contents and then there were four practice sessions to apply them in programs. The problems of linear algebra are like the equations that made us develop in school, but much more complex. This is because problems appear in many scientific fields, especially those interested in those who collaborate with CI²MA, which present unknowns and equations that we have to solve efficiently, that is to say can be put in the memory of the computer, And that it can resolve them within a reasonable time. This is the concept of high performance: to make it fast and fit into the memory of computers that is being used", explains Pep Mulet who is a member of the faculty of the Departamento de Matemáticas of the Universitat de València, Spain.

These contents enrich the knowledge of the researchers and students of our Center because, as the Iberian academic explains, in their work, they very regularly must face "problems of this type and it is important that they know what to do. For example, many people use software like MatLab, but this program is not able to solve very complex problems, so you should look for other solutions. What we reviewed in the course is a knowledge that is very transversal and basic for those who work in these areas, in the problems of interest of this Center", explains Professor Mulet, who since 2012 has been teaching other courses during the summer In the CI²MA.

Professor Mulet is an expert in numerical methods for nonlinear PDEs. Since 2008 he collaborates with Raimund Bürger on numerical methods for systems of conservation laws and related problems. As a result of this collaboration, they already have more than ten co-signed publications, as well as two co-directed doctoral theses and two others in process. Mulet's stay at CI²MA in January 2017 was partially funded by the Dirección de Postgrado of the UdeC and Conicyt's Atracción e Inserción Program (PAI), Short Stay Mode (MEC), contest 2015. This project contemplates, in addition, resources to finance passages for a memorist or thesis that wishes to make a stay in Spain with Professor Mulet.