All the receivers in the area of Numerical Analysis of PDEs
“Just today, Friday, December 29, when the exact 25th anniversary of the official creation of the Department of Mathematical Engineering, DIM, of Universidad de Concepción, is holding, a very important news for the Center for Research in Mathematical Engineering, CI²MA, and consequently for the DIM, has been announced”, Gabriel Gatica, director of CI²MA, said about the recent divulgation of results of nominations for the Regular Contest 2018 of National Fund for Scientific and Technological Development, Fondecyt. In this opportunity, funding was awarded to seven current CI²MA researchers to continue their scientific activities, four of them previously graduated from the Doctoral Programe in Applied Sciences with a minor in Mathematical Engineering directed by Raimund Bürger. Gatica also stresses that all the researchers who will receive this state financial support belong to the area of Numerical Analysis of Partial Differential Equations, NA of PDEs. “Precisely the one that Professor Hermann Alder created, back in the 1980s, who, later on, together with our colleagues Hubert Mennickent, Walter Stuven and the speaker, founded the DIM”. Two other former students of the aforementioned program, Erwin Hernandez from UTFSM, in NA of PDEs, and Ruben Lopez from UTA, in Optimization, also won Fondecyt projects this time.
Among the benefited researchers from CI²MA, six of them accomplish the role of principal investigator in their respective projects: Jessika Camaño, Leonardo Figueroa, Luis Gatica, David Mora, Mauricio Sepúlveda and Luis Miguel Villada, whereas Gabriel Gatica himself acts as co-investigator in the project entitled: Computational Micromechanics of the Lung Parenchyma, which is led by Daniel Hurtado, researcher from Pontificia Universidad Católica de Chile, PUC, with a duration of three years until March 2021.
In turn, Orthogonal Polynomials and Fast Spectral Methods in Special Geometries is the name of the project led by Leonardo Figueroa, academician from DIM at UdeC, which will last two years. “This project is about Approximation Theory, which lies at the foundation of the Numerical Analysis of Partial Differential Equations (PDE). In rough terms, I will study how does the quality of the polynomial approximation of functions depend on the regularity (smoothness) of the former”, Figueroa said. On the other hand, Mauricio Sepúlveda, also an academician at the DIM, will approach the project: Stability Analysis of Numerical Methods for Damped Dispersive Equations. "The main objective of this project is to study the stability through damping, reaching the critical and supercritical cases for several dispersive equations modelling the shallow water waves (KdV equations) and the nonlinear Schrödinger equations. In turn, we are interested in the numerical approximation of the solution of these equations to observe the explosive or highly oscillatory asymptotic behavior, and to find out what type of damping is necessary to avoid this explosion in the solution", Sepúlveda explains.
Furthermore, Jessika Camaño, an academician from the Department of Applied Mathematics and Physics at Universidad Católica de la Santísima Concepción, UCSC, and an external associate researcher at CI²MA, was granted funds for her project entitled: Finite Element Methods for Fluid Dynamics, Eigenvalue Problems and Some Related Problems, which will be performed in a period of four years. His colleague at UCSC, who is also an external associate researcher at CI²MA, Luis Gatica, will finance during four years the project: Further Applications of Hybridizable Discontinuous Galerkin Methods for Linear and Nonlinear Problems in Continuum Mechanics. “This research project is about the design and analysis of high-order discretizations using the discontinuous hybridizable Galerkin (HDG) method for the numerical solution of linear and nonlinear problems arising from fluid dynamics and solids mechanics”, he said.
At the same time, David Mora, external research associate at CI²MA and academician at the Department of Mathematics at Universidad del Bío-Bío, was awarded executable funds for 4 years (March 2018 - March 2022) to finance the project: Development and Mathematical Analysis of Virtual Element Methods to Linear and Nonlinear Problems in Continuum Mechanics and Related Applications. “The main objective of this initiative is the development and analysis of different virtual elements methods (VEM) to solve problems arising from solid and fluid mechanics. For the development of the project, the participation of Master's and doctoral thesis students, as well as international collaboration through stays in Chile and abroad, and dissemination activities, among other activities, will be considered”, Mora explained. In the same academic unit of Mora, Luis Miguel Villada, external associate researcher at CI²MA, will lead the four years long project entitled: Modelling and Numerical analysis for Non-local Systems of Conservation Laws, which "aims to develop efficient numerical schemes and apply them to problems modeled by non-linear and non-local systems of partial differential equations, in particular the so-called Conservation Laws and the convection-diffusion-reaction type, with applications arising from real physical phenomena, such as sedimentation patterns, vehicular traffic, crowd dynamics, population dynamics, mathematical biology and epidemiology", Villada emphasizes.