Researchers

His work has been focused on the analysis of numerical methods (semi-analytical and FEM-based methods), including applications to geophysics, acoustics, and electromagnetism. Right now he is particularly interested in Discontinuous Petrov-Galerkin (DPG) methods and the development of residual minimization algorithms for variational problems in Banach spaces. The working network of Professor Muga includes world-class research centers such as the Institute for Computational Engineering and Sciences (ICES) - USA, the Basque Center for Applied Mathematics (BCAM) - Spain, and the University of Nottingham - UK.

He is primarily interested in numerical analysis, scientific computing, and mathematical modeling. His research endeavors are centered on developing and analyzing residual minimization-based numerical methods to solve complex Partial Differential Equations (PDEs). These methodologies integrate various state-of-the-art approaches such as Finite Element (FE), Discontinuous Galerkin (DG), Hybridizable Discontinuous Galerkin (HDG), Minimum-Residual (MinRes), and Variational Physics-Informed Neural Networks (VPINNs) methods. Professor Rojas' professional network includes world-class research centers like the Basque Center for Applied Mathematics (BCAM-Spain), the University of Nottingham (UK), Monash University (Australia), and the AGH University of Science and Technology (Poland).

Her interests are developing accurate, stable, and efficient numerical methods for solving real-world problems based on theoretical foundations. In particular, she is interested in developing space-time methods to exploit adaptive space-time mesh-refinement techniques. Among these methods, she has worked in space-time Tent-pitching techniques, space-time Petrov-Galerkin methods, and space-time discontinuous Petrov-Galerkin methods for the Schrodinger and wave equations. She has experience developing and contributing to finite element and finite volume software libraries in different programming languages: C++, Fortran, Python, and Matlab. Her collaboration network includes researchers at Lawrence Livermore National Lab, Portland State University, US. Geological Survey, and the Basque Center for Applied Mathematics.

Her research areas are numerical solutions of partial differential equations and applied mathematics. She has employed continuous finite element methods and hybridizable discontinuous Galerkin methods to analyze linear elasticity problems defined on unbounded domains, reaction-diffusion problems used to model hydrocarbon combustion, and problems coming from modeling solar cells' energy generation. Since 2020 she has carried out research projects as a collaborator of the Colombian research group Computación Científica of the Universidad Nacional de Colombia, sede Medellín.