Numerical Analysis / Análisis Numérico
We are mainly interested in the development and analysis of numerical algorithms to approximate solutions of partial differential equations. Our group is focused on three main goals:
DEVELOPMENT. We investigate novel numerical methods that, for certain criteria, improve the existing methods and enable an efficient computational implementation.
ANALYSIS. We use mathematical analysis to give theoretical proofs about the properties and performance of numerical methods.
IMPLEMENTATION. We contribute and develope libraries to obtain numerical evidence about the performance of numerical methods. Such libraries may be used to do academic experiments or even high-performance computing.
IGNACIO MUGA. 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.
PAULINA SEPÚLVEDA. Her interests are in developing accurate, stable and efficient numerical methods for the solution of real-world problems based on theoretical foundations. In particular, she is interested in developing space-time methods with the aim of exploiting adaptive space-time mesh-refinement techniques. Among these methods, she has been working 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 in developing and contributing to finite element and finite volume software libraries, written 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.
IGNACIO BREVIS. His research has been linked to inverse problems and numerical analysis. During his PhD thesis, Ignacio worked on applied inverse problems, such as the source reconstruction for seismicity induced by mining activity using wave models and time-reversal properties. Currently, he is interested in developing reduced basis methods for parametric families of differential equations with weighted optimal functions via deep learning techniques and finite element methods. His collaboration network includes researchers at the University of Nottingham, UK; University of Basque Country (UPV/EHU), Spain; Yachay Tech University, Ecuador.
|Muga Urquiza, Ignacio
Doctor en Ciencias de la Ingeniería con Mención en Modelamiento Matemático, Universidad de Chile, Chile.
| Sepúlveda Salas, Paulina
PhD. in Mathematical Sciences, Portland State University, USA.
Doctor en Ciencias de la Ingeniería con mención en Modelación Matemática, Universidad de Chile, Chile.
| Millar Vasquez, Felipe
PhD. Student, Pontificia Universidad Católica de Valparaíso, Chile.
Visit our new Academic Website
Our new Academic Website can be found in the following link: