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Instituto de Matemáticas Aplicadas UCV

Numerical Analysis / Análisis Numérico

Numerical Analysis / Análisis Numérico

Overview


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:


  1. DEVELOPMENT. We investigate novel numerical methods that, for certain criteria, improve the existing methods and enable an efficient computational implementation.


  2. ANALYSIS. We use mathematical analysis to give theoretical proofs about the properties and performance of numerical methods.


  3. 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.



Team


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.


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