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Instituto de Matemáticas Aplicadas UCV

Numerical Analysis / Análisis Numérico

Numerical Analysis / Análisis Numérico

Resumen

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
(i) DEVELOPMENT: we investigate novel numerical methods that, for certain criteria, improve the existing methods and enable an efficient computational implementation;
(ii) ANALYSIS: we use mathematical analysis to give theoretical proofs about the properties and performance of numerical methods;
(iii) IMPLEMENTATION: we code our own libraries to show 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.

DIEGO PAREDES. Co-author of the Multiscale Hybrid-Mixed (MHM) Finite Element Method and developer of the MSL (Multiscale Solver Library). His research is focused on development, mathematical analysis, and efficient computational implementation of numerical methods. In particular, he is interested in proposing new numerical schemes to solve multiscale problems related to fluid flow in porous media and wave propagation models. The collaboration network of the Dr. Paredes includes connections to highly regarded research centres, as the Laboratório Nacional de Computação Científica (LNCC) - Brazil, and the Institut National de Recherche en Informatique et en Automatique (INRIA) - France.

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