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Instituto de Matemáticas Aplicadas UCV

Numerical Analysis / Análisis Numérico

Numerical Analysis / Análisis Numérico

Research directions


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.



SERGIO ROJAS. His research interests are numerical analysis of partial differential equations, finite element methods, discontinuous Galerkin methods.


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.


LILIANA CAMARGO. Her research interests are numerical analysis of partial differential equations, finite element methods, hybridizable discontinuous Galerkin methods, A posteriori error analysis, fluid mechanics and electromagnetism.


PATRICK VEGA. His research interests are numerical analysis of partial differential equations,finite element methods, discontinuous Galerkin methods, A posteriori error analysis, fluid mechanics and electromagnetism.



Professors

Muga Urquiza, Ignacio

Doctor en Ciencias de la Ingeniería con Mención en Modelamiento Matemático, Universidad de Chile, Chile.

mail: ignacio.muga@pucv.cl
phone: (+56) 32 227 4033
website:
Academic Website

 

 

 

Rojas, Sergio

Doctor en Ciencias de la Ingeniería, Pontificia Universidad Católica de Chile, Chile

mail: sergio.rojas.h@pucv.cl
phone: (+56) 32 227 4024
website:
Academic Website

 

Sepúlveda Salas, Paulina

PhD. in Mathematical Sciences, Portland State University, USA.

mail: paulina.sepulveda@pucv.cl
phone: (+56) 32 227 4024
website:
Academic Website

 

 

 

Postdoctoral fellows

   Camargo, Liliana

mail: lilianacamargomazuera @ gmail.com
phone: (+56) —
website:
Academic Website

 

Vega, Patrick

Doctor en Ciencias Aplicadas c/m Ingeniería Matemática, Universidad de Concepción, Chile.

mail: patrick.vega@pucv.cl
phone: (+56) 32 227 4024
website:
Academic Website

PhD. Students

  Perera, Jorge

PhD. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: jorgeperera1597@gmail.com
phone:
website:
 Academic Website

MSc. Student​s

 Mondaca, Francisco 

MS. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: francisco.mondaca.t@mail.ucv.cl
phone:
website:
 Academic Website
 Ruminot, Ignacio

MSc. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: iruminota@gmail.com
phone:
website:
 Academic Website

 

BSc. students

 Herrera, Victoria

BSc. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: victoria.herrera.b@mail.pucv.cl
phone:
website:
 Academic Website
Zamorano, Nicolas

BSc. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: nicolas.zamo12@gmail.com
phone:
website:
 Academic Website

 

International Collaborators

  • Matteo Croci, Basque Center for Applied Mathematics, Spain. (academic page)
  • Luis Espath, Nottingham University, UK. (academic page)

Former Members

Brevis, Ignacio

Doctor en Ciencias de la Ingeniería con mención en Modelación Matemática, Universidad de Chile, Chile.

mail: ignacio.brevis.v@gmail.com
phone: (+56) —
website:
Academic Website

Former PhD. Students

Millar Vasquez, Felipe

PhD. Student, Pontificia Universidad Católica de Valparaíso, Chile.

mail: felipe.millar.v@mail.pucv.cl
phone:
website:
 Academic Website

 

 

Former MSc. Students

  Pinochet Soto, Gabriel

MSc. in Mathematics, Pontificia Universidad Católica de Valparaíso, Chile.

mail: gpinochetsoto@gmail.com
phone:
website:
 Academic Website

Former BSc. Students

Gonzalez, Carlos

BSc. in mathematics, Pontificia Universidad Católica de Valparaíso, Chile.

mail: carlgonzamo98@gmail.com
phone:
website:
 Academic Website

Visitors 2023

Visitors 2023

  • Witold Dzwinel. Full Professor. AGH University of Science and Technology, Poland.
  • Maciej Paszyński. Full Professor, AGH University of Science and Technology, Poland.
  • Paweł Maczuga. PhD. Student. AGH University of Science and Technology, Poland.
  • Julen Alvarez-Aramberri. Postdoctoral Researcher, UPV/EHU, Spain
  • Judit Muñoz-Matute. Postdoctoral Researcher Oden Institute for Computational Engineering and Sciences, USA.
  • Ángel J. Omella. Postdoctoral Researcher UPV/EHU, Spain.
  • David Pardo. Research Professor. UPV/EHU, Spain.
  • Leszek Siwik. Assistant Professor. AGH University of Science and Technology, Poland.

Visitors 2022

  • Carlos Uriarte. PhD. Student. Basque Center for Applied Mathematics, Spain.
  • Otilio Rojas. Researcher, Barcelona Supercomputing Center, Spain.
  • Lisa J. Fauci. Full Profesor, Tulane University, USA.
  • Zhiqiang Cai. Full Professor, Perdue University, USA.
  • Marcin Łoś. PhD. in Computer Sciences, AGH University of Sciences and Technology, Poland
  • Maciej Woźniak. PhD. in Computer Sciences, AGH University of Sciences and Technology, Poland.

Visitors 2020

  • Rodriguez Melendez, Oscar. PhD. Student, Basque Center for Applied Mathematics, Spain.

 

Permanent Seminar

 

Past Events

Academic articles

Submitted manuscripts

Papers in refereed journals

2023

2022 

2021 

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

Visit our new Academic Website

Our new Academic Website can be found in the following link:

IMA Numerics.

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