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.

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.

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

Brevis, Ignacio Doctor en Ciencias de la Ingeniería con mención en Modelación Matemática, Universidad de Chile, Chile. mail: rodrigo.brevis@pucv.cl phone: (+56) 32 227 4024 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

	Millar Vasquez, Felipe PhD. Student, Pontificia Universidad Católica de Valparaíso, Chile. mail: felipe.millar.v@mail.pucv.cl phone: website:  Academic Website
	Hasbani, José PhD. Student, Pontificia Universidad Católica de Valparaíso, Chile. mail: jose.hasbani@pucv.cl phone: website:  Academic Website

 Former MS. Student

Pinochet Soto, Gabriel MS. Student, Pontificia Universidad Católica de Valparaíso, Chile. mail: gpinochetsoto@gmail.com phone: website:  Academic Website

Visitors 2022

	Maciej Woźniak PhD. in Computer Sciences, AGH University of Sciences and Technology. mail: mwozniak@macwozni.pl phone: website: Academic Website
	Marcin Łoś PhD. in Computer Sciences, AGH University of Sciences and Technology mail: los@agh.edu.pl phone: website: Academic Website
Visitors 2020
	Rodriguez Melendez, Oscar PhD. Student, Basque Center for Applied Mathematics, Spain. mail: orodriguez@bcamath.org phone: +34 946 567 842 website: Academic Website

Permanent Seminar

• Seminario Caleta Numérica

Past Events

• Valparaíso Numérico IV

Visit our new Academic Website

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

IMA Numerics.