Numerical Analysis, Mathematical Modeling & Scientific Computing

I have trained mathematicians at the undergraduate, master's and doctorate levels.

Current PhD student:
Felipe Millar (Pontificia Universidad Católica de Valparaíso)

Supervision of graduate students :

2018
Victor Trujillo Radrigán
Dissertation: A Multi-scale method for solving linear PDEs in layered media.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

2017
Sergio Rojas Hernández
Dissertation: ANALYTICAL AND SEMI-ANALYTICAL APPROACHES FOR ELECTROMAGNETIC PROBLEMS OVER LAYERED MEDIA.
Degree: Doctor in Engineerinf Sciences, Pontificia Universidad Católica de Chile.

2007
Aldo Cabrera Bianchetti.
Dissertation: Computation of Resonant Frequencies at the interior of a Harbour by Applying and Simulating a Mathematical Model.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

2008
Cristina Valenzuela Donoso
Dissertation: Numerical Computation of Eigenfrequencies by Integral Equations. Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

Wilmer Bazán
Dissertation: Numerical Computation of the DtN Operator for the Helmholtz Equation in a Perturbed Half-Space.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

2009
Elizabeth Avilés Rieloff
Dissertation: Compendium of Results for the Helmholtz Equation in Different Types of Domains.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

Gonzalo Espinoza Vásquez
Dissertation: The Helmholtz equation in a half-plane with a simple local perturbation.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

Juan Herrera Tobar
Dissertation: Effective computation of the Green’s function associated with two electromagnetic half-spaces.
Degree: Master degree in Mathematics, Pontificia Universidad Católica de Valparaíso.

Supervision of Bachelor Students:

Aníbal Aguilera, Bachelor in Mathematics, Pontifical Catholic University of Valparaíso. Title: Numerical estimation of stability and convergence parameters for 1D Helmholtz using hp-FEM. December 2011.

José López, Bachelor in Mathematics, Pontifical Catholic University of Valparaíso. Title: Best Approximation of Distributions by Finite-dimensional Subspaces. January 2016.

- Creator and organizer of the permanent seminar "Caleta Numérica" at the Mathematics Institute of the PUCV: http://ima.ucv.cl/seminarios/caleta-numerica/
- Our group of Numerical Analysis and Computational Simulation organizes annually the workshop "Valparaiso's Mathematics and its Applications Days": http://ima.ucv.cl/congreso/vmad2017/
- I have participated in the organizing committee of "Semana de la Matemática 2009", the meeting "Valparaíso Numérico IV" (http://www.ci2ma.udec.cl/vn4/), "Puerto Matemático" I, II & III meetings, and in the Doctoral School in Mathematics of Valparaíso.

Posters Presentations:
"Projection in negative norms & the regularization of rough linear functionals".
Workshop on Computational Modeling and Numerical Analysis 2019, National Laboratory of Scientific Computing, Brazil.

"Nonlinear Petrov-Galerkin Discretization for Linear Problems in Banach Spaces".
Advances in Mathematics of Finite Elements: A conference in honor of the 90th birthday of Prof. Ivo Babuska, Austin, Texas, USA.

Short-Courses:
"Advanced Discretization: Theory, Applications and Numerical Implementation" (Cursillo V Escuela del Doctorado en Matemáticas de Valparaíso, Ignacio Muga & Kris van der Zee).

“Análisis de nuevas técnicas de discretización” (Cursillo). III Jornada de Matemáticas. 11 al 13 de enero, 2012. Universidad de Valparaíso.

Talks:

2019
"The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces".
Jornadas de Matemáticas de la Zona Sur, Universidad de Magallanes, Chile.

"Projection in negative norms & the regularization of rough linear functionals".
Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2019), Universidad de Concepción, Chile.

2018
"The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces".
LXXXVII Encuentro de la Sociedad Matemática de Chile, Universidad de O’Higgins, Chile.

"Projection in negative norms & the regularization of rough linear functionals".
5th International Workshop on Multiphysics, Multiscale and Optimization Problems (M2OP5). BCAM, Bilbao, Spain.

"Projection in negative norms & the regularization of rough linear functionals".
Emerging Trends in Applied Mathematics & Mechanics (ETAMM2018), Jagiellonian University, Krakow, Poland.

"Projection in negative norms & the regularization of rough linear functionals".
1st Colombian Conference of Industrial & Applied Mathematics, Bogotá, Colombia.

2017
"On the Hybridization of Residual Minimization Problems in Banach Spaces".
3rd Workshop on Minimum Residual & Least-Squares Finite Element Methods, Portland, OR, USA.

“About the extension of the DPG method to Banach spaces”.
27th Biennial Numerical Analysis Conference, GLASGOW, UK.

“General 1.5D Approaches for Layered Media”.
Workshop on Geophysical Applications and HPC, Barcelona, Spain.

2016
“The nonlinear Petrov–Galerkin method in Banach spaces: yet another improvement of Babuska’s apriori error estimate”.
SUMA 2016, Valparaíso, Chile.

¨The nonlinear Petrov–Galerkin method in Banach spaces: yet another improvement of Babuska’s apriori error estimate¨.
MAFELAP 2016, Conference on the Mathematics of Finite Elements and Applications, Brunel University, United Kingdom.

¨A Quadrature-Free Method for the Approximation of DC Fundamental Solutions in Layered Media¨.
Fourth International Workshop on Multiphysics, Multiscale and Optimization Problems. BCAM, Bilbao, Spain.

“Optimal Discretization in Banach Spaces”.
5th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2016), Concepción, Chile

“Semi-Analytic techniques for 1D fast simulation of direct current (DC) borehole measurements”.
6th Valparaiso’s Mathematics and its Applications Days (V-MAD 6), Valparaíso, Chile.

2015
“Optimal Discretization in Banach Spaces: a Nonlinear Petrov-Galerkin Approach”.
Minimal Residual and Least Squares Finite Element Methods Workshop. Delft, The Netherlands.

“Optimal Discretization in Banach Spaces”.
Oberwolfach Workshop 1540: Computational Engineering. Mathematisches Forschungsinstitut Oberwolfach, Germany.

“Fast Simulation of Direct Current (DC) Borehole Measurements using Model Reduction”.
First Pan-American Congress on Computational Mechanics (PANACM 2015). Buenos Aires, Argentina.

2014
“DPG Strategies for the Helmholtz Equation”.
LMS Durham Symposium, Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Durham, UK.

“Fast Simulation of Direct Current (DC) Borehole Measurements using Model Reduction”.
Third International Workshop on Multiphysics, Multiscale and Optimization Problems. BCAM, Bilbao, Spain.

2013
“Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation”.
Valparaíso Numérico IV: Séptimo Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales. Pontificia Universidad Católica de Valparaíso, Chile.

“Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation”.
ICES/USACM Workshop on Minimum Residual ans Least Squares Finite Element Methods, Austin, Texas, EEUU.

“Recent Advances on the Simulation and Inversion of Resistivity Logging Measurements for Enhanced Reservoir Characterization”.
XII Jornadas de Mecánica Computacional, Universidad de Santiago, Chile.

“Recent Advances on the Simulation and Inversion of Resistivity Logging Measurements for Enhanced Reservoir Characterization”.
Mathematical Congress of the Americas 2013, Guanajuato, México.

“Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation”.
MAFELAP 2013, Conference on the Mathematics of Finite Elements and Applications, Brunel University, United Kingdom.

“Dispersion of the Lowest Order DPG Method for Helmholtz Equation with Scaled Norms”.
The 11th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2013). Gammarth, Tunisia.

“Dispersion of the lowest order DPG method for acoustics”.
IV Workshop of Numerical Analysis of Partial Differential Equations (WONAPDE 2013), Concepción, Chile.

2012
“Técnicas semi-analíticas para la simulación de registros sónicos descentrados”.
XI Jornadas de Mecánica Computacional, Valparaíso, Chile. 2012

“Técnicas semi-analíticas para la simulación de registros sónicos descentrados”.
The Third Valparaíso’s Mathematics and Applications Days (V-MAD III), Valparaíso, Chile. 2012

2011
“An Update of the DPG Method for Wave Propagation Problems”.
La Serena Numérica I, 6th Meeting of Numerical Analysis of Partial Differential Equations, La serena, Chile. 2011

“Analysis of the DPG Method for the Hemholtz Equation in Multi-dimensions”.
LXXX Encuentro Anual, Sociedad Matemática de Chile, Los Andes, Chile. 2011

“Semi-Analytical Response of Acoustic Logging Measurements due to Multipole Eccentered Excitations”.
X Jornadas de Mecánica Computacional, Santiago, Chile. 2011

“Analysis of the DPG Method for the Hemholtz Equation in Multi-dimensions”.
KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation, King Abdullah University of Science and Technology, Saudi Arabia. 2011

2010
“A Class of Discontinuous Petrov-Galerkin Methods: The Optimal Test Norm and Time-Harmonic Wave Porpagation”.
Santiago Numérico II, 5th Meeting of Numerical Analysis of Partial Differential Equations, Santiago, Chile. 2010

“DPG for Waves”
Spring 2010 Finite Element Rodeo, Southern Methodist University, Dallas, Texas, USA. 2010

2009
“Uniqueness for the Outgoing Elastic Wave in a Half-Plane with Free Boundary”.
The 9th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2009), Pau, France. 2009

“A radiation condition for time-harmonic elastic waves in half-spaces with free boundary”.
Santiago Numérico I, 4th Meeting of Numerical Analysis of Partial Differential Equations, Santiago, Chile. 2009

2007
“Radiation Condition for a Class of Time-Harmonic Acoustic and Elastic Wave Problems Arising in Half-Spaces”.
The 8th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2007), Reading, United Kingdom. 2007

“The Helmholtz Equation in Unbounded Domains with Unbounded Frontier: Surface Waves.”
II Workshop of Numerical Analysis of Partial Differential Equations (WONAPDE 2007), Concepción, Chile. 2007