Numerical Analysis Mathematical Modeling Scientific Computing

Dirección de tesis

Doctorado:
- Francisca Álvarez (Ph.D. in Mathematics) ongoing.

Magister:
- Elias Carú (Master in Mathematics) 2023-2024
- Francisco Mondaca (Master in Computational Simulations) 2023-2024

Licenciatura en matemáticas:

- Barbara Pávez (finishing 2024)
- Francisco Mondaca (finished 2023)
- Eileen Saavedra (finished 2023)
- Juan Venegas (finished 2022)
- Carlos Gonzalez (finished 2022)
- Elias Carú (finished 2021)

Organizer:

Miembro comité organizador SIAM Conference on Computational Science and Engineering (CSE25)
Co-organizadora de Minisimposio: Neural Networks for Partial Differential Equations, WONAPDE 2024, junto a Ignacio Muga y David Pardo
Co-organizadora de Sesión Temática: Análisis Numérico de Ecuaciones Diferenciales Parciales, SOMACHI 2023, junto a Patrick Vega.
Co-organizadora Seminario Caleta Numérica 2023-- Actualidad
Organizadora Seminario Caleta Numérica 2020-2023

Selected talks:

2023
A Deep r-Adaptive First-Order System Least Squares method for elliptic PDEs, ICCS Conference, 3-4 July, 2023.
A Deep r-Adaptive First-Order System Least Squares method for elliptic PDEs, XXXV Jornada de matemática de la Zona Sur, 19-21 Abril, 2023.

2022
A Machine Learning Least-Square approach for a wave propagation problem, 8 al 10 Diciembre, Encuentro SOMACHI, Punta de Tralca, 2022.
A machine learning least-squares method with a weighted norm. Minimum Residual & Least-Squares Finite Element Methods, PUC, Santiago, 7-9 Octubre, 2022.
Solving a space-time acoustic wave problem using a DPG method in
heterogeneous media. MAPI 2, Medellín, Colombia, 8-10 de Junio 2022.

2021
Minicurso virtual de números complejos: Una experiencia extracurricular, interinstitucional y en co-docencia, junto a Pamela González, Sergio Guzmán, Sebastián Herrero, Valeria Randolph, XXV JNEM, diciembre 2021.
La línea de Análisis Numérico, 9na V-Escuela de Doctorado 2021, 15 de octubre 2021.
Discontinuous Space-Time Techniques for the Wave Equation. Conference on Computational Science and Engineering 2021 (CSE21), 1-5 Marzo.
A proof of a well-posedness for a space-time DPG formulation for the wave equation, XXXIII Jornada de Matemática, U. de la Frontera, 21 de Abril.

2020
Programación y modelación matemática en nuestros tiempos. XLVI Semana de la Matemática , Pontificia Universidad Católica de Valparaíso, Chile. Octubre.

2019
Two adaptive discontinuous space-time methods for the wave equation.French Latin-American Conference on New Trends in Applied Mathematics, Universidad de Chile, Chile, Diciembre.
A well-posed DPG formulation for the wave equation in multiple dimensions.Minimum Residual & Least-Squares Finite Element Methods, Humboldt University, Berlin, Germany, Septiembre. (Invitada)
Estrategias numéricas espacio-temporales para la ecuación de la onda, Seminario, Universidad Técnica Federico Santa Maria, Agosto, (Invitada).
Explicit-in-time adaptive p-refinement for the heat equation. Mathematical and Computational Modelling on the Earth, Universitat Politecnica de Catalunya, Barcelona, Spain, Mayo.
A Spacetime DPG Method for the Wave Equation in Multiple Dimensions. WONAPDE 2019. Concepción, Chile, Enero.
A Spacetime Goal-Oriented Adaptivity for an Explicit in Time Finite Element Method. WONAPDE 2019. Concepción, Chile, Enero.

2018
A spacetime DPG method for the wave equation. 8th International Conference Computational Methods in Applied Mathematics: CMAM-8. Minsk, Belarus, Julio.
Implementation of weak symmetric stress tensor for linear elasticity, BCAM Scientific Seminar, Bilbao, España. Junio.
An adaptive spacetime DPG method for the wave equation in multiple dimensions, Fifth international
congress on multiphysics, multiscale, and optimization problems m2opV. Mayo, Bilbao, España.
Space-time CFOSLS systems: Adaptive Mesh Refinement, CASCADE RAIN 2018, Portland, Oregon, EstadosUnidos. Abril, 2018. (Invitada)
Spacetime numerical techniques for the Schrödinger and wave equations, Defensa pública de doctorado, Portland, Oregon, Estados Unidos, Enero, 2018.

2017
Spacetime DPG formulation for the Schrödinger and Wave Equations, Minimum Residual & Least-Squares Finite Element Methods, Portland, OR, Estados Unidos. Octubre.
Divergence-free solvers for block systems with divergence constraint, Poster Symposium, Lawrence LivermoreNational Laboratory, Livermore, California, Estados Unidos. Agosto.
Elastic waves generated by a landslide, CASCADE RAIN 2017, Vancouver, Canadá. Abril.(Premio a estudiante de posgrado.)
A spacetime DPG method for Schrödinger equation, Seventh Valparaíso’s Mathematics and its Applications Days, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile, Enero 12-13, 2017. (Invitada)

2016
A scheme with discontinuous and conforming spaces for the wave equation, WONAPDE 2016, Universidad de Concepción, Concepción, Chile, Enero. (Premio estudiante de posgrado)
A density result for the graph space of the Schrodinger operator, Applied Seminar, Portland State University, Portland, OR, Estados Unidos, October.

2015
A density result for a graph space, Applied Seminar, Portland State University, Portland, OR, Estados Unidos. Mayo, 2015.
A tent pitching scheme motivated by Friedrichs theory, Applied Seminar, Portland State University, Portland, OR, Estados Unidos, Febrero.

2014
Elastic wave propagation with CLAWPACK, Seminar, Pontificia Universidad Católica de Valparaíso,Valparaíso, Chile, Portland, OR, Estados Unidos, Marzo 28, 2014. (Invitada)
A Mixed Finite Element for the Linear Elasticity on Cubic Grids, Applied and Computational Mathematics, Portland State University, Portland, OR, Estados Unidos, 2014.