Numerical Analysis; Applied Mathematics; Scientific Computing. In particular, numerical method for partial differential equations arising from continuum mechanics and solar energy modeling.

DIRECTION OF PHD THESIS

Ph.D. Program in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción:
[1] Cinthya Rivas. Title: Efficient computation of electromagnetic fields in solar cells. In collaboration with Rodolfo Rodríguez and Peter Monk. April 2014 - September 2018.
[2] Patrick Vega. Title: Hybridizable Discontinuous Galerkin method in fluid mechanics. In collaboration with Weifenq Qiu and Rodolfo Araya. 2016 - December 2018.
[3] Felipe Vargas. Title: Discontinuous Galerkin methods in continuum mechanics . In collaboration with Jay Gopalakrishnan. 2016 - January 2019.
[4] Paulo Zúñiga. Title: High order mixed method in fluid mechanics. In collaboration with Ricardo Oyarzúa. 2017 - December 2019.
[5] Nestor Sánchez. Title: Development of numerical methods with applications in plasma physics. In collaboration with Dr. Tonatiuh Sáncez-Vizuet. 2019 - present.

DIRECTION OF UNDERGRADUATE THESIS

Undergraduate Program in Civil Mathematical Engineering, Universidad de Concepción :
[1] Juan Manuel Cárdenas. Title: An HDG method for linear elasticity in curved domains. April 2017 - March 2018.
[2] Alejandra Barrios. Title: An HDG method for the biharmonic. March 2017 - November 2018.
[3] Fernando Peña. Title: A discontinuous Galerkin method for the hear equation in non-polyginal domains. April 2019- Mayo 2020`+
[4] Jaime Manríquez. Title: A hybridizable discontinuous Galerkin method for the Stokes problem in non-mathcing meshes. March 2020 - December 2020.

PRESENTATIONS IN NATIONAL AND INTERNATIONAL MEETINGS (SINCE 2014):

[14] A piori and a posteriori error analysis of an unfitted HDG method for a semi-linear elliptic problem. Simposio Internacional de Métodos Matemáticos Aplicados a las Ciencias, XXII SIMMAC. Universidad de Costa Rica, San José, Costa Rica, 25 al 28 de febrero del 2020.
[13] An unfitted HDG method for a semi-linear elliptic problem arising from nuclear fusion reaction. Caleta Numérica, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile, 25 de septiembre del 2020.
[12] Método de Galerkin discontinuo hibridizable aplicado a un problema de física de plasmas. SUMA 2016, Universidad Nacional de Cuyo, Mendoza, Argentina, 23 al 27 de septiembre de 2019. (Invited speaker).
[11] An HDG method in a plasma physics problem. Seminar "Ingeniería Matemática y Computacional", Pontificia Universidad Católica de Chile, Santiago, Chile. April 10, 2019,
[10] A posteriori error analysis of HDG methods in fluid mechanics. XXVII Congreso de Matemáticas Capricornio, Universidad de Antofagasta, Antofagasta, Chile. July 25 – 27, 2018.
[9] A high order HDG method for Stokes flow in curved domains. XXX Jornada de la Matemaática de la Zona Sur, Universidad Católica de la Santísima Concepción, Concepción, Chile, April 26-28, 2017.
[8] Numerical simulations of photovoltaic solar cells. MAFELAP 2016, Brunel University London, Uxbridge, UK, July 14- 17, 2016.
[7] HDG approximation of boundary value problems on curved domains by extensions from polygonal subdomains. I Panamerican Congress on Computational Mechanics (PANACM 2015), Buenos Aires, Argentina, April 27-29, 2015.
[6] A priori error analysis for HDG methods in curved domains using extensions from polyhedral subdomains. XXVIII Jornada de Matemática de la Zona Sur, Termas de Chilla?n, Chile, April 22-24, 2015.
[5] A priori error analysis for HDG methods in curved domains using extensions from polyhedral subdomains. La Serena Numérica II, La Serena, Chile. January 2015.
[4] Numerical methods for simulations of photovoltaic devices. Seminario Ingeniería Matemática. Pontificia Universidad Católica de Chile, Santiago. December 2014.
[3] Hybridizable discontinuous Galerkin method on general domains. Seminario de Análisis Numérico y Matemática Aplicada, Caleta Numérica. Pontificia Universidad Católica de Valparaíso, Valparaíso. November 2014.
[2] Performance of RCWA and a FE method in simulations of photovoltaic devices. LANUS-FEM, Puerto Varas, Chile. September 2014.
[1] On the robustness of a hybridizable discontinuous Galerkin method for curved domains. XI World Congress on Computational Mechanics. Barcelona, Spain. July 2014.

EVENT ORGANIZATION

[4] Numerical Analysis of PDE's Session, XXII SIMMAC, February 25-28, 2020. Universidad de Costa Rica, San José, Costa Rica.
[3] Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2019), January 21- 25, 2019. Universidad de Concepción, Concepción, Chile.
[2] Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2019), January 11- 15, 2016. Universidad de Concepción, Concepción, Chile.
[1] Spring School on Numerical Analysis (EPANUM 2014), September 23 - October 3, Universidad de Concepción.Concepción, Chile.

RESEARCH VISITS

[10] Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. July 15 - 20, 2019.
[9] Inria, Sophia-Antipolis, France. January 28 to February 1, 2019.
[8] Courant Institute of Mathematical Sciences, New York University, New York, USA. February 12 - 16, 2018.
[7] Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA. February 5 - 10, 2018.
[6] Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. January 27 - February 3, 2018.
[5] Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA. July 2 - July 8, 2017.
[4] Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong. July 18 - 30, 2016.
[3] Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA. January 19 - February 10, 2015.
[2] Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA. July 13 - August 9, 2014.
[1] Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA. January 13 - February 23, 2014.

INTERNATIONAL COOPERATION PROJECTS
[2] MATH-AmSud Program "EOLIS-Efficient Off-LIne numerical Strategies for multi-query problems" (Brazil-Chile-France), (2020-2021)
[1] MATH-AmSud Program "PHOTOM-Photovoltaic solar devices in multiscale computational simulations (Brazil-Chile-France), (2018-2019)