Muga Urquiza, Ignacio

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

Licenciado en Matemáticas, Pontificia Universidad Católica de Valparaíso, Chile.

ignacio.muga@pucv.cl

(+56) 32 227 4033

Pagina del academico

Research
Docencia
- Direcciones de Tesis
Vinculación con el medio
- Videos

Research Interests

Mathematical Modeling, Numerical Analysis & Scientific Computing.

Check out our websites:

IMA-Numerics https://sites.google.com/view/ima-numerics

Ignacio Muga (Google Scholar)

Journal papers

Title: Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. Authors: Ignacio Brevis, Ignacio Muga, David Pardo, Óscar Rodríguez, Kristoffer G. Van der Zee. Source: Computers and Mathematics with Applications. Published: 2024. https://authors.elsevier.com/a/1i%7EqZ3CDPQAe5e

Title: Adaptive stabilized finite elements via residual minimization onto bubble enrichments. Authors: Jose Hasbani, Paulina Sepúlveda, Ignacio Muga, Victor Calo & Sergio Rojas. Source: Computers and Mathematics with Applications. Published: 2023 https://authors.elsevier.com/c/1hr5w3CDPQ6qWo

Title: An Adaptive Superconvergent Mixed Finite Element Method Based on Local Residual Minimization. Authors: Ignacio Muga, Sergio Rojas & Patrick Vega. Source: SIAM Journal on Numerical Analysis. Published: 2023

https://doi.org/10.1137/22M1526307

Title: Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices. Authors: Tomasz Służalec, Mateusz Dobija, Anna Paszyńska, Ignacio Muga, Marcin Łoś & Maciej Paszyński. Source: Computer Methods in Applied Mechanics and Engineering. Published: 2023 https://authors.elsevier.com/sd/article/S0045782523001974

Title: Nanoionics from a quantum mechanics point of view: Mathematical modeling and numerical simulation. Authors: Paulina Sepúlveda, Ignacio Muga, Norberto Sainz, René G. Rojas & Sebastián Ossandón. Source: Computer Methods in Applied Mechanics and Engineering. Published: 2023 https://authors.elsevier.com/c/1ga2Z_12dr6XyH

Title: A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks. Authors: Carlos Uriarte, David Pardo, Ignacio Muga & Judit Muñoz-Matute. Source: Computer Methods in Applied Mechanics and Engineering. Published: 2023 https://authors.elsevier.com/sd/article/S0045782523000154

Title: A Deep Fourier Residual method for solving PDEs using Neural Networks. Authors: Jamie M. Taylor, David Pardo & Ignacio Muga. Source: Computer Methods in Applied Mechanics and Engineering. Published: 2023 https://authors.elsevier.com/c/1gJmjAQEIzX80

Title: Neural control of discrete weak formulations: Galerkin, least squares & minimal-residual methods with quasi-optimal weights. Authors: Ignacio Brevis, Ignacio Muga & Kristoffer Van der Zee. Source: Computer Methods in Applied Mechanics and Engineering. Published: 2022 https://doi.org/10.1016/j.cma.2022.115716

Title: Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing. Authors: Erdozain, A.; Muga, I.; Péron, V.; Pinochet, G.; Source: GEM – International Journal on Geomathematics; Published: 2022 https://rdcu.be/cMp21

Title: Projection in negative norms and the regularization of rough linear functionals. Authors: Millar, F.; Muga, I.; Rojas, S.; Van der Zee, K.G.; Source: Numerische Mathematik; Published: 2022 https://rdcu.be/cJvUe

Title: DGIRM: Discontinuous Galerkin-based Isogeometric Residual Minimization for the Stokes problem. Authors: Łos, M.; Rojas, S.; Paszyński, M; Muga, I.; Calo, V.M.; Source: Journal of Computational Science; Published: 2021 https://doi.org/10.1016/j.jocs.2021.101306

Title: Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier–Stokes problems. Authors: Łos, M.; Muga, I.; Muñoz-Matute, J.; Paszyński, M. Source: Computers & Mathematics with Applications; Published: 2020 https://doi.org/10.1137/20M1324338

Title: Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov–Galerkin, and Monotone Mixed Methods. Authors: Ignacio Muga & Kris Van der Zee. Source: SIAM Journal of Numerical Analysis Vol. 58, No. 6, pp. 3406-3426; Published: 2020 https://doi.org/10.1137/20M1324338

Title: Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems. Authors: Victor Calo, Marcin Los, Quanling Deng, Ignacio Muga & MaciejPaszyński. Source: Computer Methods in Applied Mechanics and Engineering; Published: 2020. https://doi.org/10.1016/j.cma.2020.112891

Title: A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations. Authors: Ignacio Brevis, Ignacio Muga & Kristoffer Van der Zee. Source: Computers & Mathematics with Applications; Published: 2020. https://doi.org/10.1016/j.cma.2020.112891

Title: An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms. Authors: Victor M. Calo, Alexandre Ern, Ignacio Muga & Sergio Rojas. Source: Computer Methods in Applied Mechanics and Engineering; Published: 2020. https://doi.org/10.1016/j.cma.2020.112891

Title: Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems. Authors: Łos, M.; Muñoz-Matute, J.; Muga, I.; Paszyński, M. Source: Computers & Mathematics with Applications, 2019; DOI 10.1515/cmam-2018-0199 Published: 2019.

Title: The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces. Authors: Muga, I.; Tyler, M.J.W.; Van der Zee, K.G. Source: Comput. Methods Appl. Math. 2019; 19(3): 557–579 DOI 10.1515/cmam-2018-0199 Published: 2019.

Title: The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method. Authors: Houston, P.; Muga, I.; Roggendorf, S.; Van der Zee, K.G. Source: Comput. Methods Appl. Math. 2019; 19(3): 503–522 https://doi.org/10.1515/cmam-2018-0198. Published: 2019.

Title: The outgoing time-harmonic electromagnetic wave in a half-space with non-absorbing impedance boundary condition. Authors: Rojas, S.; Muga, I., Jerez-Hanckes, C. Source: ESAIM: M2AN, 53 1 (2019) 325-350; Published: 2019.

Title: A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements. Authors: Shahriari, M.; Rojas, S.; Pardo, D.; Rodríguez-Rozas, A.; Shaaban, A.B.; Calo, V.M.; Muga, I. Source: GEOSCIENCES 2018, 8(6), 225; Published: 2018.

Title: Goal-oriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation. Authors: Darrigrand, V.; Rodríguez-Rozas, A.; Muga, I.; Pardo, D.; Romkes, A.; Prudhomme, S. Source: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Volume 113, Issue 1, pp 22-42. Published: 2018.

Title: A quadrature free method for simulation and inversion of 1.5D direct current (DC) borehole measurements. Authors: Rojas, S.; Muga, I.; Pardo,D. Source: COMPUTATIONAL GEOSCIENCES, Volume 20, Issue 6, pp 1301–1318. Published: 2016.

Title: Semi-analytical response of acoustic logging measurements in frequency domain. Authors: Muga, I.; Pardo, D.; Matuszyk, P.; Torres-Verdín, C. Source: COMPUTERS AND MATHEMATICS WITH APPLICATIONS, Volume 70, Issue 4, pp 314-329. Published: 2015.

Title: Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation. Authors: Darrigrand, V.; Pardo, D.; Muga,I. Source: COMPUTERS AND MATHEMATICS WITH APPLICATIONS, Volume 69, Issue 9, pp 964-979. Published: 2015.

Title: Dispersive and dissipative errors in the DPG method with scaled norms for Helmholtz equation. Authors: Gopalakrishnan, J.; Muga, I.; Olivares,N. Source: SIAM JOURNAL OF SCIENTIFIC COMPUTING, Volume 36, Issue 1, pp A20-A39. Published: 2014.

Title: Influence of borehole-eccentered tools on wireline and logging-while-drilling sonic logging measurements. Authors: Pardo, D.; Matuszyk, P.J.; Torres-Verdin, C.; Mora, A.; Muga, I.; Calo, V.M. Source: GEOPHYSICAL PROSPECTING, Volume 61, Issue s1, pp 268-283. Published: 2013.

Title: Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation. Authors: Demkowicz, L.; Gopalakrishnan, J.; Muga, I.; Zitelli, J. Source: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Volume 213, pp 126-138. Published: 2012.

Title: Simulation of wireline sonic logging measurements acquired with Borehole- Eccentered tools using a high-order adaptive finite-element method. Authors: Pardo, D.; Matuszyk, P.J.; Muga, I.; Torres-Verdín, C.; Mora, A.; Calo, V.M. Source: JOURNAL OF COMPUTATIONAL PHYSICS, Volume 230, Issue 16, pp 6320-6333. Published: 2011.

Title: A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D. Authors: Zitelli J.; Muga I.; Demkowicz L.; Gopalakrishnan, J.; Pardo, D.; Calo, V.M. Source: JOURNAL OF COMPUTATIONAL PHYSICS, Volume 230, Issue 7, pp 2406-2432. Published: 2011.

Title: The outgoing time-harmonic elastic wave in a half-plane with free boundary. Authors: Durán, M.; Muga, I.; Nédélec, J.-C. Source: SIAM JOURNAL ON APPLIED MATHEMATICS, Volume 71, Issue 2, pp 443-464. Published: 2011.

Title: Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary. Authors: Durán, M.; Muga, I.; Nédélec, J.C. Source: COMPTES RENDUS MATHEMATIQUE, Volume 347, Issue 21-22, pp1 321-1324. Published: 2009.

Title: The Helmholtz Equation in a Locally Perturbed Half-Space with Non-Absorbing Boundary. Authors: Durán, M.; Muga, I.; Nédélec, J.-C. Source: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Volume 191, Issue 1 pp 143-172. Published: 2009.

Title: The Helmholtz equation in a locally perturbed half-plane with passive boundary. Authors: Durán, M.; Muga, I.; Nédélec, J.-C. Source: IMA JOURNAL OF APPLIED MATHEMATICS, Volume 71, Issue 6, pp 853-876. Published: 2006.

Title: The Helmholtz equation with impedance in a half-space. Authors: Durán, M.; Muga, I.; Nédélec, J.-C. Source: COMPTES RENDUS MATHEMATIQUE, Volume 341, Issue 9, pp 561-566. Published: 2005.

Title: The Helmholtz equation with impedance in a half-plane. Authors: Durán, M.; Muga, I.; Nédélec, J.-C. Source: COMPTES RENDUS MATHEMATIQUE, Volume 340, Issue 7, pp 483-488. Published: 2005.

arXiv, HAL & others

arXiv & HAL

Jamie M. Taylor, Manuela Bastidas, David Pardo & Ignacio Muga. “Deep Fourier Residual method for solving time-harmonic Maxwell’s equations”.
https://arxiv.org/abs/2305.09578

Brevis, I., Muga, I., Pardo, D., Rodríguez, O., & G., K. (2023). Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. ArXiv. /abs/2304.01722

J. G. Hasbani, P. Sepúlveda, I. Muga, V. M. Calo, and S. Rojas: Adaptive stabilized finite elements via residual minimization onto bubble enrichments (2023). arXiv:2303.17982 [math.NA].

Tomasz Sluzalec, Mateusz Dobija, Anna Paszynska, Ignacio Muga & Maciej Paszynski. “Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices”. arXiv:2212.12695

Carlos Uriarte, David Pardo, Ignacio Muga & Judit Muñoz-Matute. “A Deep Double Ritz Method for solving Partial Differential Equations”. arXiv:2211.03627

Jamie M. Taylor, David Pardo & Ignacio Muga. “A Deep Fourier Residual Method for solving PDEs using Neural Networks”.

arXiv:2210.14129

Ignacio Muga, Sergio Rojas & Patrick Vega. “An adaptive superconvergent finite element method based on local residual minimization”.

arXiv:2210.00390

Ignacio Brevis, Ignacio Muga & Kristoffer G. Van der Zee. “Neural Control of Discrete Weak Formulations: Galerkin, Least-Squares and Minimal-Residual Methods with Quasi-Optimal Weights”. arXiv:2206.07475

Aralar Erdozain, Ignacio Muga, Victor Péron & Gabriel Pinochet. “Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing”. hal-03373028

Felipe Millar, Ignacio Muga, Sergio Rojas & Kris Van der Zee. “Projection in negative norms and the regularization of rough linear functionals”. arXiv:2101.03044

Ignacio Brevis, Ignacio Muga & Kris Van der Zee. “Data-Driven Finite Elements Methods: Machine Learning Acceleration of Goal-Oriented Computations”. arXiv:2003.04485

Victor M. Calo, Alexandre Ern, Ignacio Muga & Sergio Rojas. “An adaptive stabilized finite element method based on residual minimization”. arXiv:1907.12605 hal-02196242

Marcin Łoś, Judit Munoz-Matute, Ignacio Muga & Maciej Paszynski. “Isogeometric Residual Minimization Method (iGRM) for Stokes and Time-Dependent Stokes Problems”.

arXiv:2001.00178

Marcin Łoś, Quanling Deng, Ignacio Muga, Victor M Calo, Maciej Paszynski. “Isogeometric Residual Minimization Method (iGRM) with Direction Splitting Preconditoner for Stationary Advection-Diffusion Problems”. arXiv:1906.06727

Muga, I.; Tyler, M.J.W.; Van der Zee, K. “The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces”. arXiv:1808.04542

Muga, I. & Van der Zee, K. ¨Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov-Galerkin, and Monotone Mixed Methods¨ arXiv:1511.04400

Gopalakrishnan, J.; Muga, I.; Olivares, N. “Dispersive and dissipative errors in the DPG method with scaled norms for Helmholtz equation” arXiv:1304.7497

ICES reports

Demkowicz, L.; Gopalakrishnan, J.; Muga, I.; Zitelli, J. “Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation“. ICES report 11-24.

Zitelli, J.; Muga, I.; Demkowicz, L.; Gopalakrishnan, J.; Pardo, D.; Calo, V. M. “A class of discontinuous Petrov-Galerkin methods. Part IV: the optimal test norm and time-harmonic wave propagation in 1D“. ICES report 10-17.

Research Projects

Externos

Fondecyt, Chile. No. 1230091. “DISCRETE-DUAL MINIMAL-RESIDUAL FINITE ELEMENT METHODS”. Investigador Responsable (vigente).

RISE Horizon 2020 European Project MATHROCKS (Ref. Nr. 777778). Investigador Asociado.

Fondecyt, Chile. No. 1160774. “Optimal Discretization in Banach Spaces”. Investigador Responsable.

RISE Horizon 2020 European Project GEAGAM (Ref. Nr. 644602). 2015-2017. Investigador Asociado.

Anillo ACT 1118: “Anillo de Investigación en Análisis Numérico de Ecuaciones Diferenciales Parciales”.  Investigador Asociado.

Fondecyt, Chile. No. 1130776. “Outstanding issues on the DPG method for wave propagation”. Investigador Responsable.

Proyecto Red Temática CYTED, No. CYTED 2011 – P711RT0278. “Métodos Avanzados para la Visualización del Subsuelo” (MAVS). Investigador Principal. 2012-2015.

Fondecyt, Chile. No. 1110272. “Discontinuous Petrov-Galerkin Methods with optimal test functions for time-harmonic wave propagation problems”. Investigador Responsable.

Talks

2023

Title: Neural Control of Discrete Weak Formulations
Venue: Workshop in Honor of Leszek F. Demkowicz’s 70th Birthday, Oden Institute, The University of Texas at Austin, April 11, 2023.

2022

Title: Neural Control: Improving the Quality of Finite-Element Solutions. Venue: @XC Encuentro Anual SOMACHI, Punta de Tralca, Chile, 8th December, 2022.

Title: Neural Control: Improving the Quality of Finite-Element Solutions. Venue: @Workshop on Scientific Machine Learning. PUC Santiago 29-30 November 2022.

Title: Neural Control of Discrete Weak Formulations of PDEs. Venue: Workshop on Minimum Residual & Least-Squares Finite Element Methods. PUC Santiago, Chile, October 5-7, 2022.

Title: Neural Control of Discrete Weak Formulations of PDEs. Venue: @XLVIII Semana de la Matemática, IMA-PUCV, Valparaíso, Chile, 12th October, 2022.

Title: Regularization of rough linear functionals & Adaptivity. Venue: September 29, 2022, @ECCOMAS, Oslo, Norway.

Title: Neural Control of Discrete Weak Formulations of PDEs. Venue: @University of Nottingham, 29th June, 2022.

Title: Neural Control of Discrete Weak Formulations of PDEs. Venue: @University of Birmingham, 28th June 2022.

Title: Neural Control of Discrete Weak Formulations of PDEs. Venue: @Imperial College London, 24th June, 2022.

Title: Learning optimal test functions for Goal-Oriented FEM. Venue: ICCS 2022, Brunel University London, 21st June, 2022.

2021

Title: A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations. Venue: A2S Group Seminar, AGH University of Science and Technology (Online, Jan 28, 2021).

Title: Projection in negative norms and the regularization of rough linear functionals. Venue: SIAM Conference on Computational Science and Engineering 2021 (Online, March 5, 2021).

Title: Learning optimal test functions for goal-oriented problems. Venue: Numerical and Applied Analysis Seminar, University of Nottingham (Online, March 31, 2021).

Title: Learning optimal test functions for goal-oriented FEM. Venue: Congreso de Matemática Capricornio, COMCA 2021 (Online, July 30, 2021).

Title: Regularization of rough linear functionals & Adaptivity. Venue: HPC, Deep Learning & Numerics in Geophysics, BCAM, Bilbao, Nov. 18, 2021.

2020

Title: A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations. Venue: Workshop on Simulation and Inversion Methods in Geophysics (online, 5-6 nov, 2020).

2019

Title: Projection in negative norms & the regularization of rough linear functionals. Venue: 6^th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2019), Concepción, Chile.

Title: Projection in negative norms & the regularization of rough linear functionals (Poster). Venue: Workshop on Computational Modeling and Numerical Analysis (WCMNA 2019), Florianópolis, Brasil.

Title: Minimización residual discreta para advección-reacción en espacios de Banach. Venue: XXXII Jornada Matemática de la Zona Sur, Punta Arenas, Chile.

Title: Why the residual minimization approach Works for stabilized dG formulations? Venue: IX Congreso Internacional de Matemática Aplicada y Computacional, Lima, Perú.

Title: A DG-based stabilized residual minimization technique. Venue: 4th Workshop on Minimum Residual & Least-Squares Finite Element Methods, Berlín, Alemania.

Title: A DG-based stabilized residual minimization technique. Venue: French Latin-American Conference on New Trends in Applied Mathematics, Santiago, Chile.

2018

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

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

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

Title: El método de Petrov-Galerkin y la evolución histórica de su constante de quasi-optimalidad. Venue: LIV Semana de la Matemática, Valparaíso, Chile.

Title: Minimización residual discreta para advección-reacción en espacios de Banach. Venue: LXXXVII Encuentro Anual Sociedad de Matemática de Chile, Rancagua, Chile.

2017

Title:On the hybridization of residual minimization problems in Banach Spaces. Venue: 3^rd Workshop on Minimum Residual & Least Squares FEM, Portland, USA.

Title:About the extension of the DPG method to Banach spaces. Venue: 27^th Biennial Numerical Analysis Conference, GLASGOW, UK.

Title:General 1.5D Approaches for Layered Media. Venue: Workshop on Geophysical Applications and HPC, Barcelona, Spain.

2016

Title:A Quadrature-Free Method for the Approximation of DC Fundamental Solutions in Layered Media. Venue: 4^th International Workshop on Multiphysics, Multiscale and Optimization Problems (M2OP4). BCAM, Bilbao, Spain.

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

Title:The nonlinear Petrov–Galerkin method in Banach spaces: yet another improvement of Babuska’s apriori error estimate. Venue: MAFELAP 2016, Brunel University, UK.

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

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

2015

Title: Optimal Discretization in Banach Spaces: a Nonlinear Petrov-Galerkin Approach. Venue: 2^nd Workshop on Minimum Residual and Least Squares Finite Element Methods Workshop. Delft, The Netherlands.

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

Title: Fast Simulation of Direct Current (DC) Borehole Measurements using Model Reduction. Venue: 1^st Pan American Congress on Computational Mechanics (PANACM 2015). Buenos Aires, Argentina.

2014

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

Title:Fast Simulation of Direct Current (DC) Borehole Measurements using Model Reduction. Venue: 3^rd International Workshop on Multiphysics, Multiscale and Optimization Problems. BCAM, Bilbao, Spain.

2013

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

Title: Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation. Venue: 1^st Workshop on Minimum Residual and Least Squares Finite Element Methods, Austin, Texas. USA.

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

Title: Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation. Venue: 14^th Conference “The Mathematics of Finite Elements and Applications” (MAFELAP 2013) Brunel University, Uxbridge, UK.

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

Title: Dispersion of the Lowest Order DPG Method for Acoustics. Venue: 4^th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2013), Concepción, Chile.

2012

Title: Borehole Acoustics Measurements: a Semi-Analytical Approach. Venue: 3^rd Valparaiso’s Mathematics and its Applications Days (V-MAD III), Valparaíso, Chile.

Title: Técnicas semi-analíticas para la simulación de registros sónicos descentrados. Venue: XI Jornadas de Mecánica Computacional, Valparaíso, Chile.

Title: Semi-analytical response of acoustic logging measurements due to multipole eccentered excitations. Venue: 2^nd Valparaiso’s Mathematics and its Applications Days (V- MAD II), Valparaíso, Chile.

2011

Title: An Update of the DPG Method for Wave Propagation Problems. Venue: La Serena Numérica I, 6^th Meeting of Numerical Analysis of Partial Differential Equations, La serena, Chile.

Title: Analysis of the DPG Method for the Hemholtz Equation in Multi-dimensions. Venue: LXXX Encuentro Anual, Sociedad Matemática de Chile, Los Andes, Chile.

Title: Semi-Analytical Response of Acoustic Logging Measurements due to Multipole Eccentered Excitations. Venue: X Jornadas de Mecánica Computacional, Santiago, Chile.

2010

Title: A Class of Discontinuous Petrov-Galerkin Methods: The Optimal Test Norm and Time- Harmonic Wave Propagation. Venue: Santiago Numérico II, 5^th Meeting of Numerical Analysis of Partial Differential Equations, Santiago, Chile.

Title: DPG for Waves. Venue: Spring 2010 Finite Element Rodeo, Southern Methodist University, Dallas, Texas, USA.

2009

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

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

2007

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

Title: The Helmholtz Equation in Unbounded Domains with Unbounded Frontier: Surface Waves. Venue: 2^nd Workshop of Numerical Analysis of Partial Differential Equations (WONAPDE 2007), Concepción, Chile

Direcciones de Tesis

Doctorado

Felipe Millar Vásquez (en curso). Programa de Doctorado en Matemáticas en Consorcio PUCV-UTFSM-UV.

Sergio Rojas Hernández. “ANALYTICAL AND SEMI-ANALYTICAL APPROACHES FOR ELECTROMAGNETIC PROBLEMS OVER LAYERED MEDIA.” Doctorado en Ciencias de la Ingeniería, Pontificia Universidad Católica de Chile, 2017.

Magister

Víctor Trujillo Radrigán, “A Multi-scale method for solving linear PDEs in layered media.” Pontificia Universidad Católica de Valparaíso. 2018.

Elizabeth Aviles Rieloff. “Compendium of Results for the Helmholtz Equation in Dierent Types of Domains”. Pontificia Universidad Católica de Valparaíso. 2009.

Gonzalo Espinoza Vásquez. “The Helmholtz equation in a half-plane with a simple local perturbation”. Pontificia Universidad Católica de Valparaíso. 2009.

Juan Herrera Tobar. “Effective computation of the Green’s function associated with two electromagnetic half-spaces”. Pontificia Universidad Católica de Valparaíso. 2009.

Cristina Valenzuela Donoso. “Numerical Computation of Eigenfrequencies by Integral Equations”. Pontificia Universidad Católica de Valparaíso. 2008.

Wilmer Bazán. “Numerical Computation of the DtN Operator for the Helmholtz Equation in a Perturbed Half-Space”. Pontificia Universidad Católica de Valparaíso. 2008.

Aldo Cabrera Bianchetti. “Computation of Resonant Frequencies at the interior of a Harbour by Applying and Simulating a Mathematical Model.Pontificia Universidad Católica de Valparaíso. 2007.