Rojas Hernández, Sergio

Research Interests

Numerical Analysis, Scientific Computing & Mathematical Modeling

Brief description

I’m primarily interested in numerical analysis, scientific computing, and mathematical modeling. My research endeavors are centered on developing and analyzing residual minimization-based numerical methods to solve complex Partial Differential Equations (PDEs). These methodologies integrate various state-of-the-art approaches such as Finite Element (FE), Discontinuous Galerkin (DG), Hybridizable Discontinuous Galerkin (HDG), Minimum-Residual (MinRes), and Variational Physics-Informed Neural Networks (VPINNs) methods. My professional network includes world-class research centers like the Basque Center for Applied Mathematics (BCAM-Spain), the University of Nottingham (UK), Monash University (Australia), and the AGH University of Science and Technology (Poland).

Webpages

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IMA Numerics

Articles

1. S. Rojas, P. Maczuga, J. Muñoz-Matute, D. Pardo and M. Paszyński. Robust Variational-Physics-Informed Neural Networks. Computer Methods in Applied Mechanics and Engineering, 425, Paper No. 116904, 2024.
2. M. Skotniczny, A. Paszyńska, S. Rojas, and M. Paszyński: Complexity of direct and iterative solvers on space-time formulations versus time-marching schemes for h-refined grids towards singularities. Journal of Computational Science, 77, Paper No. 102216, 2024.
3. J. Trynda, M. Woźniak, and S. Rojas: A study of concurrent multi-frontal solvers for modern massively parallel architectures. Journal of Computational Science, 75, Paper No. 102184, 2024.
4. J. G. Hasbani, P. Sepúlveda, I. Muga, V. M. Calo, and S. Rojas: Adaptive stabilized finite elements via residual minimization onto bubble enrichments. Computers and Mathematics with Applications, 151, pages 1-11, 2023.
   
5. I. Muga, S. Rojas, and P. Vega: An adaptive superconvergent mixed finite element method based on local residual minimization. SIAM Journal on Numerical Analysis, 61, pages 2084-2105, 2023.
6. T. Służalec, R. Grzeszczuk, S. Rojas, W. Dzwinel, and M. Paszyński: Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction. Computers and Mathematics with Applications, 142, pages 157–174, 2023.
7. M. Woźniak, A. Szyszka, and S. Rojas. A study of efficient concurrent integration methods of B-Spline basis functions in IGA-FEM. Journal of Computational Science, 64, Paper No. 101857, 2022.
8. F. Kyburg, S. Rojas, and V. M. Calo. Incompressible flow modeling using an adaptive stabilized finite element method based on residual minimization. International Journal for Numerical Methods in Engineering, 123, 1717-1735, 2022.
9. F. Millar, I. Muga, S. Rojas, and K. G. van der Zee. Projection in negative norms and the regularization of rough linear functionals.  Numerische Mathematik, 150, 1087-1121, 2022.
10. R. J. Cier, T. Poulet, S. Rojas, M. Veveakis, and V. M. Calo. Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials. International Journal for Numerical Methods in Engineering, 122, 6234-6252, 2021.
11. R. J. Cier, S. Rojas, and V. M. Calo. Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection–diffusion–reaction problems. Computer Methods in Applied Mechanics and Engineering, 385, Paper No. 114027, 2021.
12. S. Rojas,  D. Pardo, P. Behnoudfar, and V. M. Calo. Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm.  Computer Methods in Applied Mechanics and Engineering, 377, Paper No. 113686, 2021.
13. M. Łoś, S. Rojas, M. Paszyński,  I. Muga, and V. M. Calo. DGIRM: Discontinuous Galerkin based Isogeometric Residual Minimization for the Stokes problem.  Journal of Computational Science, 50, Paper No. 101306, 2021.
14. R. J. Cier,  S. Rojas, and V. M. Calo. A nonlinear weak constraint enforcement method for advection-dominated diffusion problems. Mechanics Research Communications, 112, Paper No. 103602, 2021.
15. V. M. Calo, A. Ern, I. Muga, and S. Rojas. An Adaptive Stabilized Conforming Finite Element Method via Residual Minimization on Dual Discontinuous Galerkin Norms. Computer Methods in Applied Mechanics and Engineering, 363, Paper No. 112891, 2020.
16. R. Rebolledo, S. A. Navarrete, S. Kéfi, S. Rojas, and P. A. Marquet. An Open-System Approach to Complex Biological Networks. SIAM Journal on Applied Mathematics, 79(2), 619–640. 2019.
17. S. Rojas, I. Muga, and C. Jerez-Hanckes. The outgoing time-harmonic electromagnetic wave in a half-space with non-absorbing impedance boundary condition.  ESAIM: M2AN, 53(1), 325-350, 2019.
    
18. S. Rojas, R. Hein, and M. Durán. On an equivalent representation of the Green’s function for the Helmholtz problem in a non-absorbing impedance half-plane. Computers and Mathematics with Applications, 75(11), 3903–3917, 2018.
19. M. Shahriari, S. Rojas, D. Pardo, Á. Rodríguez-Rozas, A. B. Shaaban, V. M. Calo, and I. Muga. A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements. Geosciences, 8(6), pages 225, 2018.
20. S. Rojas, I. Muga, and D. Pardo. A quadrature-free method for simulation and inversion of 1.5D direct current (DC) borehole measurements. Computational Geosciences, 20(6), pages 1301-1318, 2016.

Submitted preprints

• C. Uriarte, M. Bastidas, D. Pardo, J. M. Taylor, S. Rojas. Optimizing Variational Physics-Informed Neural Networks Using Least Squares (2024). arXiv:2407.20417 [math.NA].
• L. Camargo, S. Rojas, and P. Vega. Minimum-residual a posteriori error estimates for a hybridizable discontinuous Galerkin discretization of the Helmholtz equation (2023). arXiv:2304.00418 [math.NA].

Research project Grants

• 2024 – 2028: ANID Fondecyt No 1240643: Stabilized discretizations via residual minimization on discrete dual norms. Principal Investigator.
• 2021 – 2024: ANID Fondecyt No 3210009: Adaptive Stabilized Finite Element Methods for Nonlinear and Higher Order Problems. Principal Investigator.
• 2018 – 2023: RISE Horizon 2020 European Project MATHROCKS (Ref. Nr. 777778). Associated Researcher.

Cursos

2023

Pregrado

• IMA1303-01 Métodos Numéricos y Ecuaciones Diferenciales
• MAT499-02 Seminario
• IMAP2017-01 Introducción a la Modelación Matemática (docencia compartida)

Magister en Simulación Computacional

• MSC001-01 Introducción a la Modelación Matemática (docencia compartida)
• MSC002-01 Métodos Numéricos (docencia compartida)
• MSC003-01 Taller de Resolución de Problemas (docencia compartida)

Doctorado en Matemáticas

• IMA3103-11 Seminario de Investigación 1

2022

Pregrado

• IMA1303-02 Métodos Numéricos y Ecuaciones Diferenciales
• IMA1404-01 Análisis Numérico

2021

Pregrado

• IMA1303-02 Métodos Numéricos y Ecuaciones Diferenciales
• IMA1203-01 Programación