Publications
Submitted manuscripts
J. M. Taylor, M. Bastidas, D. Pardo, and I. Muga: Deep Fourier Residual method for solving time-harmonic Maxwell's equations (2023). arXiv:2305.09578 [math.NA]
I. Brevis, I. Muga, D. Pardo, O. Rodríguez, and K. G. van der Zee: Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach (2023). arXiv:2304.01722 [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]
Papers in refereed journals
2024
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.
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.
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.
2023
M. Łos, P. Sepúlveda and M. Paszyński: Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem, Computers & Mathematics with Applications, accepted for publication, 2023.
J. G. Hasbani, P. Sepúlveda, I. Muga, V. M. Calo, and S. Rojas: Adaptive stabilized finite elements via residual minimization onto bubble enrichments. Computers & Mathematics with Applications, 151, pages 1-11, 2023.
T. Chaumont-Frelet and P. Vega: Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell’s equations. SIAM Journal on Numerical Analysis, accepted for publication, 2023.
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, 2084-2105, 2023.
M. Łos, P. Sepúlveda, M. Dobija, and A. Paszyńska: Least-squares space-time formulation for advection-diffusion problem with efficient adaptive solver based on matrix compression. Computational Science – ICCS 2023. Part II, 547-560. Lecture Notes in Computer Science, vol. 14074. Springer, Cham, 2023.
C. Uriarte, J. M. Taylor, D. Pardo, O. A. Rodríguez and P. Vega: Memory-based Monte Carlo integration for solving partial differential equations using neural networks. Computational Science – ICCS 2023. Part II, 509-516. Lecture Notes in Computer Science, vol. 14074. Springer, Cham, 2023.
T. Służalec, M. Dobija, A. Paszyńska, I. Muga, M. Łoś, and M. Paszyński: Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices. Computer Methods in Applied Mechanics and Engineering, 411, Paper No. 116073, 2023.
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, 157-174 , 2023.
P. Sepúlveda, I. Muga, N. Sáinz, R. G. Rojas, S. Ossandón: Nanoionics from a quantum mechanics point of view: Mathematical modeling and numerical simulation. Computer Methods in Applied Mechanics and Engineering, 407, Paper No. 115926, 2023.
C. Uriarte, D. Pardo, I. Muga, and J. Muñoz-Matute: A deep double Ritz method (D²RM) for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 405, Paper No. 115892, 2023.
J. M. Taylor, D. Pardo, and I. Muga: A deep Fourier residual method for solving PDEs using neural networks. Computer Methods in Applied Mechanics and Engineering, 405, Paper No. 115850, 2023.
2022
I. Brevis, I. Muga, and K. G. van der Zee. Neural control of discrete weak formulations: Galerkin, least-squares and minimal-residual methods with quasi-optimal weights. Computer Methods in Applied Mechanics and Engineering, 402, Paper No. 115716, 2022.
A. Erdozain, I. Muga, V. Péron, G. Pinochet. Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing. GEM-International Journal on Geomathematics, 13, 1-20, 2022.
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.
T. Chaumont-Frelet and P. Vega. Frequency-explicit a posteriori error estimates for finite element discretizations of Maxwell’s equations. SIAM Journal on Numerical Analysis, 60, 1774-1798, 2022.
T. Chaumont-Frelet and P. Vega. Frequency-explicit approximability estimates for finite element discretizations of Maxwell’s equations. Calcolo, 59, Paper No. 22, 2022.
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.
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.
2021
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.
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.
T. Chaumont-Frelet, S. Lanteri, and P. Vega. A posteriori error estimates for finite element discretizations of Maxwell’s equations coupled with a non-local hydrodynamic Drude model. Computer Methods in Applied Mechanics and Engineering, 385, Paper No. 114002, 2021.
M. Łoś, J. Muñoz-Matute, I. Muga, and M. Paszyński. Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier–Stokes problems. Computers and Mathematics with Applications, 95, 200-214, 2021.
I. Brevis, I. Muga, and K. G. van der Zee. A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations. Computers and Mathematics with Applications, 95, 186-199, 2021.
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.
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.
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.
V. M. Calo, M. Łoś, Q. Deng, I. Muga, and M. Paszyński. Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems. Computers Methods in Applied Mechanics and Engineering, 373, Paper No. 113214 , 2021.
2020
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.
M. Łoś, J. Muñoz-Matute, I. Muga, and M. Paszyński. Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems. Computers and Mathematics with Applications, 79(2), pages 213-229 , 2020.
I. Muga, and K. G. van der Zee. Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov-Galerkin, and Monotone Mixed Methods. SIAM J. Numer. Anal., 58(6), pages 3406-3426, 2020.
2019
I. Brevis, Á. Rodríguez-Rozas, J. H. Ortega, and D. Pardo. Source Time Reversal (STR) Method for Linear Elasticity, Computers and Mathematics with Applications, 77(5), 1358-1375, 2019.
J. Gopalakrishnan and P. Sepúlveda. A space-time DPG method for the wave equation in multiple dimensions. In collection “Space-Time Methods: Applications to Partial Differential Equations” , 117-140, 2019.
P. Houston, I. Muga, S. Roggendorf, and K. G. van der Zee. The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method. Comput. Methods Appl. Math., 19(3), 503–522, 2019.
I. Muga, M. J. W. Tyler, and K. G. van der Zee. The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces. Comput. Methods Appl. Math., 19(3), 557-579.
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.
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.
2018
V. Darrigrand, Á. Rodríguez‐Rozas, I. Muga, D. Pardo, A. Romkes, and S. Prudhomme. Goal‐oriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation. Int. J. Numer. Meth. Engng., 113(1), 22–42, 2018.
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 & Mathematics with Applications, 75(11), 3903–3917, 2018.
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.
K. Voronin, C. S. Lee, M. Neumüller, P. Sepulveda, and P. Vassilevski. Space-time discretizations using constrained first-order system least-squares (CFOSLS). Journal of Computational Physics, 373, pages 863-876, 2018.
2017
I. Brevis, J. H. Ortega, and D. Pardo. A Source Time Reversal Method for Seismicity Induced by Mining, Inverse Problems and Imaging, vol. 10(1), 25-45, 2017.
L. Demkowicz, J. Gopalakrishnan, S. Nagaraj, and P. Sepúlveda. A Spacetime DPG Method for the Schrödinger Equation. SIAM J. Numer. Anal., 55(4), pages 1740–1759, 2017.
2016
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.
2015
V. Darrigrand, D. Pardo, and I. Muga. Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation. Computers and Mathematics with Applications, 69(9), pages 964-979, 2015.
J. Gopalakrishnan, P. Monk, and P. Sepúlveda. A tent pitching scheme motivated by Friedrichs theory. Computers and Mathematics with Applications, 70(5), pages 1114-1135, 2015.
F. Millar and D. Mora. A finite element method for the buckling problem of simply supported Kirchhoff plates. Journal of Computational and Applied Mathematics, 286(1), pages 68-78, 2015.
I. Muga, D. Pardo, P. J. Matuszyk, C. Torres-Verdín. Semi-analytical response of acoustic logging measurements in frequency domain. Computers and Mathematics with Applications, 70(4), pages 314-329, 2015.
2014
J. Gopalakrishnan, I. Muga, and N. Olivares. Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation. SIAM J. Sci. Comput., 36(1), pages A20–A39, 2014.
2013
D. Pardo, P. J. Matuszyk, C. Torres-Verdin, A. Mora, I. Muga, and V. M. Calo. Influence of borehole-eccentered tools on wireline and logging-while-drilling sonic logging measurements. Geophysical Prospecting, 61(s1), pages 268-283, 2013.
2012
L. Demkowicz, J. Gopalakrishnan, I. Muga, and J. Zitelli. Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation. Comput. Methods Appl. Mech. Engrg., 213–216, pages 126-138, 2012.
2011
M. Durán, I. Muga, and J.-C. Nédélec. The outgoing time-harmonic elastic wave in a half-plane with free boundary. SIAM Journal on Applied Mathematics, 71(2), pages 443-464, 2011.
D. Pardo, P. J. Matuszyk, I. Muga, C. Torres-Verdin, A. Mora, and V. M. Calo. Simulation of wireline sonic logging measurements acquired with Borehole- Eccentered tools using a high-order adaptive finite-element method. Journal of Computational Physics, 230(16), pages 6320-6333, 2011.
J. Zitelli, I. Muga, L. Demkowicz, J. Gopalakrishnan, D. Pardo, and V. M. Calo. A class of discontinuous Petrov-Galerkin methods. Part IV: the optimal test norm and time-harmonic wave propagation in 1D. Journal of Computational Physics, 230(7), pages 2406-2432, 2011.