Rafael Vazquez Hernandez
EPFL SB MATH MNS
MA C2 563 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Web site: Site web: https://mns.epfl.ch/
+41 21 693 55 09
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Web site: Site web: https://sma.epfl.ch/
Publications
Publications Infoscience
Publications
Journal Articles
2023
High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations
2023-02-09. DOI : 10.48550/arXiv.2302.04979.2022
Adaptive analysis-aware defeaturing
2022-12-10. DOI : 10.48550/arXiv.2212.05183.High Order Geometric Methods With Splines: An Analysis of Discrete Hodge-Star Operators
SIAM Journal on Scientific Computing. 2022-11-22. DOI : 10.1137/22M1481762.An a posteriori error estimator for isogeometric analysis on trimmed geometries
Ima Journal Of Numerical Analysis. 2022-10-27. DOI : 10.1093/imanum/drac063.Torque Computation With the Isogeometric Mortar Method for the Simulation of Electric Machines
Ieee Transactions On Magnetics. 2022-09-01. DOI : 10.1109/TMAG.2022.3186247.Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains
Computer Methods In Applied Mechanics And Engineering. 2022-05-15. DOI : 10.1016/j.cma.2022.114949.Analysis-aware defeaturing: Problem setting and a posteriori estimation
Mathematical Models and Methods in Applied Sciences. 2022-01-31. DOI : 10.1142/S0218202522500099.2021
BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines
Computer Methods In Applied Mechanics And Engineering. 2021-06-01. DOI : 10.1016/j.cma.2021.113742.2020
Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries
Computers & Mathematics with Applications. 2020-12-01. DOI : 10.1016/j.camwa.2020.03.018.A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries
SIAM Journal on Numerical Analysis. 2020-09-30. DOI : 10.1137/19M1244718.Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
Computer Methods in Applied Mechanics and Engineering. 2020-02-29. DOI : 10.1016/j.cma.2020.112925.Isogeometric Mortar Coupling for Electromagnetic Problems
SIAM Journal on Scientific Computing. 2020. DOI : 10.1137/18M1235211.Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
Numerische Mathematik. 2020. DOI : 10.1007/s00211-019-01079-x.Hierarchical B-spline complexes of discrete differential forms
IMA Journal of Numerical Analysis. 2020. DOI : 10.1093/imanum/dry077.BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
IMA Journal of Numerical Analysis. 2020. DOI : 10.1093/imanum/dry032.2019
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
Computer Methods In Applied Mechanics And Engineering. 2019-05-01. DOI : 10.1016/j.cma.2019.01.044.Adaptive Isogeometric Methods With Hierarchical Splines: An Overview
Discrete And Continuous Dynamical Systems. 2019-01-01. DOI : 10.3934/dcds.2019010.2018
Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines
Axioms. 2018-09-01. DOI : 10.3390/axioms7030043.An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations
Journal of Computational Physics. 2018. DOI : 10.1016/j.jcp.2018.01.025.Algorithms for the implementation of adaptive isogeometric methods using hierarchical B-splines
Applied Numerical Mathematics. 2018. DOI : 10.1016/j.apnum.2017.08.006.2016
A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0
Computers and Mathematics with Applications. 2016. DOI : 10.1016/j.camwa.2016.05.010.Unstructured spline spaces for isogeometric analysis based on spline manifolds
Computer Aided Geometric Design. 2016. DOI : 10.1016/j.cagd.2016.05.004.2015
Approximation estimates for isogeometric spaces in multipatch geometries
Numerical Methods for Partial Differential Equations. 2015. DOI : 10.1002/num.21943.2014
Isogeometric Finite Elements With Surface Impedance Boundary Conditions
IEEE Transactions on Magnetics. 2014. DOI : 10.1109/TMAG.2013.2280293.Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
Journal of Computational Physics. 2014. DOI : 10.1016/j.jcp.2013.08.015.Mathematical analysis of variational isogeometric methods
Acta Numerica. 2014. DOI : 10.1017/S096249291400004X.2013
Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties
Mathematical Models and Methods in Applied Sciences. 2013. DOI : 10.1142/S0218202513500231.2012
NURBS-Based BEM Implementation of High-Order Surface Impedance Boundary Conditions
IEEE Transactions on Magnetics. 2012. DOI : 10.1109/TMAG.2012.2204897.2011
Isogeometric discrete differential forms in three dimensions
SIAM Journal on Numerical Analysis. 2011. DOI : 10.1137/100786708.A thermo-electrical problem with a nonlocal radiation boundary condition
Mathematical and Computer Modelling. 2011. DOI : 10.1016/j.mcm.2010.07.019.2010
Isogeometric Analysis for Electromagnetic Problems
IEEE Transactions on Magnetics. 2010. DOI : 10.1109/TMAG.2010.2044563.Isogeometric analysis in electromagnetics: B-splines approximation
Computer Methods in Applied Mechanics and Engineering. 2010. DOI : 10.1016/j.cma.2009.12.002.Analysis of two stationary magnetohydrodynamics systems of equations including Joule heating
Journal of Mathematical Analysis and Applications. 2010. DOI : 10.1016/j.jmaa.2010.03.046.2009
Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace
Applied Numerical Mathematics. 2009. DOI : 10.1016/j.apnum.2008.12.005.A formulation of the eddy current problem in the presence of electric ports
Numerische Mathematik. 2009. DOI : 10.1007/s00211-009-0241-7.Iterative methods for the saddle-point problem arising from the H_C/ E_I formulation of the eddy current problem
SIAM Journal on Scientific Computing. 2009. DOI : 10.1137/080722278.Conference Papers
2016
An introduction to the numerical analysis of isogeometric methods
2016. XVI ‘Jacques-Louis Lions’ Spanish-French School on Numerical Simulation in Physics and Engineering, Pamplona (Navarra, Spain), September 2014. p. 3-69. DOI : 10.1007/978-3-319-32146-2_1.2015
Dual compatible splines on non tensor product meshes
2015. ICIAM 2015, Beijing, China, August 10-14, 2015. p. 41-63.Reviews
2022
Mathematical Foundations of Adaptive Isogeometric Analysis
Archives Of Computational Methods In Engineering. 2022-09-30. DOI : 10.1007/s11831-022-09752-5.Theses
2022
Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-8472.Book Chapters
2014
Dual compatible splines on nontensor product meshes
Approximation theory XIV: San Antonio 2013; Springer, Cham, 2014. p. 15-26.2008
Numerical simulation of induction furnaces for silicon purification
Progress in industrial mathematics at ECMI 2006; Springer, Berlin, 2008. p. 48-65.Working Papers
2022
MATHICSE Technical Report : Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains
2022-04-212021
MATHICSE Technical Report : Mathematical Foundations of Adaptive Isogeometric Analysis
2021-07-05MATHICSE Technical Report : Analysis-aware defeaturing: problem setting and a posteriori estimation
2021-04-212019
MATHICSE Technical Report: Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
2019-10-09Isogeometric Mortar Coupling for Electromagnetic Problems
2019-01-012018
ADAPTIVE ISOGEOMETRIC METHODS WITH HIERARCHICAL SPLINES: AN OVERVIEW
20182017
MATHICSE Technical Report : Hierarchical B-spline Complexes of Discrete Differential Forms
2017-08-04Enseignement & Phd
Enseignement
Mathematics
A dirigé les thèses EPFL de
Puppi Riccardo ,Cours
Numerical analysis and computational mathematics
Le cours est une introduction au calcul scientifique. Plusieurs méthodes numériques sont présentées pour la solution au ordinateur de problèmes mathématiques dans différentes applications. Le logiciel MATLAB est utilisé pour résoudre les problèmes et vérifier les propriétés théoriques des méthodes.