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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SMA-ENS
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