Rafael Vazquez
POSITIONS From 2011, researcher (permanent) at IMATI-CNR 2009-2011, researcher at IMATI-CNR EDUCATION Ph.D. in Mathematics, University of Santiago de Compostela, Spain, 2008. Advisors: Alfredo Bermúdez de Castro and Rafael Muñoz Sola Title: Contributions to the mathematical study of some problems in magnetohydrodynamics and induction heating Master degree in Applied Mathematics (Diploma de Estudios Avanzados) Advisors: Rafael Muñoz Sola and Carmen Rodriguez Iglesias Title: Introduction to the mathematical modelling of microwave heating Bachelor degree in Mathematics (Licenciatura), University of Santiago de Compostela, Spain, 2002.
Research Activity
- Numerical methods for PDEs - Isogeometric analysis - Finite element methods - Computational electromagnetism
Publications
2023, Journal article
Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains
C. Bracco, C. Giannelli, M. Kapl, and R. Vazquez
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structur...
CNR@People | DOI: 10.1142/S0218202523500434
2022, Journal article
An a posteriori error estimator for isogeometric analysis on trimmed geometries
A. Buffa, O. Chanon, and R. Vazquez
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes...
CNR@People | DOI: 10.1093/imanum/drac063
2022, Journal article
Analysis-aware defeaturing: Problem setting and a posteriori estimation
A. Buffa, O. Chanon, and R. Vazquez
Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aide...
CNR@People | DOI: 10.1142/S0218202522500099
2022, Journal article
Mathematical foundations of adaptive isogeometric analysis
A. Buffa, G. Gantner, C. Giannelli, D. Praetorius, and R. Vazquez
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of av...
CNR@People | DOI: 10.1007/s11831-022-09752-5
2022, Journal article
Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains
B. Kapidani, M. Merkel, S. Schoeps, and R. Vazquez
When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mo...
CNR@People | DOI: 10.1016/j.cma.2022.114949
2021, Journal article
BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines
C. Bracco, D. Cho, C. Giannelli, and R. Vazquez
We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) h...
CNR@People | DOI: 10.1016/j.cma.2021.113742
2020, Journal article
A minimal stabilization procedure for isogeometric methods on trimmed geometries
A. Buffa, R. Puppi, and R. Vazquez
Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After t...
CNR@People | DOI: 10.1137/19M1244718
2020, Journal article
Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
L. Coradello, P. Antolin, R. Vazquez, and A. Buffa
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic ...
CNR@People | DOI: 10.1016/j.cma.2020.112925
2020, Journal article
BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
D. Cho, Durkbin and R. Vazquez
We propose and analyse optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern & ...
CNR@People | DOI: 10.1093/imanum/dry032
2020, Journal article
Hierarchical B-spline complexes of discrete differential forms
J.A. Evans, M.A. Scott, K.M. Shepherd, D.C. Thomas, and R. Vazquez Hernandez
In this paper we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of proble...
CNR@People | DOI: 10.1093/imanum/dry077
2020, Journal article
Isogeometric analysis with C^1 hierarchical functions on planar two-patch geometries
C. Bracco, C. Giannelli, M. Kapl, and R. Vazquez
Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to ap...
CNR@People | DOI: 10.1016/j.camwa.2020.03.018
2020, Journal article
Isogeometric mortar coupling for electromagnetic problems
A. Buffa, J. Corno, C. de Falco, S. Schoeps, and R. Vazquez Hernandez
This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nedelec-type polynomial finite elements o...
CNR@People | DOI: 10.1137/18M1235211
2020, Journal article
Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
A. Buffa, J. Dolz, S. Kurz, S. Schops, R. Vazquez, and F. Wolf
We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t...
CNR@People | DOI: 10.1007/s00211-019-01079-x
2019, Journal article
Adaptive isogeometric methods with hierarchical splines: An overview
C. Bracco, A. Buffa, C. Giannelli, and R. Vazquez
We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates o...
CNR@People | DOI: 10.3934/dcds.2019010
2019, Journal article
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
M. Carraturo, C. Giannelli, A. Reali, and R. Vazquez
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably...
CNR@People | DOI: 10.1016/j.cma.2019.01.044
2018, Journal article
Algorithms for the implementation of adaptive isogeometric methods using hierarchical B-splines
E.M. Garau and R. Vazquez
In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening...
CNR@People | DOI: 10.1016/j.apnum.2017.08.006
2018, Journal article
An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations
R.N. Simpson, Z. Liu, R. Vázquez, and J.A. Evans
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments)...
CNR@People | DOI: 10.1016/j.jcp.2018.01.025
2018, Journal article
Refinement algorithms for adaptive isogeometric methods with hierarchical splines
C. Bracco, C. Giannelli, and R. Vazquez
The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeome...
CNR@People | DOI: 10.3390/axioms7030043
2016, Journal article
A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0
R. Vázquez
GeoPDEs (http://rafavzqz.github.io/geopdes) is an Octave/Matlab package for the solutionof partial differential equations with isogeometric analysis, first released in 2010. In thiswork we present in ...
CNR@People | DOI: 10.1016/j.camwa.2016.05.010
2016, Journal article
Unstructured spline spaces for isogeometric analysis based on spline manifolds
G. Sangalli, T. Takacs, and R. Vázquez
Based on Grimm and Hughes (1995) we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure which...
CNR@People | DOI: 10.1016/j.cagd.2016.05.004
2015, Journal article
Approximation estimates for isogeometric spaces in multipatch geometries
A. Buffa, R.H. Vázquez, G. Sangalli, and L. Beirão da Veiga
In this article, we extend this approximation theory developed in (Bazilevs et al., Math Models Methods Appl Sci 16 (2006), 1031-1090) and (Beirão da Veiga et al., Comput Methods Appl Mech Eng ...
CNR@People | DOI: 10.1002/num.21943
2014, Journal article
Isogeometric FEM Implementation of High-Order Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, and L. Di Rienzo
High-order surface impedance boundary conditions are introduced in a 2-D variational formulation in terms of magnetic vector potential. The formulation is then discretized using the isogeometric analy...
CNR@People | DOI: 10.1109/TMAG.2014.2298435
2014, Journal article
Isogeometric Finite Elements With Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, L. Di Rienzo, and D. Li
First- and second-order surface impedance boundary conditions are introduced in the harmonic 2-D variational formulation based on the magnetic vector potential. The problem is discretized with isogeom...
CNR@People | DOI: 10.1109/TMAG.2013.2280293
2014, Journal article
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm...
CNR@People | DOI: 10.1016/j.jcp.2013.08.015
2014, Journal article
Mathematical analysis of variational isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines...
CNR@People | DOI: 10.1017/S096249291400004X
2013, Journal article
Analysis-suitable T-Splines of arbitrary degree: Definition, linear independence and approximation properties
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence ...
CNR@People | DOI: 10.1142/S0218202513500231
2012, Journal article
NURBS-Based BEM Implementation of High-Order Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, and L. Di Rienzo
When implementing high-order surface impedance boundary conditions in collocation boundary element method (BEM) with constant or linear elements, difficulties arise due to the computation of the curva...
CNR@People | DOI: 10.1109/TMAG.2012.2204897
2011, Journal article
A thermo-electrical problem with a nonlocal radiation boundary condition
A. Bermúdez, D. Gómez, M.C. Muñiz, and R. Vázquez
A coupled problem arising in induction heating furnaces is studied. The thermal problem, which involves a change of phase, has a nonlocal radiation boundary condition. Convective heat transfer in the ...
CNR@People | DOI: 10.1016/j.mcm.2010.07.019
2011, Journal article
GeoPDEs: a research tool for Isogeometric Analysis of PDEs
C. de Falco, A. Reali, and R. Vázquez
GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of ...
CNR@People | DOI: 10.1016/j.advengsoft.2011.06.010
2011, Journal article
Isogeometric discrete differential forms in three dimensions
A. Buffa, J. Rivas, G. Sangalli, and R. Vázquez
The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010),...
CNR@People | DOI: 10.1137/100786708
2010, Journal article
Analysis of two stationary magnetohydrodynamics systems of equations including Joule heating
A. Bermúdez, R. Muñoz-Sola, and R. Vázquez
N/A
CNR@People | DOI: 10.1016/j.jmaa.2010.03.046
2010, Journal article
Isogeometric analysis for electromagnetic problems
R. Vázquez and A. Buffa
N/A
CNR@People | DOI: 10.1109/TMAG.2010.2044563
2010, Journal article
Isogeometric analysis in electromagnetics: B-splines approximation
A. Buffa, G. Sangalli, and R. Vázquez
We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in Hughes et al. (2005) [16], we propose an algo...
CNR@People | DOI: 10.1016/j.cma.2009.12.002
Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains
C. Bracco, C. Giannelli, M. Kapl, and R. Vazquez
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structur...
CNR@People | DOI: 10.1142/S0218202523500434
2022, Journal article
An a posteriori error estimator for isogeometric analysis on trimmed geometries
A. Buffa, O. Chanon, and R. Vazquez
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes...
CNR@People | DOI: 10.1093/imanum/drac063
2022, Journal article
Analysis-aware defeaturing: Problem setting and a posteriori estimation
A. Buffa, O. Chanon, and R. Vazquez
Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aide...
CNR@People | DOI: 10.1142/S0218202522500099
2022, Journal article
Mathematical foundations of adaptive isogeometric analysis
A. Buffa, G. Gantner, C. Giannelli, D. Praetorius, and R. Vazquez
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of av...
CNR@People | DOI: 10.1007/s11831-022-09752-5
2022, Journal article
Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains
B. Kapidani, M. Merkel, S. Schoeps, and R. Vazquez
When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mo...
CNR@People | DOI: 10.1016/j.cma.2022.114949
2021, Journal article
BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines
C. Bracco, D. Cho, C. Giannelli, and R. Vazquez
We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) h...
CNR@People | DOI: 10.1016/j.cma.2021.113742
2020, Journal article
A minimal stabilization procedure for isogeometric methods on trimmed geometries
A. Buffa, R. Puppi, and R. Vazquez
Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After t...
CNR@People | DOI: 10.1137/19M1244718
2020, Journal article
Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
L. Coradello, P. Antolin, R. Vazquez, and A. Buffa
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic ...
CNR@People | DOI: 10.1016/j.cma.2020.112925
2020, Journal article
BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
D. Cho, Durkbin and R. Vazquez
We propose and analyse optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern & ...
CNR@People | DOI: 10.1093/imanum/dry032
2020, Journal article
Hierarchical B-spline complexes of discrete differential forms
J.A. Evans, M.A. Scott, K.M. Shepherd, D.C. Thomas, and R. Vazquez Hernandez
In this paper we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of proble...
CNR@People | DOI: 10.1093/imanum/dry077
2020, Journal article
Isogeometric analysis with C^1 hierarchical functions on planar two-patch geometries
C. Bracco, C. Giannelli, M. Kapl, and R. Vazquez
Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to ap...
CNR@People | DOI: 10.1016/j.camwa.2020.03.018
2020, Journal article
Isogeometric mortar coupling for electromagnetic problems
A. Buffa, J. Corno, C. de Falco, S. Schoeps, and R. Vazquez Hernandez
This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nedelec-type polynomial finite elements o...
CNR@People | DOI: 10.1137/18M1235211
2020, Journal article
Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
A. Buffa, J. Dolz, S. Kurz, S. Schops, R. Vazquez, and F. Wolf
We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t...
CNR@People | DOI: 10.1007/s00211-019-01079-x
2019, Journal article
Adaptive isogeometric methods with hierarchical splines: An overview
C. Bracco, A. Buffa, C. Giannelli, and R. Vazquez
We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates o...
CNR@People | DOI: 10.3934/dcds.2019010
2019, Journal article
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
M. Carraturo, C. Giannelli, A. Reali, and R. Vazquez
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably...
CNR@People | DOI: 10.1016/j.cma.2019.01.044
2018, Journal article
Algorithms for the implementation of adaptive isogeometric methods using hierarchical B-splines
E.M. Garau and R. Vazquez
In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening...
CNR@People | DOI: 10.1016/j.apnum.2017.08.006
2018, Journal article
An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations
R.N. Simpson, Z. Liu, R. Vázquez, and J.A. Evans
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments)...
CNR@People | DOI: 10.1016/j.jcp.2018.01.025
2018, Journal article
Refinement algorithms for adaptive isogeometric methods with hierarchical splines
C. Bracco, C. Giannelli, and R. Vazquez
The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeome...
CNR@People | DOI: 10.3390/axioms7030043
2016, Journal article
A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0
R. Vázquez
GeoPDEs (http://rafavzqz.github.io/geopdes) is an Octave/Matlab package for the solutionof partial differential equations with isogeometric analysis, first released in 2010. In thiswork we present in ...
CNR@People | DOI: 10.1016/j.camwa.2016.05.010
2016, Journal article
Unstructured spline spaces for isogeometric analysis based on spline manifolds
G. Sangalli, T. Takacs, and R. Vázquez
Based on Grimm and Hughes (1995) we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure which...
CNR@People | DOI: 10.1016/j.cagd.2016.05.004
2015, Journal article
Approximation estimates for isogeometric spaces in multipatch geometries
A. Buffa, R.H. Vázquez, G. Sangalli, and L. Beirão da Veiga
In this article, we extend this approximation theory developed in (Bazilevs et al., Math Models Methods Appl Sci 16 (2006), 1031-1090) and (Beirão da Veiga et al., Comput Methods Appl Mech Eng ...
CNR@People | DOI: 10.1002/num.21943
2014, Journal article
Isogeometric FEM Implementation of High-Order Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, and L. Di Rienzo
High-order surface impedance boundary conditions are introduced in a 2-D variational formulation in terms of magnetic vector potential. The formulation is then discretized using the isogeometric analy...
CNR@People | DOI: 10.1109/TMAG.2014.2298435
2014, Journal article
Isogeometric Finite Elements With Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, L. Di Rienzo, and D. Li
First- and second-order surface impedance boundary conditions are introduced in the harmonic 2-D variational formulation based on the magnetic vector potential. The problem is discretized with isogeom...
CNR@People | DOI: 10.1109/TMAG.2013.2280293
2014, Journal article
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm...
CNR@People | DOI: 10.1016/j.jcp.2013.08.015
2014, Journal article
Mathematical analysis of variational isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines...
CNR@People | DOI: 10.1017/S096249291400004X
2013, Journal article
Analysis-suitable T-Splines of arbitrary degree: Definition, linear independence and approximation properties
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence ...
CNR@People | DOI: 10.1142/S0218202513500231
2012, Journal article
NURBS-Based BEM Implementation of High-Order Surface Impedance Boundary Conditions
R. Vázquez, A. Buffa, and L. Di Rienzo
When implementing high-order surface impedance boundary conditions in collocation boundary element method (BEM) with constant or linear elements, difficulties arise due to the computation of the curva...
CNR@People | DOI: 10.1109/TMAG.2012.2204897
2011, Journal article
A thermo-electrical problem with a nonlocal radiation boundary condition
A. Bermúdez, D. Gómez, M.C. Muñiz, and R. Vázquez
A coupled problem arising in induction heating furnaces is studied. The thermal problem, which involves a change of phase, has a nonlocal radiation boundary condition. Convective heat transfer in the ...
CNR@People | DOI: 10.1016/j.mcm.2010.07.019
2011, Journal article
GeoPDEs: a research tool for Isogeometric Analysis of PDEs
C. de Falco, A. Reali, and R. Vázquez
GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of ...
CNR@People | DOI: 10.1016/j.advengsoft.2011.06.010
2011, Journal article
Isogeometric discrete differential forms in three dimensions
A. Buffa, J. Rivas, G. Sangalli, and R. Vázquez
The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010),...
CNR@People | DOI: 10.1137/100786708
2010, Journal article
Analysis of two stationary magnetohydrodynamics systems of equations including Joule heating
A. Bermúdez, R. Muñoz-Sola, and R. Vázquez
N/A
CNR@People | DOI: 10.1016/j.jmaa.2010.03.046
2010, Journal article
Isogeometric analysis for electromagnetic problems
R. Vázquez and A. Buffa
N/A
CNR@People | DOI: 10.1109/TMAG.2010.2044563
2010, Journal article
Isogeometric analysis in electromagnetics: B-splines approximation
A. Buffa, G. Sangalli, and R. Vázquez
We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in Hughes et al. (2005) [16], we propose an algo...
CNR@People | DOI: 10.1016/j.cma.2009.12.002
2016, Essay or book chapter
An introduction to the numerical analysis of isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This paper gives an introduction to isogeometric methods from a mathematical point of view, with special focus on some theoretical results that arepart of the mathematical foundation of the method. Th...
CNR@People | DOI: 10.1007/978-3-319-32146-2_1
2016, Essay or book chapter
An introduction to the numerical analysis of isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This paper gives an introduction to isogeometric methods from a mathematical point of view, with special focus on some theoretical results that are part of the mathematical foundation of the method. T...
CNR@People | DOI: 10.1007/978-3-319-42309-8_3
2011, Essay or book chapter
Numerical Modelling of Industrial Induction
A. Bermúdez, D. Gómez, M.C. Muñiz, P. Salgado, and R. Vázquez
N/A
CNR@People | DOI: 10.5772/562
An introduction to the numerical analysis of isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This paper gives an introduction to isogeometric methods from a mathematical point of view, with special focus on some theoretical results that arepart of the mathematical foundation of the method. Th...
CNR@People | DOI: 10.1007/978-3-319-32146-2_1
2016, Essay or book chapter
An introduction to the numerical analysis of isogeometric methods
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
This paper gives an introduction to isogeometric methods from a mathematical point of view, with special focus on some theoretical results that are part of the mathematical foundation of the method. T...
CNR@People | DOI: 10.1007/978-3-319-42309-8_3
2011, Essay or book chapter
Numerical Modelling of Industrial Induction
A. Bermúdez, D. Gómez, M.C. Muñiz, P. Salgado, and R. Vázquez
N/A
CNR@People | DOI: 10.5772/562
2015, Conference proceedings
Dual compatible splines on non tensor product meshes
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce the concept of dual compatible splines on non tensor product meshes, study the properties of this class and discuss their possibleuse within the isogeometric framework. We s...
CNR@People
2014, Conference proceedings
Dual Compatible Splines on Nontensor Product Meshes
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce the concept of dual compatible (DC) splines on nontensor product meshes, study the properties of this class, and discuss their possible use within the isogeometric framework...
CNR@People | DOI: 10.1007/978-3-319-06404-8_2
2014, Conference proceedings
Isogeometric analysis for electromagnetic scattering problems
A. Buffa and R. Vázquez
This paper is about the solution of electromagneticscattering, when the scatterer is a conductor. The related equa-tions are of integro-differential type and their fast discretizationis a real challen...
CNR@People | DOI: 10.1109/NEMO.2014.6995712
2011, Conference proceedings
Contributions to the mathematical study of some problems in magnetohydrodynamics and induction heating
R. Vázquez Hernández
The aim of the work is to numerically simulate an induction furnace in order to understand its behaviorand to predict its performance under the variation of some parameters. An axisymmetric mathematic...
CNR@People
2010, Conference proceedings
Isogeometric analysis in electromagnetism: analysis and testing
R. Vázquez (joint with A. Buffa and G. Sangalli)
Isogeometric Analysis (IGA) is a method for the discretization of partial differentialequations, that was recently introduced by T.J.R. Hughes et al. in [7]. Theconcept of IGA was born with the aim of...
CNR@People
2009, Conference proceedings
Numerical solution of Maxwell's equations using B-splines
A. Buffa and R. Vázquez
N/A
CNR@People
Dual compatible splines on non tensor product meshes
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce the concept of dual compatible splines on non tensor product meshes, study the properties of this class and discuss their possibleuse within the isogeometric framework. We s...
CNR@People
2014, Conference proceedings
Dual Compatible Splines on Nontensor Product Meshes
L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez
In this paper we introduce the concept of dual compatible (DC) splines on nontensor product meshes, study the properties of this class, and discuss their possible use within the isogeometric framework...
CNR@People | DOI: 10.1007/978-3-319-06404-8_2
2014, Conference proceedings
Isogeometric analysis for electromagnetic scattering problems
A. Buffa and R. Vázquez
This paper is about the solution of electromagneticscattering, when the scatterer is a conductor. The related equa-tions are of integro-differential type and their fast discretizationis a real challen...
CNR@People | DOI: 10.1109/NEMO.2014.6995712
2011, Conference proceedings
Contributions to the mathematical study of some problems in magnetohydrodynamics and induction heating
R. Vázquez Hernández
The aim of the work is to numerically simulate an induction furnace in order to understand its behaviorand to predict its performance under the variation of some parameters. An axisymmetric mathematic...
CNR@People
2010, Conference proceedings
Isogeometric analysis in electromagnetism: analysis and testing
R. Vázquez (joint with A. Buffa and G. Sangalli)
Isogeometric Analysis (IGA) is a method for the discretization of partial differentialequations, that was recently introduced by T.J.R. Hughes et al. in [7]. Theconcept of IGA was born with the aim of...
CNR@People
2009, Conference proceedings
Numerical solution of Maxwell's equations using B-splines
A. Buffa and R. Vázquez
N/A
CNR@People
2011, Software
GeoPDEs: an Octave/Matlab library for Isogeometric Analysis
C. de Falco, A. Reali, and R. Vázquez
GeoPDEs is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the disc...
CNR@People | Link
GeoPDEs: an Octave/Matlab library for Isogeometric Analysis
C. de Falco, A. Reali, and R. Vázquez
GeoPDEs is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the disc...
CNR@People | Link
