On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems
SIAM Journal on Numerical Analysis
Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
SIAM Journal on Numerical Analysis
ACM SIGGRAPH 2003 Papers
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
SIAM Journal on Numerical Analysis
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Discrete Compactness for the $p$-Version of Discrete Differential Forms
SIAM Journal on Numerical Analysis
GeoPDEs: A research tool for Isogeometric Analysis of PDEs
Advances in Engineering Software
Discrete spectrum analyses for various mixed discretizations of the Stokes eigenproblem
Computational Mechanics
Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution
Journal of Computational Physics
Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations
Journal of Computational Physics
Computer Aided Geometric Design
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
Journal of Computational Physics
Journal of Computational Physics
High order geometric methods with exact conservation properties
Journal of Computational Physics
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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), pp. 1143-1152]. The method is based on the construction of suitable B-spline spaces such that they verify a De Rham diagram. Its main advantages are that the geometry is described exactly with few elements, and the computed solutions are smoother than those provided by finite elements. In this paper we develop the theoretical background to the approximation of vector fields in IGA. The key point of our analysis is the definition of suitable projectors that render the diagram commutative. The theory is then applied to the numerical approximation of Maxwell source problems and eigenproblems, and numerical results showing the good behavior of the scheme are also presented.