The NURBS book
Edge Elements on Anisotropic Meshes and Approximation of the Maxwell Equations
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
Algebraic convergence for anisotropic edge elements in polyhedral domains
Numerische Mathematik
Whitney Forms of Higher Degree
SIAM Journal on Numerical Analysis
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Some estimates for h–p–k-refinement in Isogeometric Analysis
Numerische Mathematik
GeoPDEs: A research tool for Isogeometric Analysis of PDEs
Advances in Engineering Software
On the instability in the dimension of splines spaces over T-meshes
Computer Aided Geometric Design
Converting an unstructured quadrilateral mesh to a standard T-spline surface
Computational Mechanics
On linear independence of T-spline blending functions
Computer Aided Geometric Design
Isogeometric Discrete Differential Forms in Three Dimensions
SIAM Journal on Numerical Analysis
An Arbitrary High-Order Spline Finite Element Solver for the Time Domain Maxwell Equations
Journal of Scientific Computing
Polynomial splines over locally refined box-partitions
Computer Aided Geometric Design
Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations
Journal of Computational Physics
Linear independence of the blending functions of T-splines without multiple knots
Expert Systems with Applications: An International Journal
| Hi-index | 31.45 |
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, we map them on domains which are (piecewise) spline or NURBS geometries. We analyze their geometric and topological structure, as related to the connectivity of the underlying mesh, and we present degrees of freedom together with their physical interpretation. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.