Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 257, Issue -, Pages 1291-1320Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.08.015
Keywords
Maxwell equations; De Rham diagram; Exact sequences; Isogeometric methods; Splines; T-splines
Funding
- European Research Council
- Italian MIUR through the FIRB [RBFR08CZ0S]
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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. (C) 2013 Elsevier Inc. All rights reserved.
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