Volume 14, Issue 3
On the Construction of Well-conditioned Hierarchical Bases for H(div)-conforming Rn Simplicial Elements

Jianguo Xin, Wei Cai & Nailong Guo

Commun. Comput. Phys., 14 (2013), pp. 621-638.

Published online: 2013-09

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  • Abstract

Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedralelements areconstructed withthegoal ofimproving theconditioning ofthe mass and stiffness matrices. For the basis with the triangular element, it is found numerically thatthe conditioning is acceptableuptothe approximationof orderfour, and is better than a corresponding basis in the dissertation by Sabine Zaglmayr [High Order Finite Element Methods for Electromagnetic Field Computation, Johannes Kepler Universita¨t, Linz, 2006]. The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four. The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four. For the tetrahedral element, it is identified numerically that the conditioning is acceptable only up to the approximation of order three. Compared with the newly constructed basis for the triangular element, the sparsity of the mass matrices from the basis for the tetrahedral element is relatively sparser.


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@Article{CiCP-14-621, author = {Jianguo Xin, Wei Cai and Nailong Guo}, title = {On the Construction of Well-conditioned Hierarchical Bases for H(div)-conforming Rn Simplicial Elements}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {3}, pages = {621--638}, abstract = {

Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedralelements areconstructed withthegoal ofimproving theconditioning ofthe mass and stiffness matrices. For the basis with the triangular element, it is found numerically thatthe conditioning is acceptableuptothe approximationof orderfour, and is better than a corresponding basis in the dissertation by Sabine Zaglmayr [High Order Finite Element Methods for Electromagnetic Field Computation, Johannes Kepler Universita¨t, Linz, 2006]. The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four. The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four. For the tetrahedral element, it is identified numerically that the conditioning is acceptable only up to the approximation of order three. Compared with the newly constructed basis for the triangular element, the sparsity of the mass matrices from the basis for the tetrahedral element is relatively sparser.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.100412.041112a}, url = {http://global-sci.org/intro/article_detail/cicp/7175.html} }
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