Please use this identifier to cite or link to this item: https://doi.org/10.1002/nme.2818
Title: Dual-grid-based tree/cotree decomposition of higher-order interpolatory H(∇∧,Ω) basis
Authors: Beig, D.A.O.
Leong, M.-S. 
Keywords: Dual/primal graph;H(∇∧Ω)/curl-conforming basis
Finite element method (FEM)
Krylov solver(s)
Null-space
Spurious/non-physical solutions;high-order interpolatory vector basis
Tree/cotree (TC)
Issue Date: 25-Jun-2010
Source: Beig, D.A.O., Leong, M.-S. (2010-06-25). Dual-grid-based tree/cotree decomposition of higher-order interpolatory H(∇∧,Ω) basis. International Journal for Numerical Methods in Engineering 82 (13) : 1689-1719. ScholarBank@NUS Repository. https://doi.org/10.1002/nme.2818
Abstract: This work extends the zeroth-order tree/cotree (TC) decomposition method into higher order (HO) interpolatory elements and develops the constraints operator required for the elimination of spurious solutions for general HO spectral basis. Earlier methods explicitly enforce the divergence condition that requires a mixed finite element (FE) formulation with both H1 and H(∇∧) expansions and involves repeated solutions of the Poisson equation. A recent approach, which avoids the mixed formulation and the Poisson problem, uses TC decomposition of edge DoF over the primal graph and construction of integration and gradient matrices. The approach is easily applied to HO hierarchical elements but becomes quite complex for HO spectral elements. In the presence of internal DoF, it is difficult to utilize the primal graph for an explicit decomposition of the spectral DoF. In contrast, this work utilizes the dual grid, resulting in an explicit decomposition of DoF and construction of constraint equations from a fixed element matrix. Thus, mixed formulation and the Poisson problems are avoided while eliminating the need for evaluation of integration and gradient matrices. The proposed constraints matrix is element-geometry independent and possesses an explicit sparsity formulation reducing the need for dynamic memory allocation. Numerical examples are included for verification. © 2010 John Wiley & Sons, Ltd.
Source Title: International Journal for Numerical Methods in Engineering
URI: http://scholarbank.nus.edu.sg/handle/10635/82183
ISSN: 00295981
DOI: 10.1002/nme.2818
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