In the present paper, we consider multigrid strategies for the resolution of linear systems arising from the Qk Finite Elements approximation of one-and higher-dimensional elliptic partial differential equations with Dirichlet boundary conditions and where the operator is div (-a(x)∇•), with a continuous and positive over Ω, Ω being an open and bounded subset of R2. While the analysis is performed in one dimension, the numerics are carried out also in higher dimension d ≥ 2, showing an optimal behavior in terms of the dependency on the matrix size and a substantial robustness with respect to the dimensionality d and to the polynomial degree k.

Ferrari, P., Rahla, R., Tablino-Possio, C., Belhaj, S., Serra-Capizzano, S. (2020). Multigrid for Q k Finite Element Matrices Using a (Block) Toeplitz Symbol Approach. MATHEMATICS, 8(1), 1-17 [10.3390/math8010005].

Multigrid for Q k Finite Element Matrices Using a (Block) Toeplitz Symbol Approach

Tablino-Possio, C
;
2020

Abstract

In the present paper, we consider multigrid strategies for the resolution of linear systems arising from the Qk Finite Elements approximation of one-and higher-dimensional elliptic partial differential equations with Dirichlet boundary conditions and where the operator is div (-a(x)∇•), with a continuous and positive over Ω, Ω being an open and bounded subset of R2. While the analysis is performed in one dimension, the numerics are carried out also in higher dimension d ≥ 2, showing an optimal behavior in terms of the dependency on the matrix size and a substantial robustness with respect to the dimensionality d and to the polynomial degree k.
Articolo in rivista - Articolo scientifico
Multigrid; Matrix-sequences; Spectral analysis; Finite Element approximations
English
18-dic-2019
2020
8
1
1
17
5
reserved
Ferrari, P., Rahla, R., Tablino-Possio, C., Belhaj, S., Serra-Capizzano, S. (2020). Multigrid for Q k Finite Element Matrices Using a (Block) Toeplitz Symbol Approach. MATHEMATICS, 8(1), 1-17 [10.3390/math8010005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/252378
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