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.

Multigrid for Qk finite element matrices using a (block) Toeplitz symbol approach

Serra Capizzano S.
2020-01-01

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.
2020
Finite element approximations; Matrix-sequences; Multigrid; Spectral analysis
Ferrari, P.; Rahla, R. I.; Tablino-Possio, C.; Belhaj, S.; Serra Capizzano, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2119508
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