V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes
In this paper we analyze the convergence properties of V -cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spa...
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| Veröffentlicht in: | Journal of scientific computing Jg. 78; H. 1; S. 625 - 652 |
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| Abstract | In this paper we analyze the convergence properties of
V
-cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spaces that stands at the basis of the multigrid scheme is possibly non-nested and is obtained based on employing agglomeration algorithms with possible edge/face coarsening. We prove that the method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree
p
, provided that the minimum number of smoothing steps, which depends on
p
, is chosen sufficiently large. |
|---|---|
| AbstractList | In this paper we analyze the convergence properties of
V
-cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spaces that stands at the basis of the multigrid scheme is possibly non-nested and is obtained based on employing agglomeration algorithms with possible edge/face coarsening. We prove that the method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree
p
, provided that the minimum number of smoothing steps, which depends on
p
, is chosen sufficiently large. In this paper we analyze the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization of second-order elliptic partial differential equations on polytopic meshes. Here, the sequence of spaces that stands at the basis of the multigrid scheme is possibly non-nested and is obtained based on employing agglomeration algorithms with possible edge/face coarsening. We prove that the method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the minimum number of smoothing steps, which depends on p, is chosen sufficiently large. |
| Author | Pennesi, G. Antonietti, P. F. |
| Author_xml | – sequence: 1 givenname: P. F. orcidid: 0000-0002-2138-3878 surname: Antonietti fullname: Antonietti, P. F. organization: MOX-Laboratory for Modelling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano – sequence: 2 givenname: G. orcidid: 0000-0003-3118-9283 surname: Pennesi fullname: Pennesi, G. email: giorgio.pennesi@polimi.it organization: MOX-Laboratory for Modelling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano |
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| CitedBy_id | crossref_primary_10_1002_nme_6519 crossref_primary_10_1016_j_jcp_2025_113773 crossref_primary_10_1137_21M1466864 crossref_primary_10_1145_3664924 crossref_primary_10_1016_j_cma_2022_114971 crossref_primary_10_1137_18M1204383 crossref_primary_10_1137_19M1275929 crossref_primary_10_1016_j_rineng_2024_102949 crossref_primary_10_1137_18M1206357 crossref_primary_10_1007_s10013_022_00566_3 crossref_primary_10_1007_s10444_022_09968_w crossref_primary_10_1016_j_camwa_2023_11_015 crossref_primary_10_1137_20M1349503 crossref_primary_10_1016_j_camwa_2024_05_013 crossref_primary_10_1016_j_finel_2019_02_002 crossref_primary_10_1016_j_jcp_2021_110861 crossref_primary_10_1007_s11075_023_01635_5 |
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Sci. doi: 10.1142/S0218202514400028 |
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V
-cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from... In this paper we analyze the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from... |
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| SubjectTerms | Algorithms Coarsening Computational Mathematics and Numerical Analysis Convergence Elliptic functions Galerkin method Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Multigrid methods Partial differential equations Polynomials Theoretical |
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| Title | V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes |
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