Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zampini, Stefano [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: © Archived with thanks to SIAM Journal on Scientific Computing |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: SIAM journal on scientific computing - Philadelphia, Pa. : SIAM, 1980, (2017) |
|---|---|
| Übergeordnetes Werk: |
year:2017 |
| Links: |
|---|
| DOI / URN: |
10.1137/16m1080653 |
|---|
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OLC1996082981 |
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| 520 | |a Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications. | ||
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10.1137/16m1080653 doi PQ20171228 (DE-627)OLC1996082981 (DE-599)GBVOLC1996082981 (PRQ)kaust_dspace_oai_repository_kaust_edu_sa_10754_6253180 (KEY)0101056520170000000000000000multilevelbalancingdomaindecompositionbyconstraint DE-627 ger DE-627 rakwb eng 004 510 DNB 31.76 bkl Zampini, Stefano verfasserin aut Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications. Nutzungsrecht: © Archived with thanks to SIAM Journal on Scientific Computing domain decomposition adaptive coarse space Darcy flow PETSc BDDC Tu, Xuemin oth Enthalten in SIAM journal on scientific computing Philadelphia, Pa. : SIAM, 1980 (2017) (DE-627)130498483 (DE-600)759833-6 (DE-576)016080416 1064-8275 nnns year:2017 http://dx.doi.org/10.1137/16m1080653 Volltext http://hdl.handle.net/10754/625318 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4323 31.76 AVZ AR 2017 |
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Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media |
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Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media |
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Zampini, Stefano |
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004 510 |
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multilevel balancing domain decomposition by constraints deluxe algorithms with adaptive coarse spaces for flow in porous media |
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Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media |
| abstract |
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications. |
| abstractGer |
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications. |
| abstract_unstemmed |
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications. |
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| title_short |
Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media |
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