A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
We propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/859424 |
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| _version_ | 1832552889176817664 |
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| author | Yaqin Jiang |
| author_facet | Yaqin Jiang |
| author_sort | Yaqin Jiang |
| collection | DOAJ |
| description | We propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis. |
| format | Article |
| id | doaj-art-fc95e4c79a26456da7ed0fa71c5a738f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fc95e4c79a26456da7ed0fa71c5a738f2025-02-03T05:57:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/859424859424A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous CoefficientsYaqin Jiang0School of Sciences, Nanjing University of Posts and Telecommunications, Nanjing 210046, ChinaWe propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.http://dx.doi.org/10.1155/2014/859424 |
| spellingShingle | Yaqin Jiang A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients Journal of Applied Mathematics |
| title | A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients |
| title_full | A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients |
| title_fullStr | A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients |
| title_full_unstemmed | A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients |
| title_short | A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients |
| title_sort | bddc preconditioner for the rotated q1 fem for elliptic problems with discontinuous coefficients |
| url | http://dx.doi.org/10.1155/2014/859424 |
| work_keys_str_mv | AT yaqinjiang abddcpreconditionerfortherotatedq1femforellipticproblemswithdiscontinuouscoefficients AT yaqinjiang bddcpreconditionerfortherotatedq1femforellipticproblemswithdiscontinuouscoefficients |