A Two-Level Additive Schwarz Preconditioner for Local C0 Discontinuous Galerkin Methods of Kirchhof Plates

doi:10.1007/s42967-019-0003-1

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (2): 167-185.doi: 10.1007/s42967-019-0003-1

A Two-Level Additive Schwarz Preconditioner for Local C⁰ Discontinuous Galerkin Methods of Kirchhof Plates

Jianguo Huang¹, Xuehai Huang²

1 School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China;
2 School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China

Received:2018-06-04 Revised:2018-08-14 Online:2019-06-20 Published:2019-06-20
Contact: Jianguo Huang, Xuehai Huang E-mail:jghuang@sjtu.edu.cn;huang.xuehai@sufe.edu.cn
Supported by:
The authors thank the referees for their valuable comments leading to improvement of an early version of the paper. The frst author was supported under NSFC (Grant no. 11571237). The second author was supported under NSFC (Grant no. 11771338), and the Fundamental Research Funds for the Central Universities.

Abstract

Abstract: A two-level additive Schwarz preconditioner based on the overlapping domain decomposition approach is proposed for the local C⁰ discontinuous Galerkin (LCDG) method of Kirchhof plates. Then with the help of an intergrid transfer operator and its error estimates, it is proved that the condition number is bounded by O(1 + (H⁴/δ⁴)), where H is the diameter of the subdomains and δ measures the overlap among subdomains. And for some special cases of small overlap, the estimate can be improved as O(1 + (H³/δ³)). At last, some numerical results are reported to demonstrate the high efciency of the two-level additive Schwarz preconditioner.

Key words: Kirchhof plate, C⁰ discontinuous Galerkin, Two-level additive Schwarz preconditioner, Intergrid transfer operator

CLC Number:

65N30
65N55

Jianguo Huang, Xuehai Huang. A Two-Level Additive Schwarz Preconditioner for Local C⁰ Discontinuous Galerkin Methods of Kirchhof Plates[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 167-185.

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References 1.

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A Two-Level Additive Schwarz Preconditioner for Local C⁰ Discontinuous Galerkin Methods of Kirchhof Plates

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