Skip to main content
×
Home
    • Aa
    • Aa

A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations

  • Zhongguo Zhou (a1) (a2) and Dong Liang (a3)
Abstract
Abstract

In the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor’s expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable condition r≤3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.

Copyright
Corresponding author
*Corresponding author. Email: zhouzhongguo@mail.sdu.edu.cn (Z. G. Zhou), dliang@mathstat.yorku.ca (D. Liang)
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2] J. Bear , Hydraulics of Groundwater, McGraw-Hill, New York, 1978.

[3] D. Amitai , A. Averbuch , M. Israeli and S. Itzikowitz , Implicit-explicit parallel asyn-chronous solver of parabolic PDEs, SIAM J. Sci. Comput., 19 (1998), pp. 13661404.

[4] C. N. Dawson , Q. Du and T. F. Dupont , A finite difference domain decomposition algorithm for numerical solution of the heat equation, Math. Comput., 57 (1991), pp. 6371.

[5] M. Dryja and X. Tu , A domain decomposition discretization of parabolic problems, Numerische Mathematik, 107 (2007), pp. 625640.

[6] Q. Du , M. Mu and Z. Wu , Efficient parallel algorithms for parbolic problems, SIAM J. Numer. Anal., 39 (2001), pp. 14691487.

[7] C. Du and D. Liang , An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media, J. Comput. Phys., 229 (2010), pp. 45014521.

[8] D. Evans and A. Abdullah , Group explicit methods for parabolic equations, Int. J. Comput. Math., 14 (1983), pp. 73105.

[11] D. Liang and C. Du , The efficient S-DDM scheme and its analysis for solving parabolic equations, I. Comput. Phys., 272 (2014), pp. 4669.

[12] H. Shi and H. Liao , Unconditional stability of corrected explicit-implicit domain decomposition algorithms for parallel approximation of heat equations, SIAM J. Numer. Anal., 44 (2006), pp. 15841611.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 54 *
Loading metrics...

Abstract views

Total abstract views: 161 *
Loading metrics...

* Views captured on Cambridge Core between 18th January 2017 - 28th July 2017. This data will be updated every 24 hours.