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Volume 22, Issue 4
Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations

Qiya Hu & Lin Zhao

DOI: 10.4208/cicp.240515.040517a

Commun. Comput. Phys., 22 (2017), pp. 1069-1100.

Published online: 2017-10

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  • Abstract

In this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.

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@Article{CiCP-22-1069, author = {Qiya Hu and Lin Zhao}, title = {Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {4}, pages = {1069--1100}, abstract = {

In this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.240515.040517a}, url = {http://global-sci.org/intro/article_detail/cicp/9994.html} }
TY - JOUR T1 - Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations AU - Qiya Hu & Lin Zhao JO - Communications in Computational Physics VL - 4 SP - 1069 EP - 1100 PY - 2017 DA - 2017/10 SN - 22 DO - http://doi.org/10.4208/cicp.240515.040517a UR - https://global-sci.org/intro/article_detail/cicp/9994.html KW - AB -

In this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.

Qiya Hu and Lin Zhao. (2017). Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations. Communications in Computational Physics. 22 (4). 1069-1100. doi:10.4208/cicp.240515.040517a
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