Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations. (28th July 2017)

• Record Type: Journal Article
• Authors: Hu, Qiya; Zhao, Lin
• Is Part Of: Communications in computational physics. Volume 22:Number 4(2017:Oct.)
• Page Start: 1069
• Page End: 1100
• Publication Date: 2017-07-28
• Subjects: 35K51, -- 35K55, -- 65M55, -- 65M60; 2D-3T heat conduction equations, -- discontinuous Galerkin method, -- domain decomposition preconditioner, -- iterative numbers; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.240515.040517a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.