Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations (Communications in Computational Physics, 2017)
In this paper we are concerned with numerical methods for nonlinear time-dependentproblem coupled by electron, ion and photon temperatures in two dimensions,which is called the 2D-3T heat conduction equations. We propose discontinuousGalerkin (DG) methods for the discretization of the equations. For solving the resultingdiscrete system, we employ two domain decomposition (DD) preconditioners, oneof which is associated with the non-overlapping DDM and the other is based on DDMwith small overlap. The preconditioners are constructed by dropping the couplings betweenparticles and each preconditioner consists of three preconditioners with smallermatrix size. To gauge the efficiency of the preconditioners, we test two examples andmake different settings of parameters. Numerical results show that the proposed preconditionersare very effective to the 2D-3T problem.