Computational aspects of the multiscale discontinuous Galerkin method for convection-diffusion-reaction problems
Shin-Ja Jeong, Miyoung Kim · Electronic Research Archive · 2020
We investigate the matrix structure of the discrete system of the multiscale discontinuous Galerkin method (MDG) for general second order partial differential equations [10]. The MDG solution is obtained by composition of DG and the inter-scale operator. We show that the MDG matrix is given by the product of the DG matrix and the inter-scale matrix of the local problem. We apply an ILU preconditioned GMRES to solve the matrix equation effectively. Numerical examples are presented for convection dominated problems.