| Citation: | LI Liang, WU Songping. Application of matrix bandwidth reduction technique in implicit discontinuous Galerkin[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 532-540. doi: 10.13700/j.bh.1001-5965.2019.0281(in Chinese)
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To numerically solve the two-dimensional Euler equations, discontinuous Galerkin method and backward difference formula (BDF) are used as spatial and temporal discretization, respectively. The Newton-Raphson method is taken to solve the nonlinear equations arising from the implicit time integration. The Jacobia matrix is constructed. Owing to the high-order, sparsity and non-symmetry of the matrix, the preconditioned generalized minimal residual (GMRES) method is chosen in every time step for solving the linear equations. The preconditioner is constructed using incomplete lower-upper (ILU) decomposition method. The bandwidth reduction technique is applied to the solution of the linear equations. Without extra storage cost, the application narrows the difference between the preconditioner and the coefficient matrix, thus accelerating the convergence of GMRES method and increasing the available time step size for temporal integration. Typical aerodynamic problems are solved to test the effectiveness of the application.
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