Preconditioning GMRES for discontinuous Galerkin approximations - Banaś, Krzysztof; Wheeler, Mary F. (Computer Assisted Methods in Engineering and Science, 2023)
The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems. The preconditioners are applied for the restarted GMRES method and test problems are taken mainly from subsurface flow modeling. Discontinuous Galerkin approximation is implemented within an hp-adaptive finite element code that uses hierarchical 3D meshes. The hierarchy of meshes is utilized for multi-level (multigrid) preconditioning. The results of numerical computations show the necessity of using multi-level preconditioning and insufficiency of simple stationary preconditioners, like Jacobi or Gauss- Seidel. Successful preconditioners comprise a multi-level block ILU algorithm and a special multi-level block Gauss- Seidel method.