Abstract
Traditionally, preconditioners are used to damp slowly varying error modes in the linear solver stage. State-of-the-art multilevel preconditioners use a sequence of aggressive restriction, coarse-grid correction and prolongation operators to handle low-frequency modes on the coarse grid. High-frequency errors are then resolved by employing a smoother on fine grid. In this paper, the algebraic smoothing aggregation two level preconditioner is implemented to solve different coupled problems.
The proposed method generalizes the existing MsRSB and smoothing aggregation AMG methods. This method does not require any coarse partitioning and, hence, can be applied to general unstructured topology of the fine scale. Inspired by smoothing aggregation algebraic multigrid solver, the algebraic smoothing aggregation preconditioner constructs basis functions which allow mapping of some high-frequency modes from fine scale to low-frequency modes on the coarse scale. These basis functions are also used to reconstruct unknown primary variables at the fine scale using their approximations at the coarse level.
The proposed preconditioner has been adopted to challenging multiphysical problems, including fully coupled simulation of filtration and geomechanics processes including non-isothermal fluid flow problems. The preconditioner provides a reasonably good approximation to the coupled physical processes and speeds up the convergence. Compared to traditional ILU0+GMRES linear solvers, our preconditioner with GMRES solver reduces the number of iterations by about 3 times. In addition, the proposed method obeys a good theoretical scalability essential for parallel simulations.
