Robust Two-Level Lower-Order Preconditioners for a Higher-Order Stokes Discretization with Highly Discontinuous Viscosities
Duilio Conceição (IMPA)Marcus Sarkis (IMPA)
Paulo Goldfeld (UFRJ)
Abstract:
The main goal of this paper is to present new robust and scalable
preconditioned conjugate gradient algorithms for solving
Stokes equations with large viscosities jumps across subregion interfaces and discretized on non-structured meshes.
The proposed algorithms do not require the construction of a coarse
mesh and avoid expensive communications between coarse and fine levels.
The algorithms belong to the family of preconditioners based
on non-overlapping decomposition of subregions known as
balancing domain decomposition methods. The local problems employ
two-level element-wise/subdomain-wise direct factorizations to
reduce the size and the cost of the local Dirichlet and Neumann Stokes
solvers. The Stokes coarse problem is based on subdomain constant pressures and on connected subdomain interface flux functions and rigid body motions. This guaranties scalability and solvability for the local Neumann problems. Estimates on the condition numbers and
numerical experiments based on unstructured mesh parallel
implementation are also discussed.
Keywords:
Numerical Methods (Linear algebra), Numerical Methods (PDE), Parallel and Distributed Computing,
