A hybrid geometric + algebraic multigrid method with semi-iterative smoothers

The Mixed Finite Element Multigrid Method for Stokes Equations

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution o...

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

On the use of relaxation parameters in hybrid smoothers

The use of relaxation parameters in hybrid smoothers within algebraic multigrid (AMG) is analyzed both theoretically and practically. Relaxation parameters that are optimal under the assumptions of the theory are determined. The implementation of a procedure to automatically determine outer relaxation parameters for symmetric positive definite smoothers is described. Numerical results are prese...

Mixed-Precision GPU-Multigrid Solvers with Strong Smoothers

• Sparse iterative linear solvers are the most important building block in (implicit) schemes for PDE problems • In FD, FV and FE discretisations • Lots of research on GPUs so far for Krylov subspace methods, ADI approaches and multigrid • But: Limited to simple preconditioners and smoothing operators •Numerically strong smoothers exhibit inherently sequential data dependencies (impossible to p...