4 papers
Bootstrap Algebraic Multigrid: status report, open problems, and outlook
Achi Brandt, James Brannick, Karsten Kahl +1
This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effect…
Shifted Laplacian based multigrid preconditioners for solving indefinite Helmholtz equations
Ira Livshits
Shifted Laplacian multigrid preconditioner has become a tool du jour for solving highly indefinite Helmholtz equations. The idea is to add a complex damping to the original Helmhol…
Wave-ray algorithms for Helmholtz equations with variable wave numbers: a one-dimensional implementation of two-dimensional ideas
Ira Livshits
The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to…
An algebraic distances measure of AMG strength of connection
Achi Brandt, James Brannick, Karsten Kahl +1
Algebraic multigrid is an iterative method that is often optimal for solving the matrix equations that arise in a wide variety of applications, including discretized partial differ…