6 papers
A Theory of Relaxation-Based Algebraic Multigrid
Rayan Moussa, Karsten Kahl
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formu…
Nodal Coarsening and Approximate Ideal Interpolation for H(curl) in Algebraic Multigrid
Taoli Shen, James Brannick, Robert Falgout +2
We propose an approximate interpolation construction and a practical coarsening algorithm for algebraic multigrid (AMG) method when applied to H(curl) problems. Building on the gen…
Nodal AMG Coarsening and Interpolation for PDE Systems
James Brannick, Robert Falgout, Karsten Kahl +2
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial dif…
Generalized Optimal AMG Convergence Theory for Stokes Equations Using Smooth Aggregation and Vanka Relaxation Strategies
Ahsan Ali, James J. Brannick, Karsten Kahl +4
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements…
Generalized Optimal AMG Convergence Theory for Nonsymmetric and Indefinite Problems
Ahsan Ali, James Brannick, Karsten Kahl +3
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is wel…
Multigrid methods combined with low-rank approximation for tensor structured Markov chains
Matthias Bolten, Karsten Kahl, Daniel Kressner +2
Markov chains that describe interacting subsystems suffer, on the one hand, from state space explosion but lead, on the other hand, to highly structured matrices. In this work, we…