On long-range interpolation operators for aggressive coarsening

Algebraic multigrid (AMG) is a very efficient scalable preconditioner for solving sparse linear systems on unstructured grids. Currently, AMG solvers with good numerical scalability can still have larger than desired complexities, whereas variants with very low complexities exhibit decreased numerical scalability, which presents a problem for future high‐performance computers with millions of cores and decreased memory per core. It is therefore necessary to design more sophisticated interpolation operators to improve numerical scalability while preserving low memory usage. Two new long‐range interpolation operators to be used in combination with aggressive coarsening are presented. Their convergence and performance are examined and compared with multipass interpolation, the interpolation currently most commonly used with aggressive coarsening, and a higher complexity AMG variant. While the new interpolation operators require a more complex setup, leading to larger setup times, they exhibit better convergence than multipass interpolation, often resulting in better solve times. Copyright © 2009 John Wiley & Sons, Ltd.