New Multigrid Solver Advances in TOPS

Rob Falgout, LLNL

In this poster, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations ISIC. Multigrid methods are so-called optimal methods because they can solve a linear system with N unknowns with only O(N) work. This property makes it possible to solve ever larger problems on proportionally larger parallel machines in constant time, that is, they are scalable methods. Classical iterative methods like conjugate gradients are not scalable.

The poster will focus on new algebraic multigrid (AMG) developments in TOPS and how this work relates to SciDAC's simulation science goals. Highlights include compatible relaxation techniques for selecting high-quality coarse grids and adaptive methods that improve themselves as they solve the linear system. Our adaptive AMG technology is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications