Mathematics

Problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. These systems contain localized features which, even with adaptive mesh refinement, result in linear systems that can be on the order of 100+ million unknowns. The current state-of-the-art solvers often make use of AMG methods which tend to deteriorate for these highly adaptive problems. I will present a matrix-free GMG v-cycle which works on adaptively refined, distributed meshes, and compare it against the current AMG preconditioner (Trilinos ML) used in the ASPECT mantle convection software. I will demonstrate the robustness of GMG with respect to problem size, refinement level, and processor count, and show scaling results up to 24576 cores and 2.2B unknowns.