# The Spherical Shell NSinker benchmark#

This folder contains the “Spherical Shell NSinker” benchmark, which is loosely based on the NSinker benchmark defined in

Weighted BFBT Preconditioner for Stokes Flow Problems with Highly Heterogeneous Viscosity, Johann Rudi, Georg Stadler, Omar Ghattas, SIAM Journal of Scientific Computing, Vol 39, Issue 5, 2017. https://doi.org/10.1137/16M108450X

but adapted to a spherical shell geometry. See the “nsinker” benchmark in this repository for the version in a unit box. The motivation for creating this benchmark was the desire to test linear solver performance with a spherical geometry, which is often used in practice and that turns out to be more challenging.

This benchmark is defined and used in

Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations, Peter Munch, Timo Heister, Laura Prieto Saavedra, Martin Kronbichler, ACM Transactions on Parallel Computing, 2023, 10, 1-38. https://doi.org/10.1145/3580314

We consider a spherical shell with inner radius 0.54 and outer radius 1.0 with N spherical, high-viscosity, high-density sinking spheres at random (but predetermined in the code) locations in the domain. Additionally, a transition zone with distance 0.89583 from the origin (or about 660km depth if this is assumed to be a non-dimensionalized Earth-like computation) with a sharp viscosity jump can be enabled.