Speaker: Dr. Alexander Pletzer, TechX, Boulder, CO
Chompst is a Small Business Innovation & Research (SBIR) project funded by DoE to address the need for exposing the large collection of PETSc iterative solvers from within the adaptive mesh refinement (AMR) tool Chombo. As a motivation, we review the basic principles behind multi-grid techniques, which are among the most efficient, O(N), to solve elliptic partial differential equations. Multi-grid relies on the smoothing properties of the differential operator to remove large and low wave-number components in the error by applying Gauss-Seidel relaxations on grids with multiple resolutions. However, standard multi-grid is known to be ill-suited for some elliptic operators, notably some Helmholtz operators, and thermal diffusion problems where the heat conductivity is highly anisotropic and/or exhibits strong spatial dependency. Here, we will walk through some of the difficult multi-grid problems and show how the ability to go beyond multi-grid relaxation schemes by exposing PETSc's rich set of iterative solvers will allow Chombo users to solve some of these hard problems.