Composite matrix construction for structured grid adaptive mesh refinement

The solution of elliptic partial differential equations on block-structured meshes is the major computational expense in many real-world problems. For example, solving the elliptic stress balance equation is the most time-consuming computational task when simulating Antarctica with the BISICLES adaptive mesh ice sheet model. Up till now, BISICLES and other applications based on the Chombo multiphysics library have depended on a geometric multigrid (GMG) method. This paper describes the extension of Chombo to make use of the general purpose algebraic multigrid (AMG) methods available in PETSc (Portable, Extensible Toolkit for Scientific Computation). Tests with the BISICLES model indicate that an AMG method (BoomerAMG) outperforms the GMG method