Extending Chombo with PETSc

Among the most challenging problems in computational physics are elliptic equations with vastly different spatial and temporal scales. The block structured Adaptive Mesh Refinement (AMR) technique is particularly amenable to such problems, as it combines the benefits of ¿classical¿ finite difference/finite volume discretization with the advantage of locally increased resolution. The Chombo software infrastructure has been developed to apply AMR to problems ranging from magnetohydrodynamics to combustion, and has proven to be 1-2 orders of magnitude more efficient than standard finite differences. However, Chombo¿s built-in linear solvers can encounter convergence difficulties, particularly in regimes where time steps are large and where heat conductivity, electric resistivity, and/or viscosity have strong spatial variation, as in fusion devices. This project will extend Chombo to allow users to invoke linear matrix solves implemented by the Portable, Extensible Toolkit for Scientific (PETSc) library. PETSc is the leading library for sparse matrix solves, offering a large choice of direct and iterative solver algorithms. Commercial Applications and other Benefits as described by the awardee The Chombo extension would enable users to apply the most appropriate algorithm for solving linear systems, which will in turn improve numerical efficiency and robustness. In particular, the extension would benefit the AMR-MHD application, which simulates pellet injection in fusion devices. Commercial computational fluid dynamics applications also could benefit from these extensions.