A Comparison of PETSc Library and HPF Implementations of an Archetypal PDE Computation

this paper is as follows. Section 2 describes a model nonlinear PDE problem and its discretization and solution algorithm. Sections 3 and 4, respectively, discuss the PETSc and HPF implementations of the algorithm. The performance of the implementations is compared, side-by-side, in Section 5, and we conclude in Section 6. Our target audience includes both potential users of parallel systems for PDE simulation and developers of future versions of parallel languages and libraries. For the latter, we go into some detail on our algorithmic framework of Newton-Krylov-Schwarz. It is not novel, but it is progressive, and it cannot be found in textbooks as a composite framework. For the former, we encourage looking beyond the very simple model problem described herein to more advanced applications of PETSc, such as the CFD applications in [5,12,14]. Two of these three applications involve global structured grids and would be amenable to an HPF implementation, as well. 2. Problem and Algorith