Numerical solution of PDEs with hybrid and heterogeneous computing models

This study is a first part of a longer project investigating hybrid and hetero-geneous computing models in computational science. This is joint work with Fujitsu Laboratories Europe (FLE) with the purpose of developing numerical software libraries under the Open Petascale Libraries Project. We overview some current work and trends relating to petascale algorithms and their im-plementation in two application areas. The focus here is on the solution of partial differential equations. The work is aligned with the Work Pack-age 4 of the OPL project Enabling Technologies for Large-Scale PDE-Based Simulations. We consider mostly initial value problems arising in computational fluid dynamics (tsunami modelling), plasma physics (fusion reactor modelling) and other domains. We discuss the mathematical technology which under-lies scalability. Approaches discussed should include domain decomposition and subspace correction methods, iterative Krylov solvers, extrapolation and combination techniques, multiscale approximations and adaptive approxima-tion. For all the studied algorithms, earlier work regarding their scalability and implementations will be reviewed and their limitations will be described. In the following we will provide a review of the literature on algorithms including a discussion of their scalability and limitations.