Implementation of a non-linear solver on heterogeneous architectures

Heterogeneous architectures seem to be not only the present but also the future of the HPC world (eg, see the Exascale Project of U.S. Department of Energy or the European Horizon 2020 FET Proactive - High Performance Computing Call). A lot of work has been done in developing software libraries useful to solve problem described by linear equations on such computing systems. Instead, not the same effort is spent in such context for the implementation of software modules to be used to solve non-linear problem. In this work, we present some experiences related with the implementation of a Quasi-Newton method able to exploit, using a combination of "Task Scheduling," "matrix-free," and "look-ahead" approaches, both the CPUs and the GP-GPUs components of a heterogeneous system.