A nonlinear domain decomposition (DD) solver is considered with respect to improved energy efficiency. In this method, nonlinear problems are solved using Newton’s method on the subdomains in parallel and in asynchronous iterations. The method is compared to the more standard Newton-Krylov approach, where a linear domain decomposition solver is applied to the overall nonlinear problem after...
The idea behind ffddm is to simplify the use of parallel solvers in the open source finite element software FreeFEM. The ffddm framework is entirely written in the FreeFEM language. Thanks to ffddm, FreeFEM users have access to high-level functionalities for specifying and solving their finite element problems in parallel using scalable two-level Schwarz domain decomposition methods. The...
With the commencement of the exascale computing era, we realize that the majority of the leadership supercomputers are heterogeneous and massively parallel even on a single node with multiple co-processors such as GPU's and multiple cores on each node. For example, ORNL's Summit accumulates six NVIDIA Tesla V100's and 42 core IBM Power9's on each node.
At this scale of parallelism, the...
In many numerical simulations, there is a need to solve a sparse linear system ($Ax=b$) at every iteration. The solution of these linear systems, using iterative methods such as Krylov Subspace Methods, consumes around 80% of the simulation's runtime on modern architectures. Recently, enlarged Krylov subspace methods were introduced in the aim of reducing communication and speeding-up the...
