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We focus on the extension of the MLD2P4 package of parallel Algebraic MultiGrid (AMG) preconditioners, with the objective of improving its robustness and efficiency when dealing with sparse linear systems arising from anisotropic PDE problems on general meshes. We present a parallel implementation of a new coarsening algorithm for symmetric positive definite matrices, which is based on a weighted matching approach. We discuss preliminary results obtained by combining this coarsening strategy with the AMG components available in MLD2P4, on linear systems arising from applications considered in the Horizon 2020 Project “Energy oriented Centre of Excellence for computing applications” (EoCoE).

Domain decomposition ideas have long been an essential tool for the solution of PDEs on parallel computers. In recent years many research efforts have been focused on recursively employing domain decomposition methods to obtain multilevel preconditioners to be used with Krylov solvers. In this context, we developed MLD2P4 (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS), a package of parallel multilevel preconditioners that combines additive Schwarz domain decomposition methods with a smoothed aggregation technique to build a hierarchy of coarse-level corrections in an algebraic way. The design of MLD2P4 was guided by objectives such as extensibility, flexibility, performance, portability, and ease of use. They were achieved by following an object-based approach while using the Fortran 95 language, as well as by employing the PSBLAS library as a basic framework. In this article, we present MLD2P4 focusing on its design principles, software architecture, and use.

We describe some activities devoted to extending Parallel Sparse BLAS (PSBLAS), a library of routines providing basic Linear Algebra operations needed to build iterative sparse linear system solvers on distributed-memory parallel computers. We focus on the extension of PSBLAS functionalities for implementing parallel Additive Schwarz preconditioners, that are widely used in the solution of linear systems arising from a variety of applications. An analysis of the performance of PSBLAS-based Additive Schwarz preconditioners with Krylov solvers is reported, that has been carried out on test matrices arising from automotive engine simulations. Some comparisons with Additive Schwarz preconditioners implemented in the well-known PETSc library are also shown.

Numerical simulations of reactive flows are among the most computational demanding applications in the scientific computing world. KIVA-3V, a widely used computer program for CFD, specifically tailored to engine applications, had been deeply modified in order to improve accuracy and stability, while reducing computational time. The original methods included in KIVA to solve equations of fluid dynamics had been fully replaced by new solvers, with the aim of both improving performance and writing a fully parallel code. Almost every feature of original KIVA-3V has been partially or entirely rewritten, a full 1D code has been included and a strategy to link directly 3D zones with zero dimensional models has been developed. The result is a reliable program, noticeably faster than the original KIVA-3V in serial mode and obviously even more in parallel, capable of treating more complex cases and bigger grids, with the desired level of details where required.