Webinar: Algebraic MultiGrid Preconditioners for Sparse Linear Solvers at Extreme Scales on Hybrid Architectures

Abstract

The challenge of exascale requires rethinking numerical algorithms and mathematical software for efficient exploitation of heteregeneous massively parallel supercomputers. In this talk, I present some activities aimed at developing highly scalable and robust sparse linear solvers for solving scientific and engineering applications with a huge number of degrees of freedom (dof). I discuss algorithmic advances and implementation aspects in the design of Algebraic MultiGrid (AMG) preconditioners based on aggregation, to be used in conjunction with Krylov-subspace projection methods, suitable to exploit high levels of parallelism of current petascale supercomputers. These activities are carried out within two ongoing European Projects, the Energy-oriented Center of Excellence (EoCoE-11) and the EuroHPC TEXTAROSSA project, having the final aim to provide methods and tools for preparing scientific applications in facing and successful grasping of the near future exascale challenge.

Beyond possible advances in base software technology to make available programming environments that tend to hide the details of the hardware, we still need to rethink and redesign numerical methods and applications, especially for irregular computations and memory-bound kernels, like sparse solvers. Algorithms that express a high level of data parallelism should be preferred to algorithms that induce data dependency even though, sometimes, the former may have worse convergence properties; extra computations are often well tolerated and balanced by a very efficient execution on multi/many-core architectures. Such is the case, for example, of some smoothers and coarsest solvers in AMG cycles or sub-optimal maximum weight matching algorithms employed in the setup of the AMG matrix hierarchy, which avoid intrinsically sequential computational kernels.

Memory footprint, measured in terms of hierarchy complexity, is also a key issue in pursuing scalability in AMG preconditioners; balancing hierarchy complexity and convergence property of the final AMG is another main challenge in the current research on the topic. I discuss the above tasks while presenting a software framework for Parallel Sparse Computations (PSCToolkit), which has recently been selected by EU Innovation Radar as Excellent Innovation. Results obtained with PSCToolkit, on some of the most powerful European supercomputers, for solving systems with tens of billions of dof arising from isotropic and anisotropic scalar elliptic PDEs, will be presented.
 

About the Speaker

Pasqua D'Ambra graduated in Mathematics summa cum laude at the University of Naples Federico II in 1990, and she earned her PhD in Applied Mathematics and Computer Science from the same University in 1995. She is CNR senior research scientist with a permanent position at the Institute for Applied Computing “M. Picone” (IAC) in Naples. Her main research activities are in designing and developing numerical methods, algorithms and mathematical software for high-performance and parallel scientific computing. In this context, her main contributions are in the area of parallel numerical linear algebra and parallel solution of partial/ordinary differential equations with applications to fluid dynamics and data analysis. A large part of the research results is freely available as mathematical software packages. Research activities are carried out within national and international projects where she plays PI and WP leader roles.

Download the Summer 2021 Online EuroCC & SimEA Seminar Series Programme here.

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