The work in the NLAFET project has focused on fundamental scientific issues and software development, including novel algorithms, prototype and library software for a critical set of fundamental linear algebra operations. The results are presented in 39 deliverables and 23 NLAFET Working Notes available on the NLAFET web-site (www.nlafet.eu). Here follows a brief overview of the work performed including some highlights.
The work package Dense Linear Systems and Eigenvalue Problem Solvers has designed algorithms efficient, scalable, and robust parallel software for fundamental dense matrix computations far above and beyond those covered by standard packages today. This WP delivers:
• novel linear system solvers
• novel BLAS for heterogeneous systems
• novel non-symmetric standard and generalized eigenvalue problem solvers including robust eigenvector computation
• novel singular value problem solvers
The work package Direct Solution of Sparse Linear Systems has designed parallel algorithms and software for the direct solution of sparse linear equations. This WP delivers:
• novel lower bounds on communication for sparse matrices
• novel direct solvers for (near-)symmetric systems
• novel direct solvers for highly unsymmetric systems
• novel hybrid direct-iterative solvers
The work package Communication-Optimal Algorithms for Iterative Methods has designed new iterative methods that allow to drastically reduce the communication, and even minimize it whenever possible. This WP delivers:
• novel computational kernels for preconditioned iterative methods
• novel iterative (enlarged Krylov) methods
• novel multilevel preconditioners
The work package Cross-Cutting Issues has investigated and designed a sustainable set of methods and tools for scheduling and runtime systems, auto-tuning, and algorithm-based fault tolerance (ABFT) packaged into open source library modules. This WP delivers:
• novel parallel critical path (PCP) scheduling for improving scalability; evaluation of several scheduling strategies for solving dense linear algebra problems on various HPC systems,
• novel self-adaptive approaches for on-line tuning
• novel implementation of a task-based ABFT Cholesky factorization
The work package Challenging applications – a selection has integrated and evaluated software parts of the NLAFET Library in the following applications:
• Task-based shared memory parallelism into 2DRMP software for modelling of electron scattering from H-like atoms and ions
• Load flow based calculations in large-scale power systems and PowerFactory code
• Communication avoiding iterative methods for solving linear systems arising from several different applications, in particular linear elasticity problems
• Data analysis in astrophysics and Midapack
One main achievement of the NLAFET project is the software developed and deployed, and made available via the NLAFET website
http://www.nlafet.eu/software/(s’ouvre dans une nouvelle fenêtre). The public repositories that together constitute the NLAFET library software are structured in five groups:
• Dense matrix factorizations and solvers
• Solvers and tools for standard and generalized dense eigenvalue problems
• Sparse direct factorizations and solvers
• Communication optimal algorithms for iterative methods
• Cross-cutting tools
The parallel programming models used in various combinations are MPI, OpenMP, PaRSEC and StarPU.
Dissemination and outreach activities of the NLAFET results have been extensive and received much positive attention. This includes presentations in a number of highly ranked conferences and workshops; in total: 25 invited/keynote presentations, >70 contributed and poster presentations, organization of 17 workshops/ minisymposia. There is more to come; including both invited and contributed presentations as well as various training opportunities for users of the NLAFET Library software.
