The course will present state of the art topics in the development of parallel direct and iterative methods for linear systems with sparse matrices. Some dedicated hand-on sessions will take place.
Sparse matrices:
- Renumbering, structure, properties, assembling;
- Mesh generation, graph model, graph partitioning;
- Hands-on session with ParMETIS.
Direct solvers:
- Elimination strategies, elimination graph, factorization, complexity;
- Parallel methods and algorithms, balancing the computations and communications;
- Hands-on session with MUMPS.
Iterative solvers:
- Krylov subspace methods, convergence, parallel implementation;
- Preconditiong, algebraic multigrid (AMG), robustness, parallel scalability;
- Hands-on session with parallel AMG solvers.
The workshop will address application driven topics including but not limited to parallel scalability of basic numericallinear algebra algorithms:
- tuning/optimization of threaded and vectorised functions;
- Intel MKL; parallel implementation of finite difference, finite element, finite volume, etc. mesh methods;
- balancing/overlapping the computations and communications;
- balancing sparse and dense matrices computations;
- applications in computational mechanics, biomedical and environmental engineering;
- sparse matrix applications in advanced voxel image segmentation.
Lecturers:
- Gundolf Haase (University of Graz, Austria)
- Svetozar Margenov (IICT-BAS, Sofia, Bulgaria)
- Stanislav Stoykov (IICT-BAS, Sofia, Bulgaria)
- Yavor Vutov (IICT-BAS, Sofia, Bulgaria)
- Zahari Zlatev (Aarhus University, Denmark)
Discalimer: The material used in this training event has been prepared by the involved lecturers and solely reflects their own opinion. Please note that the content of this training material has not been approved by the PRACE Project Partners and therefore does not emanate from them nor should it be considered to reflect their individual or collective opinion.
