Course and Workshop on Parallel Numerical Linear Algebra with Applications

Institute of Information and Communication Technologies (IICT-BAS), Sofia, Bulgaria

Institute of Information and Communication Technologies (IICT-BAS), Sofia, Bulgaria


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.


  • 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.

Scientific program
    • 13:30 13:45
    • 13:45 14:00

      Stoyan Markov
      Svetozar Margenov

    • 14:00 15:30
      Sparse Matrices: Mesh Methods, Mass Matrix, Stiffness Matrix, Assembling, Structure, Properties, Condition Number, Robustness, Graph Model, Graph Partitioning, Nested Dissections

      Svetozar Margenov

    • 15:30 16:00
      Coffee Break 30m
    • 16:00 17:30
      Mesh Generation, Partitioning of Unstructured graphs and Meshes, Computing Fill-Reducing Orderings of Sparse Matrices; Hands-on Session with NETGEN and ParMETIS

      Yavor Vutov

    • 10:30 12:00
      Computational Methods for General Sparse Matrices: Storage Schemes, General Scheme for Linear Algebraic Problems; Pivotal Strategies; Implementation of the Algorithms; Parallelization

      Zahari Zlatev

    • 12:00 14:00
      Lunch Break 2h
    • 14:00 15:30
      Parallel Direct Solvers: Multifrontal Method; Libraries for Parallel Solution of Systems with General Sparse Matrices; Hands-on Session with MUMPS and Intel MKL PARDISO

      Stanislav Stoykov

    • 15:30 16:00
      Coffe Break 30m
    • 16:00 17:30
      Iterative Solvers: Krylov subspace methods; Convergence; Preconditiong; Multilevel Methods; Complexity, Convergence, Robustness

      Svetozar Margenov

    • 10:30 12:00
      Iterative Solvers: Multigrid for FEM-meshes, Basic Principles, Basic Algorithms; Parallelization of (Geometrical) Multigrid - MPI/OpenMP/Accelerators; Overlapping Communication and computations (Non-synchronous Communication)

      Gundolf Haase

    • 12:00 14:00
      Lunch Break 2h
    • 14:00 15:30
      What is Different with Algebraic Multigrid? Non-linear Systems of Equations: Low Hanging Parallelization Fruits; Results from our AMG Solver in a Cardiovascular Application; Hands-on Session: Demonstrating Overlapping Communication and Computations on a Simple Poison Solver

      Gundolf Haase

    • 15:30 16:00
      Coffee Break 30m
    • 16:00 16:30
      Comparative study of pseudo-random and quasi-random number generators on Intel MIC architecture

      Emanouil Atanassov, Aneta Karaivanova, Todor Gurov, Sofia Ivanovska

    • 16:00 17:30
      Workshop on PNLAA
    • 16:30 17:00
      Efficient Scalable Monte Carlo Preconditioners and Hybrid Methods for Solving Systems of Linear Algebraic Equations

      Vassil Alexandrov, Aneta Karaivanova, Oscar Esquevel

    • 17:00 17:30
      Parallel Elliptic Solvers Revisited - Code Modernisation and Scalability

      Gergana Bencheva

    • 10:30 11:00
      Parallel Methods and Algorithms for Dynamical Analysis of Nonlinear Systems

      Stanislav Stoykov

    • 10:30 12:30
      Workshop on PNLAA
    • 11:00 11:30
      Parallel Algorithm for Restoring Large-scale CT Images

      Ivan Lirkov

    • 11:30 12:00
      Scales Compatibility in biomolecular modelling

      Nevena Ilieva

    • 12:00 12:30
      Using Highly Efficient Molecular Dynamics Simulations to Study the Effect of Tagging on SignalingProteins

      Elena Lilkova