The main purpose of this group is to develop, implement, test and optimize FETI-based algorithms for the solution of large scale engineering problems. Developement of C/C++ library of FETI solvers based on PETSc and Trilinos frameworks is in progress. Our codes has already been tested on more than 4000 cores (at EPCC, UK). The goal is to extend the scalability up to tens of thousands of cores.

Project leader | |

Ing. David Horak, Ph.D. | david.horak at vsb.cz |

Junior Researchers | |

Ing. Lubomir Riha | |

Ing. Martin Cermak, Ph.D. | martin.cermak at vsb.cz |

Research assistants | |

Ing. Vaclav Hapla | vaclav.hapla at vsb.cz |

Ing. Martin Mensik | martin.mensik at vsb.cz |

Ing. Michal Merta | michal.merta at vsb.cz |

**FLLOP: A Novel Package for Quadratic Programming including FETI Computations - Václav Hapla and David Horák**

FLLOP (FETI Light Layer on top of PETSc) is a not yet published novel package for constrained quadratic programming (like MATLAB's quadprog) and FETI domain decomposition, built on top of PETSc as its extension (similarly to TAO or SLEPc). FLLOP API is carefully designed to be user-friendly allowing natural specification of a QP problem, QP transformations independent of a particular solver, automatic or manual choice of a sensible solver. Still it remains efficient and targeted at HPC. Current applications include mainly engineering problems of structure mechanics: linear elasticity, contact problems (also with friction), elasto-plasticity, and shape optimization. Interesting and quite unusual experiments include medical image registration. But our long-term tight cooperation with the Elmer FEM team should lead soon to other applications like modeling of ice-sheet melting or electrical engines.**Trilinos FETI Solvers**- another package for the parallel solution of PDEs using FETI method. Based on the Trilinos framework. Uses mainly Epetra, Tpetra, Belos and Amesos packages from Trilinos. Contrary to FLLOP, this package is developed from scratch, however it exploits modern features of C++ and has modular, object oriented design. Contains algorithms for the parallel solution of constrained quadratic problems, input from MATLAB data format etc.**Other software**- Members of our group have participated in the development of other software packages, namely MatSol (MATLAB® library for domain decomposition and solution of arising quadratic programming problems) or OOSol (Object oriented solvers in C++).- We are also participating in the solution of problems arising from our membership in the PRACE organization. (e.g. cooperation with CSC Finland on the development of ELMER software, organization of PRACE seasonal schools (Ostrava, Krakow) etc.

Members of the group are also members of the Department of Applied Mathematics, VSB-TU Ostrava, SPOMECH project and Centre of Excellence IT4Innovations the aim of which is to build a national Centre of Excellence in the field of information technologies.

Centre of Excellence IT4Innovations

VŠB-Technical University of Ostrava

17. listopadu 15/2172, 708 33 Ostrava-Poruba

Czech Republic

VŠB-Technical University of Ostrava

17. listopadu 15/2172, 708 33 Ostrava-Poruba

Czech Republic

**27-30 May 2013**: HPCSE 2013, Soláň, Czech Republic, M. Cermak and M. Merta: Parallel solution of elasto-plastic problems (talk), L. Riha: A method for communication efficient work distributions in stencil operation based applications on heterogeneous clusters (talk), V. Hapla and D. Horak: FLLOP library (poster)**9-11 April 2013**: EASC2013, Edinburgh, UK, V. Hapla and D. Horak: A Novel Package for Quadratic Programming including FETI Computations (poster)**25-27 March 2013:**PARENG2013, Pécs, Hungary, V. Hapla and D. Horak: A Comparison of FETI Natural Coarse Space Projector Implementation Strategies (talk), M. Merta and M. Cermak: Parallel Implementation of the Total-FETI Domain Decomposition Method for the Solution of Elasto-Plastic Problems (talk)**21-25 January 2013:**SNA'13, Rožnov p. R., Czech Republic, M. Merta: Parallel Fast Multipole BEM (talk), V. Hapla: FLLOP - a massively parallel QP solver (talk)**25 June 2012**: Michal Merta actively participated in DD21 conference, Rennes, France.**10 June 2012**: David Horak and Vaclav Hapla actively participated in PARA conference, Helsinki, Finland.**23 May 2012**: David Horak and Vaclav Hapla are currently on a month stay in CSC, Finland.**17 May 2012**: D. Horak, V. Hapla and M. Merta participated on PRACE Spring School 2012 in Krakow, Poland with the talk Introduction to Scientific Computing Using PETSc and Trilinos.**29 January 2012**: D. Horak, V. Hapla and M. Merta participated in Seminar on Numerical analysis in Roznov p. Radhostem, Czech Republic, with talk Software design of TFETI massively parallel implementation. M. Mensik participated on the talks Hybrid Total-FETI and Faster gradient descent methods.**20 December 2011**: Michal Merta received Babuska award for the best diploma thesis in the field of computational mechanics.**13 September 2011**: V. Hapla presented joint results with David Horak in the presentation "TFETI coarse space projectors parallelization strategies" at the 9th International Conference on Parallel Processing and Applied Mathematics (PPAM 2011), Torun, Poland.**25 August 2011**: V. Hapla, M. Merta and P. Kotas presented talk Modern parallel numerical methods with Trilinos framework**3 April 2011**: D. Horak and V. Hapla participated on Elmer & FETI Workshop at CSC, Finland.

HAPLA, Václav; HORÁK, David; MERTA, Michal. Use of direct solvers in TFETI massively parallel implementation. Lecture Notes in Computer Science. Springer, 2013, 7782, pp. 192-205. DOI: 10.1007/978-3-642-36803-5_14. |

HAPLA, V., HORAK, D.: TFETI coarse space projectors parallelization strategies, PPAM 2011, Lecture Notes in Computer Science, 7203 LNCS (PART 1), Springer, 2012, pp. 152-162, DOI: 10.1007/978-3-642-31464-3_16 |

HAPLA, V., HORAK, D., MERTA, M.: Software design of TFETI massively parallel implementation, Proceedings of SNA 2012, Technical University of Liberec, pp. 60-63, ISBN: 978-80-7372-821-2, URL. |

KOZUBEK T.; VONDRAK, V.; MENSIK M.; HORAK, D.; DOSTAL, Z.; HAPLA V.; KABELIKOVA, P.; CERMAK M. Total FETI domain decomposition method and its massively parallel implementation. Accepted for publishing in Advances in Engineering Software. |

DOSTAL, Z.; KOZUBEK, T.; MARKOPOULOS, A.; MENSIK, M. Cholesky decomposition and a generalized inverse of the stiffness matrix of a floating structure with known null space. Applied Mathematics and Computation. 2011; 217:6067–6077. |

DOSTAL, Z.; KOZUBEK, T.; VONDRAK, V; BRZOBOHATY, T.; MARKOPOULOS, A. Scalable TFETI algorithm for the solution of multibody contact problems of elasticity. Int. J. Numer. Meth. Engng. 82(11), 1384-1405, (2010). |

DOSTAL, Z.; KOZUBEK, T.; MARKOPOULOS, A.; BRZOBOHATY, T.; VONDRAK, V.; HORYL, P. Theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction. CMAME, 2011, DOI: 10.1016/j.cma.2011.02.015. |

HORAK, D.; DOSTAL, Z. Parallelization of the Total-FETI-1 Algorithm for Contact Problems using PETSc. In IVÁNYI, P.; TOPPING, B. H. V. Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Stirlingshire : Civil-Comp Press, 2011. |

MENSIK, M. The Inexact Solution of the Primal Part in the Domain Decomposition Method. In IVÁNYI, P.; TOPPING, B. H. V. Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Stirlingshire : Civil-Comp Press, 2011. |

VONDRAK, V.; KOZUBEK, T.; SADOWSKA, M.; DOSTAL, Z. TBETI and TFETI Algorithms for Contact Shape Optimization Problems. In IVÁNYI, P.; TOPPING, B. H. V. Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Stirlingshire : Civil-Comp Press, 2011. |

HORAK, D.; KABELIKOVA, P.; MERTA, M.; VONDRAK, V. The OOSol Scalable Library Based on a Domain Decomposition Method. In IVÁNYI, P.; TOPPING, B. H. V. Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. Stirlingshire : Civil-Comp Press, 2011. |