MatSol: MATLAB efficient solvers for problems in engineering. The algorithms implemented in MatSol library are based on our long-term research focused on the development of scalable algorithms for multibody contact and contact shape optimization problems, 2D or 3D, with or without friction. Isotropic and anisotropic, Tresca and Coulomb friction models are supported. Matsol library serves as a referential implementation of those algorithms. Variants of FETI and BETI known for their parallel and numerical scalability are used for domain decomposition. The resulting class of QP problems are solved using our special QP algorithms. The unique feature of them is their capability to solve these QP problems with a bounded spectrum in O(1) iterations. Theory yields the error bounds that are independent of conditioning of constraints and the results are valid even for linearly dependent equality constraints. ...

References in zbMATH (referenced in 20 articles )

Showing results 1 to 20 of 20.
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  1. Cermak, M.; Haslinger, J.; Kozubek, T.; Sysala, S.: Discretization and numerical realization of contact problems for elastic-perfectly plastic bodies. II: Numerical realization, limit analysis (2015)
  2. Dostál, Z.; Kozubek, T.; Vlach, O.; Brzobohatý, T.: Reorthogonalization-based stiffness preconditioning in FETI algorithms with applications to variational inequalities. (2015)
  3. Kučera, Radek; Motyčková, Kristina; Markopoulos, Alexandros: The R-linear convergence rate of an algorithm arising from the semi-smooth Newton method applied to 2D contact problems with friction (2015)
  4. Beremlijski, Petr; Haslinger, Jaroslav; Outrata, Jiří; Pathó, Róbert: Numerical solution of 2D contact shape optimization problems involving a solution-dependent coefficient of friction (2014)
  5. Bouchala, Jiří; Dostál, Zdeněk; Kozubek, Tomáš; Pospíšil, Lukáš; Vodstrčil, Petr: On the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature (2014)
  6. Dostál, Zdeněk; Brzobohatý, Tomáš; Horák, David; Kozubek, Tomáš; Vodstrčil, Petr: On R-linear convergence of semi-monotonic inexact augmented Lagrangians for bound and equality constrained quadratic programming problems with application (2014)
  7. Kučera, R.; Kozubek, T.; Markopoulos, A.: On large-scale generalized inverses in solving two-by-two block linear systems (2013)
  8. Kučera, R.; Machalová, J.; Netuka, H.; Ženčák, P.: An interior-point algorithm for the minimization arising from 3D contact problems with friction (2013)
  9. Pospíšil, Lukáš: An optimal algorithm with Barzilai-Borwein steplength and superrelaxation for QPQC problem. (2013)
  10. Dostál, Zdeněk; Kozubek, Tomáš: An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications (2012)
  11. Dostál, Z.; Kozubek, T.; Markopoulos, A.; Brzobohatý, T.; Vondrák, V.; Horyl, P.: A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction (2012)
  12. Sadowská, Marie; Dostál, Zdeněk; Kozubek, Tomáš; Markopoulos, Alexandros; Bouchala, Jiří: Engineering multibody contact problems solved by scalable TBETI (2012)
  13. Brzobohatý, T.; Dostál, Z.; Kozubek, T.; Kovář, P.; Markopoulos, A.: Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure (2011)
  14. Dostál, Zdeněk; Kozubek, Tomáš; Markopoulos, Alexandros; Menšík, Martin: Cholesky decomposition of a positive semidefinite matrix with known kernel (2011)
  15. Haslinger, Jaroslav; Kučera, Radek; Ligurský, Tomáš: Qualitative analysis of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coefficients of friction (2011)
  16. Sadowská, M.; Dostál, Z.; Kozubek, T.; Markopoulos, A.; Bouchala, J.: Scalable total BETI based solver for 3D multibody frictionless contact problems in mechanical engineering (2011)
  17. Dostál, Zdeněk; Kučera, Radek: An optimal algorithm for minimization of quadratic functions with bounded spectrum subject to separable convex inequality and linear equality constraints (2010)
  18. Dostál, Z.; Kozubek, T.; Horyl, P.; Brzobohatý, T.; Markopoulos, A.: A scalable TFETI algorithm for two-dimensional multibody contact problems with friction (2010)
  19. Dostál, Z.; Kozubek, T.; Vondrák, V.; Brzobohatý, T.; Markopoulos, A.: Scalable TFETI algorithm for the solution of multibody contact problems of elasticity (2010)
  20. Vondrák, Vít; Kozubek, Tomáš; Markopoulos, Alexandros; Dostál, Zdeněk: Parallel solution of contact shape optimization problems based on total FETI domain decomposition method (2010)