Numerical libraries solving large-scale problems developed at IT4Innovations Research Programme Supercomputing for Industry ☆

Summary The team of Research Programme Supercomputing for Industry at IT4Innovations National Supercomputing Center is focused on development of highly scalable algorithms for solution of linear and non-linear problems arising from different engineering applications. As a main parallelisation technique, domain decomposition methods (DDM) of FETI type are used. These methods are combined with finite element (FEM) or boundary element (BEM) discretisation methods and quadratic programming (QP) algorithms. All these algorithms were implemented into our in-house software packages BEM4I, ESPRESO and PERMON, which demonstrate high scalability up to tens of thousands of cores.

[1]  Martin Cermák,et al.  Total-FETI domain decomposition method for solution of elasto-plastic problems , 2015, Adv. Eng. Softw..

[2]  Charbel Farhat,et al.  An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems , 1992, SIAM J. Sci. Comput..

[3]  Martin Cermák,et al.  Total FETI domain decomposition method and its massively parallel implementation , 2013, Adv. Eng. Softw..

[4]  Z. Dostál,et al.  Solution of contact problems by FETI domain decomposition with natural coarse space projections , 2000 .

[5]  Joachim Schöberl,et al.  Minimizing Quadratic Functions Subject to Bound Constraints with the Rate of Convergence and Finite Termination , 2005, Comput. Optim. Appl..

[6]  S. Rjasanow,et al.  The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering) , 2007 .

[7]  Z. Dostál,et al.  Total FETI—an easier implementable variant of the FETI method for numerical solution of elliptic PDE , 2006 .

[8]  Michal Merta,et al.  A parallel library for boundary element discretization of engineering problems , 2018, Math. Comput. Simul..

[9]  Vaclav Hapla,et al.  TFETI Coarse Space Projectors Parallelization Strategies , 2011, PPAM.

[10]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[11]  Zdenek Dostál,et al.  Cholesky decomposition of a positive semidefinite matrix with known kernel , 2011, Appl. Math. Comput..

[12]  Z. Dostál,et al.  Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure , 2011 .

[13]  David Horák,et al.  Scalable FETI with optimal dual penalty for a variational inequality , 2004, Numer. Linear Algebra Appl..

[14]  Zdenek Dostál,et al.  Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints , 2002, SIAM J. Optim..

[15]  Jaroslav Kruis,et al.  Solving laminated plates by domain decomposition , 2002 .

[16]  P. Gosselet,et al.  Non-overlapping domain decomposition methods in structural mechanics , 2006, 1208.4209.

[17]  Jan Zapletal,et al.  Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D , 2014 .

[18]  Olof B. Widlund,et al.  FETI‐DP, BDDC, and block Cholesky methods , 2006 .

[19]  Zdenek Dostl.  Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities , 2009 .

[20]  Michal Merta,et al.  Acceleration of boundary element method by explicit vectorization , 2015, Adv. Eng. Softw..

[21]  Olaf Steinbach,et al.  The all-floating boundary element tearing and interconnecting method , 2009, J. Num. Math..

[22]  Axel Klawonn,et al.  A Parallel Implementation of Dual-Primal FETI Methods for Three-Dimensional Linear Elasticity Using a Transformation of Basis , 2006, SIAM J. Sci. Comput..

[23]  Olaf Steinbach,et al.  Boundary Element Tearing and Interconnecting Methods , 2003, Computing.

[24]  A. Klawonn,et al.  Highly scalable parallel domain decomposition methods with an application to biomechanics , 2010 .

[25]  Olof B. Widlund,et al.  Dual‐primal FETI methods for linear elasticity , 2006 .

[26]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[27]  Zdene caron,et al.  Theoretically Supported Scalable FETI for Numerical Solution of Variational Inequalities , 2007 .

[28]  Z. Dostál,et al.  Scalable TFETI with optional preconditioning by conjugate projector for transient frictionless contact problems of elasticity , 2012 .

[29]  Jaroslav Kruis.  Domain Decomposition Methods for Distributed Computing , 2007 .

[30]  J. Haslinger,et al.  FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction , 2005 .

[31]  C. Farhat,et al.  Optimal convergence properties of the FETI domain decomposition method , 1994 .

[32]  Z. Dostál,et al.  Scalable TFETI algorithm for the solution of multibody contact problems of elasticity , 2009 .