Open AccessApplication of a recycling Krylov subspace strategy for discrete element method applied to brittle crack problems
Author(s) -
Sylvain Gavoille,
Arnaud Delaplace,
Christian Rey
Publication year - 2009
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/ejcm.18.647-667
Subject(s) - krylov subspace , sequence (biology) , stiffness matrix , convergence (economics) , subspace topology , discrete element method , finite element method , matrix (chemical analysis) , mathematical optimization , reduction (mathematics) , iterative method , algorithm , computer science , stiffness , element (criminal law) , simple (philosophy) , mathematics , structural engineering , engineering , geometry , mathematical analysis , materials science , philosophy , law , economic growth , mechanics , composite material , biology , genetics , epistemology , political science , physics , economics
This paper deals with a comparative study of two iterative Krylov solvers (GIRKS and SRKS) dedicated to the solution to a sequence of large linear problems. We apply these two algorithms to brittle crack problems modelized with a discrete element method. We show that these algorithms still reduce the total number of iterations but not the total CPU time. By considering the specific modification of the stiffness matrix for discrete modeling, we propose a simple evolution of the SRK algorithm leading to a reduction of the factor time (greater than 2). Efficiency of the algorithm is illustrated on 2D and 3D examples of crack propagation.