Principles of the Method of Large Time Increments

Abstract

AbstractThe large time increment method (acronym: LATIN) was introduced by Ladevèze [1985a, b]. It represents a break with classical incremental methods in the sense that it is not built on the notion of small increments; the interval of time studied, [0, T] does not have to be partitioned into small pieces. It is an iterative method that sometimes starts with a relative gross approximation (generally coming from an elastic analysis) for displacements, strains, and stresses at each point M belonging to the domain Ω and for all t belonging to [0, T]. At each iteration, an improvement is always made to these different quantities for all t ∈ [0, T] and for all M ∈ Ω. For the interval of study, [0, T] the method is built on three principles: P1, separation of the difficulties—partition of the equations into two groups: a group of equations local in space and time, possibly nonlinear a group of linear equations, possibly global in the spatial variable. P2,a two-step iterative approach where, at each iteration, one constructs, alternatively, a solution to the first group of equations and then a solution to the second group. The first problem is local in the spatial variable, perhaps nonlinear, and the second is linear but generally global P3,use of an ad hoc space-time approximation based on mechanics for the treatment of the global problem defined on Ω × [0,T]. KeywordsConstitutive RelationPosteriori ErrorMaximal MonotoneNonlinear MechanicError IndicatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.