Numerical methods
===================


Nonlinear methods
----------------------

Newton's method


* No adaptive times, event-driven DEFI_LIST_INST


* Mixed linear research: extension to mechanical, thermal, THM

Alternative to Newton: IMPLEX


* Robust for softening problems: approximate solutions, dependence on the time step


* Supports automatic time step management

Large deformations [Miehe*et al.*]


* Isotropic and kinematic work hardening, anisotropy


* Any law written in HPP


* Symmetric matrix, quadratic convergence GDEF_LOG

Mixed formulation :math:`u\mathrm{-}p`


* Incompressibility treatment


*Linear and quadratic elements*_ INCO_UP


Contact
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New operator dedicated to contact DEFI_CONTACT


* Data sharing common to all methods


* Better readability


* Significant performance gains

New methodological documentation to help the user:


* U2.04.04 contact user manual