Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems

A Feti Solver for Corotational Nonlinear Problems

Substructured formulations of nonlinear structure problems - influence of the interface condition

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD, so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objecti...

Regularized formulations of FETI

FETI 205 A conforming FEM for (2.7) results in the discrete optimality system   K1 0 B T 1 0 0 K̃2 −B2 −C2 Υ B1 −B2 0 0 0 −ΥC2 0 Υ     u1 u2 λ μ   =   f1 f2 0 0   (2.8) where K̃2 ≡ K2 +C2 ΥC2. Elimination of the primal variables in (2.8) results in the coarse grid problem [ B1K −1 1 B T 1 +B2K̃ −1 2 B T 2 B2K̃ −1 2 C T 2 Υ ΥC2K̃ −1 2 B T 2 ΥC2K̃ −1 2 C T 2 Υ−Υ ] [ λ μ ] = [ d1 d1 ] ...

A new impedance accounting for short and long range effects in mixed substructured formulations of nonlinear problems

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal v...

Nonlinearly Preconditioned Inexact Newton Algorithms

Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations F (u∗) = 0 arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust region, the methods often stagnate at local minima of ‖F‖, especially for problems with unbalanced nonlinearities, because the methods do not have bui...