Reduced Basis and Iterative Algorithms for Non-Linear Elastic Thin Shells

International audience; In this work, we propose an iterative linear solver for the linearized equations coming from the Newton-Raphson method. In structural mechanics, the computation of the non-linear solution, with a Newton-Raphson method for example, requires the solution of sparse linear systems of equations: $K^i U^i = F(U^j )$ with $i = 1,...,k$ and $j = 1,...,i − 1$ with $K^i$ designates a $N × N$ symmetric matrix (the tangent matrix), $U^i$ is the unknown displacement vector $(U^i ∈ \mathbb{R}^N)$ and $F(U^j )$ is a load vector which depends on the previous solutions $U^j$ with $j = 1,...,i − 1$.