Numerical Solution of a Pile Problem

In this work, we are interested in the numerical solution of a nonlinear partial differential equation modeling the displacement of a pile in a multi-layer ground. In the first part, the module of the ground is assumed to be constant by layer and the considered model is linear. The computation of the analytical solution requires the calculation of a great number of coefficients. Hence, a domain decomposition method is proposed where each layer is assumed to be a sub-domain. On the other hand, the problem is solved using a discretization by finite differences method.For the nonlinear model, the existence of a solution is established. The discrete problem is then solved numerically using a Newton type method.