We propose 4 series of practical exercises (TP for "Travaux Pratiques") using XLiFE++.

Helmholtz problem in a wave guide (TP1)

Download TP1
The goal of this TP is to experiment several strategies to compute the solution of a wave propagation problem in a closed wave guide. The 2D acoustic Helmholtz problem is considered with an obstacle inside the wave guide.

This TP is proposed by N. Kielbasiewicz and E. Lunéville.

The goal of this TP is to see how to compute the eigenvalues and some properties of these computations.
The operator is the Dirichlet Laplacian on a square $\pi \times \pi$.
The exact eigenvalues are all sums of squares of two integers $m^2+n^2$, with $m>0$, $n>0$.

Exercise 1 consists in performing the "p-version" (i.e. increasing the interpolation degree) to compare different interpolations (uniform and Gauss-Lobatto).
Exercise 2 consists in performing the "h-version" on nested trianglular meshes with different types of finite elements (Lagrange and Crouzeix-Raviart).

This TP is proposed by Zoïs Moitier as an illustration of the talks by Monique Dauge.

BEM, FEM-BEM coupling (TP3)

Download TP3
The goal of this TP is to solve a scattering problem using BEM, in 2D and in 3D. In a second part, we consider a scattering problem by a penetrable body leading to a coupling FEM-BEM strategy.

This TP is proposed by N. Kielbasiewicz and E. Lunéville.

Multi-unkknowns (TP4)

Download TP4
This TP deals with multi-unknowns problems. We first consider the Laplace problem written in a mixed formulation leading to a multi-unknowns problem to be solve in 2D and 3D. In a second part, we consider a Stokes problem in 2D.

This TP is proposed by N. Kielbasiewicz and E. Lunéville.