Andrés Prieto

An Exact Bounded Perfectly Matched Layer for Time-Harmonic Scattering Problems

The aim of this paper is to introduce an “exact” bounded perfectly matched layer (PML) for the scalar Helmholtz equation. This PML is based on using a nonintegrable absorbing function. “Exactness” must be understood in the sense that this technique allows exact recovering of the solution to time-harmonic scattering problems in unbounded domains. In spite of the singularity of the absorbing function, the coupled fluid/PML problem is well posed when the solution is sought in an adequate weighted Sobolev space. The resulting weak formulation can be numerically solved by using standard finite elements. The high accuracy of this approach is numerically demonstrated as compared with a classical PML technique.

Finite element computation of leaky modes in stratified waveguides

Using guidedwaves can greatly facilitate the inspection of large structures such as pipes or plates. One can wonder if it remains possible for waveguides which are embedded in an elastic matrix. For NDT, guided modes could be replaced by the so-called ”leaky modes”: these modes are attenuated in the axial direction while they increase exponentially in the transverse ones. We are interested here in the finite element computation of leaky modes. The difficulty comes precisely from this exponential behaviour, which prevents us from simply truncating the infinite medium. This is the reason why we use PerfectlyMatched layers (PMLs) in order to bound the domain of calculation.We checked this approach in the simple case of SH waves in a stratified waveguide, where the analytic dispersion relation is available. Numerical experiments show that the main parameter is the distance between the PML and the guide. Finally, we illustrate in this simple case a numerical application using leaky modes: the Green function of the embedded waveguide is given by modal expansion.

Automatic Analysis of Floating Offshore Structures

In the coming years offshore wind energy will be one of the most promising areas in the renewable power generation field. Achieving the optimum design of floating platforms requires a rigorous analysis chain to establish the response of the whole platform under different scenarios. With this aim, we have developed a software package that automatically analyzes the feasibility of a floating structure. The structure of the platform is defined according to a very general set of parameters, allowing us to consider a wide range of designs. The package calls some commercial applications and some own codes, to complete the analysis process. Returned results include the hydrostatic equilibrium position, hydrodynamic pressure, RAOs (response-amplitude operators), material costs and static stresses.