The Halfspace Matching Method: a New Method to Solve Scattering Problem in Infinite Media

Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss and Antoine Tonnoir
submitted
Publication type:
Paper in peer-reviewed journals
Journal:
JCAM
Keywords :
Integral operators; plane-waves representations; Fourier Transform; Anisotropic Helmholtz equation; Domain Decomposition Methods;
Abstract:
We are interested in acoustic wave propagation in time harmonic regime in a two-dimensional medium which is a local perturbation of an infinite isotropic or anisotropic homogeneous medium. We investigate the question of finding artificial boundary conditions to reduce the numerical computations to a neighborhood of this perturbation. Our objective is to derive a method which can extend to the anisotropic elastic problem for which classical approaches fail. The idea consists in coupling several semi-analytical representations of the solution in halfspaces surrounding the defect with a Finite Element computation of the solution around the defect. As representations of the same function, they have to match in the infinite intersections of the halfspaces. It leads to a formulation which couples, via integral operators, the solution in a bounded domain including the defect and its traces on the edge of the halfspaces. A stability property is shown for this new formulation.
BibTeX:
@article{Bon-Fli-Ton-2200,
    author={Anne-Sophie Bonnet-Ben Dhia and Sonia Fliss and Antoine 
           Tonnoir },
    title={The Halfspace Matching Method: a New Method to Solve 
           Scattering Problem in Infinite Media },
    journal={JCAM },
    year={submitted },
    month={7},
}