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Section: New Results
Direct scattering problems
Finite element methods for eigenvalue problems with sign-changing coefficients
C. Carvalho, P. Ciarlet and L. Chesnel
We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We analyse the main spectral properties of these problems according to the features of the coefficients. Under some assumptions on the mesh, we study how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious modes. We also prove localisation results of the eigenfunctions for certain sets of coefficients.
A Volume integral method for solving scattering problems from locally perturbed periodic layers
H. Haddar and T.P. Nguyen
We investigate the scattering problem for the case of locally perturbed periodic layers in , . Using the Floquet-Bloch transform in the periodicity direction we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.