4 papers
A neural operator framework for solving inverse scattering problems
Victor Chenu, Houssem Haddar, Hadrien Montanelli
We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropri…
Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
Luiz Maltez Faria, Pierre Marchand, Hadrien Montanelli
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our…
Nonlocal vector calculus on the sphere
Hadrien Montanelli, Richard Mikael Slevinsky, Qiang Du
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar…
The linear sampling method for data generated by small random scatterers
J. Garnier, H. Haddar, H. Montanelli
We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scat…