Hearing the shape of a general convex domain: an extension to higher dimensions
Hearing the shape of membranes: Further results.
Hierarchical grid coarsening for the solution of the Poisson equation in free space.
High Frequency limit of the Helmholtz Equations
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term (which does not share the...
High frequency limit of the Helmholtz equations.
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term ( which does not share the...
Highfrequency asymptotics of the field scattered by an obstacle near tangential rays.
Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example
Homogenization of the Poisson equation in a thick periodic junction.