We are concerned with the numerical computation of electrostatic forces/torques in only piecewise homogeneous materials using the boundary element method (BEM). Conventional force formulas based on the Maxwell stress tensor yield functionals that fail to be continuous on natural trace spaces. Thus their use in conjunction with BEM incurs slow convergence and low accuracy. We employ the remedy discovered in {\sc P.~Panchal and R.~Hiptmair}, ...

We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear forced and damped oscillators, coupled via the adjacency structure of the underlying graph. The flexibility of our framework permits any basic GNN layer (e.g. convolutional or attentional) as the coupling ...

We propose a mathematical theory of acoustic wave scattering in one-dimensional finite high-contrast media. The system considered is constituted of a finite alternance of high-contrast segments of arbitrary lengths and interdistances, called the ``resonators'', and a background medium. We prove the existence of subwavelength resonances, which are the counterparts of the well-known Minnaert resonances in 3D systems. Our main contribution ...

We demonstrate that a fourfold redundancy in the measurements is sufficient for uniqueness in sampled Gabor phase retrieval with bandlimited signals and thereby draw a parallel between the sampled Gabor phase retrieval problem and finite-dimensional phase retrieval problems. Precisely, we show that sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval for signals in the Paley-Wiener space.

We propose preconditioners for the Helmholtz scattering problems by a planar, disk-shaped screen in R3. Those preconditioners are approximations of the square-roots of some partial differential operators acting on the screen. Their matrix-vector products involve only a few sparse system resolutions and can thus be evaluated cheaply in the context of iterative methods. For the Laplace equation (i.e. for the wavenumber k=0) with Dirichlet ...