Related papers: On shape and topological optimization problems wit…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
In recent years, several studies have been made in which atmospheric and oceanic data were used to decompose horizontal velocity statistics into a rotational component, associated with vertical vorticity, and a divergent component,…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
This paper is dedicated to the spectral optimization problem $$ \mathrm{min}\left\{\lambda_1^s(\Omega)+\cdots+\lambda_m^s(\Omega) + \Lambda \mathcal{L}_n(\Omega)\colon \Omega\subset D \mbox{ s-quasi-open}\right\} $$ where $\Lambda>0,…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…
We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be…
We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator $H=-\Delta_{x}-\Delta_{y}+V(x,y)$ with Dirichled boundary condition on an unbounded domain $\Omega$,…
The mechanism that causes an interdecadal oscillation in a coarse resolution sector ocean model forced by mixed boundary conditions is studied. The oscillation is characterized by large fluctuations in convective activity and air/sea heat…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
Propulsion at microscopic scales is often achieved through propagating traveling waves along hair-like organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of…
The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for elliptic problems, this paper presents a novel…
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…
A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…
The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability…