This paper analyzes the Krylov convergence rate of a Helmholtz problem preconditioned with Multigrid. The multigrid is applied to the Helmholtz problem formulated on a complex contour and uses polynomial smoothers at each level. A one-dimensional model is analyzed both in a continuous and discrete way. It is shown that the Krylov convergence rate of the continuous problem is independent of the ...

We present, to the best of our knowledge, the first exact analytical solitons of a nonlinear Helmholtz equation with a saturable refractive-index model. These new two-dimensional spatial solitons have a bistable characteristic in some parameter regimes, and they capture oblique (arbitrary-angle) beam propagation in both the forward and backward directions. New conservation laws are reported, an...

This paper introduces a novel surface model registration technique based on the Helmholtz reciprocity principle. Initially, a 3D surface model is generated for an object of interest. Two images of the object are then acquired under controlled lighting conditions. Given one of the images and an estimate of the surface pose, Helmholtz reciprocity is used to predict the appearance of the object su...

The onset of monami – the synchronous waving of seagrass beds driven by a steady flow – is modelled as a linear instability of the flow. Unlike previous works, our model considers the drag exerted by the grass in establishing the steady flow profile, and in damping out perturbations to it. We find two distinct modes of instability, which we label modes 1 and 2. Mode 1 is closely related to Kelv...

Many features of a molecule which are of physical interest (e.g. molecular conformations, reaction rates) are described in terms of its dynamics in configuration space. This article deals with the projection of molecular dynamics in phase space onto configuration space. Specifically, we study the situation that the phase space dynamics is governed by a stochastic Langevin equation and study its...

Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski ...

The numerical solution of Helmholtz’ equation at large wavenumber is very expensive if attempted by ”traditional” discretisation methods (FDM, standard Galerkin FEM). For reliable results, the mesh has to be very fine. The bad performance of the traditional FEM for Helmholtz problems can be related to the deterioration of stability of the Helmholtz differential operator at high wavenumber. As a...