This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem ...

The classical Helmholtz theory of accommodation has, over the years, not gone unchallenged and most recently has been opposed by Schachar at al. (1993) (Annals of Ophthalmology, 25 (1) 5-9) who suggest that increasing the zonular tension increases rather than decreases the power of the lens. This view is supported by a numerical analysis of the lens based on a linearised form of the governing e...

We continue our study of the statistical properties of particles in equilibrium obeying Smoluchowski dynamics. We show that the system is governed by a kinetic equation of the memory function form and that the memory function is given by one of the self-energies available via perturbation theory as introduced in previous work. We determine the memory function explicitly to second order in an ex...

We study coupled nonlinear parabolic equations for a fluid described by a material density ρ and a temperature Θ, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on the boundary, with no-escape boundary conditions for the material. For the special case, where the temperature on the boundary is the same at both ends, t...

We investigate the transmission and reflection properties at the interfaces between the lossy positive-index materials (PIM) and negative-index materials (NIM) with graded permittivity and permeability. We present an exact analytical solution to Helmholtz’ equation for the oblique incidence on profile with the graded real parts of permittivity and permeability profile changing according to a hy...