Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

A one-dimensional periodic array of circular dielectric cylinders surrounded by air is a
simple structure on which guided modes above the light line, also called bound states in the …

This paper considers the effect of Anderson acceleration (AA) on the convergence order of
nonlinear solvers in fixed point form xk+ 1= g (xk), that are looking for a fixed point x∗ of g …

This work introduces, analyzes, and demonstrates an efficient and theoretically sound
filtering strategy to ensure the condition of the least-squares problem solved at each iteration …

In many problems, one wishes to solve the Helmholtz equation with variable coefficients
within the Laplacian-like term and use a high order accurate method (eg, fourth order …

In this paper, we reconsider the inverse Lax-Wendroff (ILW) procedure, which is a numerical
boundary treatment for solving hyperbolic conservation laws, and propose a new approach …

In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical
coordinates which introduces variable coefficients within the differentiated terms. Fourth …

The well-posedness of a nonlinear Helmholtz equation with an impedance boundary
condition is established for high frequencies in two and three dimensions. Stability estimates …

We propose a multiscale approach for a nonlinear Helmholtz problem with possible
oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The …

Recently, a so-called direct method has been developed for solving 2D Maxwell's equations
in Kerr-type nonlinear media. This method is free of iteration error and more efficient than …