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-step analysis of Anderson acceleration with general algorithmic depths is presented.
The resulting residual bounds within both contractive and noncontractive settings reveal 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 …

The method of difference potentials was originally proposed by Ryaben'kii and can be
interpreted as a generalized discrete version of the method of Calderon's operators in the …

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, third-and fourth-order compact finite difference schemes are proposed for
solving Helmholtz equations with discontinuous media along straight interfaces in two space …

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 …

In this chapter, we discuss computational problems, solution methods, and their efficient
implementation. We describe different approaches to writing algorithms to solve a particular …

In this paper, the electromagnetic scattering from a rectangular large open cavity embedded
in an infinite ground plane is studied. By introducing a nonlocal artificial boundary condition …