The aim of this paper is to describe concisely the recent theoretical and numerical
developments concerningabsorbing boundary conditions and perfectly matched layers for …

We analyze rigorously error estimates and compare numerically spatial/temporal resolution
of various numerical methods for the discretization of the Dirac equation in the nonrelativistic …

We consider quantum graphs with transparent branching points. To design such networks,
the concept of transparent boundary conditions is applied to the derivation of the vertex …

This paper is devoted to the construction and analysis of uniformly accurate nested Picard
iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit regime. In this …

We consider the dynamics of relativistic spin-half particles in quantum graphs with
transparent branching points. The system is modeled by combining the quantum graph …

We consider the reflectionless transport of solitons in networks. The system is modeled in
terms of the nonlinear Schrödinger equation on metric graphs, for which transparent …

Pseudospectral numerical schemes for solving the Dirac equation in general static curved
space are derived using a new pseudodifferential representation of the Dirac equation along …

We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral
(MTI-FP) method for the (linear) Dirac equation with a dimensionless parameter ε∈(0,1 …

We propose a new fourth-order compact time-splitting (S_ 4c S 4 c) Fourier pseudospectral
method for the Dirac equation by splitting the Dirac equation into two parts together with …

This paper is dedicated to the study of the computational performance of basic and efficient
pseudo-spectral methods (Braun et al.(1999), Grant (2006)[1], Mocken and Keitel (2004)[2] …