This review article revisits and outlines the perfectly matched layer (PML) method and its
various formulations developed over the past 25 years for the numerical modeling and …

A digital twin (DT) is a numerical model (in silico) of a system that runs alongside its physical
counterpart and exchanges (bidirectional) information with it. The digital twin, once suitably …

The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) for the
two-dimensional peridynamics equation of motion which describes nonlocal phenomena …

A general method is proposed to build exact artificial boundary conditions for the one-
dimensional nonlocal Schrödinger equation. To this end, we first consider the spatial semi …

A general method is proposed forc constructing accurate artificial boundary conditions for
the two-dimensional nonlocal Schrödinger equation (where the derivative term is replaced …

Abstract Perfectly Matched Layers (PML) are proposed for time-dependent space fractional
PDEs. Within this approach, widely used powerful Fourier solvers based on FFTs can be …

In this paper, we first propose a general strategy to implement the Perfectly Matched Layer
(PML) approach in the most standard numerical schemes used for simulating the dynamics …

The aim of this paper is to design some accurate artificial boundary conditions for the semi-
discretized linear Schrödinger and heat equations in rectangular domains. The Laplace …

The purpose of this paper is to discuss some recent developments concerning the numerical
simulation of space and time fractional Schrödinger and Gross–Pitaevskii equations. In …

To simulate waves on unbounded domain, absorbing boundary conditions are usually
needed to bound the computational domain and avoid boundary reflections as much as …