Related papers: New optimized Schwarz algorithms for one dimension…
We study non-local exchange and scattering operators arising in domain decomposition algorithms for solving elliptic problems on domains in $\mathbb{R}^2$. Motivated by recent formulations of the Optimized Schwarz Method introduced by…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\"odinger equation, which describes the evolution of the signal in the link, numerically.…
We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission…
By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…
Schr\"odinger equations with time-dependent potentials are of central importance in quantum physics and theoretical chemistry, where they aid in the simulation and design of systems and processes at atomic scales. Numerical approximation of…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Solving linear and nonlinear differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed…
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
The performance of Schwarz Waveform Relaxation is critically dependent on the choice of transmission conditions. While classical absorbing conditions work well for wave propagation, they prove insufficient for damped wave equations,…
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is…
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known…
We establish the existence of positive segregated solutions for competitive nonlinear Schr\"odinger systems in the presence of an external trapping potential, which have the property that each component is obtained from the previous one by…
This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…