Related papers: High Order Phase Fitted Multistep Integrators for …
In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schroedinger equation by…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
Conventional dual-frequency fringe projection algorithm often suffers from phase unwrapping failure when the frequency ratio between the high frequency and the low one is too large. Zhang et.al. proposed an enhanced two-frequency…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as…
In this paper, we improve slightly Erd\'elyi's version of the stationary phase method by replacing the employed smooth cut-off function by a characteristic function, leading to more precise remainder estimates. We exploit this refinement to…
This article aims at developing a model based optimization for reduction of temporal unwrapping and field estimation errors in multi-echo acquisition of Gradient Echo sequence. Using the assumption that the phase is linear along the…
As a classical time-stepping method, it is well-known that the Strang splitting method reaches the first-order accuracy by losing two spatial derivatives. In this paper, we propose a modified splitting method for the 1D cubic nonlinear…
Integrated nonlinear photonic technologies, even with state-of-the-art fabrication with only a few nanometer geometry variations, face significant challenges in achieving wafer-scale yield of functional devices. A core limitation lies in…
The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping…
A class of self-similar solutions to the derivative nonlinear Schr\"odinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.
Building on the scientific understanding and technological infrastructure of single-mode fibers, multimode fibers are being explored as a means of adding new degrees of freedom to optical technologies such as telecommunications, fiber…
Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…
Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these…
The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a simple multichannel phase-noise model is considered and the maximum a posteriori detector for this…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
The spectral deferred correction (SDC) method is class of iterative solvers for ordinary differential equations (ODEs). It can be interpreted as a preconditioned Picard iteration for the collocation problem. The convergence of this method…
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently…