An exponential transformation based splitting method for fast computations of highly oscillatory solutions

An exponential integrator for a highly oscillatory Vlasov equation

In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.

Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers

This paper explores applications of the exponential splitting method for approximating highly oscillatory solutions of the n-dimensional paraxial Helmholtz equation. An eikonal transformation is introduced for oscillation-free platforms and matrix operator decompositions. It is found that the sequential, parallel and combined exponential splitting formulas possess not only anticipated algorithm...

Transformation-based Sentence Splitting method for Statistical Machine Translation

We propose a transformation based sentence splitting method for statistical machine translation. Transformations are expanded to improve machine translation quality after automatically obtained from manually split corpus. Through a series of experiments we show that the transformation based sentence splitting is effective pre-processing to long sentence translation.

An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs

An Efficient Method for Computing Highly Oscillatory Physical Optics Integral

Abstract—In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes’ phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are careful...