Related papers: New Phase-Integral Method Platform Function
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve…
The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are…
The design of a complex phase mask (CPM) for inscribing aperiodic filters in fibers is presented. The complex structure of the mask surface relief consists of discrete aperiodic phase-steps at periodic intervals. We show that the…
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization…
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach,…
Phase imaging techniques extract the optical path-length information of a scene, whereas wavefront sensors provide the shape of an optical wavefront. Since these two applications have different technical requirements, they have developed…
We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple…
Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the…
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element (IFE) method is efficient for solving interface problems on…
Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
Quantitative phase imaging (QPI) has been widely applied in characterizing cells and tissues. Spatial light interference microscopy (SLIM) is a highly sensitive QPI method, due to its partially coherent illumination and common path…
This article presents a numerical model dedicated to the simulation of field ion microscopy (FIM). FIM was the first technique to image individual atoms on the surface of a material. By a careful control of the field evaporation of the…
The pseudoparticle approach is a numerical method to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number…
We present novel approaches for solving Milne's equation, which was introduced in 1930 as an efficient numerical scheme for the Schr\"odinger equation. Milne's equation appears in a wide class of physical problems, ranging from astrophysics…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian…
It is a challenge for Phase Measurement Profilometry (PMP) to measure objects with a large range of reflectivity variation across the surface. Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to…