We present an ab initio three-dimensional quantum study of high-order harmonic generation ~HHG! of atomic H in intense pulsed laser fields. Accurate time-dependent wave functions are obtained by means of the time-dependent generalized pseudospectral method recently developed and wavelet transform is used to perform time-frequency analysis of the resulting HHG power spectra. The results reveal s...

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for nonintrusive pseudospectral approximation, based on Smolyak’s algorithm with generalized sparse grids. We rigorously analyze and extend the nonadaptive method proposed in [P. G. Constantine, M. S. Eldred, and E. T. Phipps, Comput. Methods Appl. Mec...

We present a new reduced scaling multireference singles and doubles configuration interaction ~MRSDCI! algorithm based upon the combination of local correlation and pseudospectral methods. Taking advantage of the locality of the Coulomb potential, the weak-pairs approximation of Saebo” and Pulay is employed to eliminate configurations having simultaneous excitations out of pairs of distant, wea...

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization probl...

New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose-Einstein condensates (BECs) described by a three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulatio...

One of the operational requirements for unmanned aerial vehicles is the autonomous navigation and control along a given sequence of waypoints, or along a predefined trajectory. Existing autonomous navigation procedures are mostly done in 3D because of the stringent certification requirements for 4D flight and due to the complexity in coping with time of arrival at waypoints, whilst actual fligh...

The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents and other maneuvers are necessary. In this paper, the problem of determining constrained, three-dimensional, minimum-time-to-climb and minimum-fuel-to-climb trajectories for an aircraft in an airspace defined by a rectang...

A numerical simulation of steady and unsteady two-dimensional flows past cylinder with dimples based on highly accurate pseudospectral method is the subject of the present paper. The vorticity and streamfunction formulation of two-dimensional incompressible NavierStokes equations with no-slip boundary conditions is used. The system is formulated on a unit disk using curvilinear body fitted coor...

Multivariate global polynomial approximations – such as polynomial chaos or stochastic collocation methods – are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two ...