Poisson equation is frequently encountered in mathematical modeling for scientific and engineering applications. Fast Poisson numerical solvers for 2D and 3D problems are, thus, highly requested. In this paper, we consider solving the Poisson equation ∇2u = f(x, y) in the Cartesian domain Ω = [−1, 1] × [−1, 1], subject to all types of boundary conditions, discretized with the Chebyshev pseudosp...

We describe Fourier pseudospectral time-domain simulations, carried out in order to study light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to accurately predict the electromagnetic scattering in such problems arises from the discontinuity in the dielectric function along the surface of the metallic object. Standard Fourier methods lead to oscillatory b...

By systematically altering the in-plane flight path and velocity of an aircraft and the rate at which the cable is deployed, the tip of a cable being towed behind an aircraft is shown to rendezvous with a ground-based surface location in minimum time, with minimum control effort required. This is achieved through optimal control, formulated as a nonlinear programming problem using the Legendre-...

In our previous work, we have shown that the pseudospectral method is an effective and flexible computation scheme for deriving pulses for optimal control of quantum systems. In practice, however, quantum systems often exhibit variation in the parameters that characterize the system dynamics. This leads us to consider the control of an ensemble (or continuum) of quantum systems indexed by the s...

The estimate derived by Henshaw, Kreiss, and Reyna for the smallest scale present in solutions of the two-dimensional incompressible Navier-Stokes equations is employed to obtain convergent pseudospectral approximations. These solutions are then compared with those obtained by a number of commonly used numerical methods. If the viscosity term is deleted and the energy in high wave numbers remov...

ABSTRACT We present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, including unique algorithms AR-Radau, AR-Sym6, AR-ABITS, and AR-chain+ which we show outperform other methods in literature allow for fast, precise, accurate computations to deal with problems ranging from interacting black holes planetary dynamics. that AR-Sym6 A...