A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK

Simulating Self-gravitating Hydrodynamic Flows

An efficient algorithm for solving Poisson's equation in two and three spatial dimensions is discussed. The algorithm, which is described in detail, is based on the integral form of Poisson's equation and utilizes spherical coordinates and an expansion into spherical harmonics. The solver can be applied to and works well for all problems for which the use of spherical coordinates is appropriate. We also briefly discuss the implementation of the algorithm into hydrodynamic codes which are based on a conservative finite--difference scheme.Comment: 15 pages, compressed uu-encoded postscript file (232kB), to appear in Computer Physics Communications, special issue Computational Hydrodynamics in Astrophysic

Nonlinear dynamics and control of a vibrating rectangular plate

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined

The solution by fast Fourier transforms of Laplace's equation in a toroidal region with a rectangular cross-section

AbstractThe fast Fourier transform method is described for Laplace's equation in a toroidal region using the 9-point difference approximation to the Laplacian operator. Numerical results are given which indicate the efficiency and accuracy of the method. Accurate difference approximations are also derived for the determination of the electrostatic field in a toroidal region

A preconditioned formulation of the Cauchy-Riemann equations

A preconditioning of the Cauchy-Riemann equations which results in a second-order system is described. This system is shown to have a unique solution if the boundary conditions are chosen carefully. This choice of boundary condition enables the solution of the first-order system to be retrieved. A numerical solution of the preconditioned equations is obtained by the multigrid method

Spectral methods in fluid dynamics

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results

Power system applications of fiber optics

Power system applications of optical systems, primarily using fiber optics, are reviewed. The first section reviews fibers as components of communication systems. The second section deals with fiber sensors for power systems, reviewing the many ways light sources and fibers can be combined to make measurements. Methods of measuring electric field gradient are discussed. Optical data processing is the subject of the third section, which begins by reviewing some widely different examples and concludes by outlining some potential applications in power systems: fault location in transformers, optical switching for light fired thyristors and fault detection based on the inherent symmetry of most power apparatus. The fourth and final section is concerned with using optical fibers to transmit power to electric equipment in a high voltage situation, potentially replacing expensive high voltage low power transformers. JPL has designed small photodiodes specifically for this purpose, and fabricated and tested several samples. This work is described