An asymptotic expansion for product integration applied to Cauchy principal value integrals

Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic expansion in even powers of the step-size does not exist. The relative merits of a quadrature method which employs values of both the integrand and its first derivative and for which the truncation error has an asymptotic expansion in even powers of the step-size are discussed

A Two-Variable Asymptotic Solution for Three - Dimensional, Solar-Powered, Low-Thrust Trajectories in the Vicinity of the Ecliptic Plane

Two-variable asymptotic solution for three-dimensional solar powered low thrust trajectories in vicinity of ecliptic plan

Solution of the Boussinesq equations by means of the finite element method

A finite element method is presented for the computation of flows that are influenced by buoyancy forces. The accuracy of several finite elements is studied by solving the Bénard problem and determining the critical Rayleigh number. It is found that the accuracy is greatly enhanced if the shape functions satisfy a certain requirement that arises from the physical nature of the problem

Introduction to multigrid methods

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered

Modeling of droplet breakup in a microfluidic T--shaped junction with a phase--field model

A phase--field method is applied to the modeling of flow and breakup of droplets in a T--shaped junction in the hydrodynamic regime where capillary and viscous stresses dominate over inertial forces, which is characteristic of microfluidic devices. The transport equations are solved numerically in the three--dimensional geometry, and the dependence of the droplet breakup on the flow rates, surface tension and viscosities of the two components is investigated in detail. The model reproduces quite accurately the phase diagram observed in experiments performed with immiscible fluids. The critical capillary number for droplet breakup depends on the viscosity contrast, with a trend which is analogous to that observed for free isolated droplets in hyperbolic flow

A new wireless underground network system for continuous monitoring of soil water contents

A new stand-alone wireless embedded network system has been developed recently for continuous monitoring of soil water contents at multiple depths. This paper presents information on the technical aspects of the system, including the applied sensor technology, the wireless communication protocols, the gateway station for data collection, and data transfer to an end user Web page for disseminating results to targeted audiences. Results from the first test of the network system are presented and discussed, including lessons learned so far and actions to be undertaken in the near future to improve and enhance the operability of this innovative measurement approac

Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated