~- This research was supported by the National Aeronautics and Space

Agglomeration Multigrid for the Three-dimensional Euler Equations

A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the threedimensional Euler equations on unstructured grids about complex con gurations. It is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratio...

Final Report to the NATIONAL AERONAUTICS AND SPACE ADMINISTRATION on Research Supported by Grant NAG3-2116 Thermocapillary-Induced Phase Separation with Coalescence

Representation of Feedback Operators for Hyperbolic Systems

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numeric...

Stability Analysis of Intermediate Boundary Conditions in Approximate Factorization Schemes

The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. We show that the treatment suggested by Holst led to a restriction on the time step and suggest ways to overcome this restriction. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neum...

Chebyshev Polynomials are Not Always Optimal bY

We are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on 1. Here, I is a given ellipse with both foci on the real axis and c is a given real point not contained in E. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referen...