We present benchmark simulations for the 8:1 di erentially heated cavity problem, the focus of a special session at the rst MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order nite di erence method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme wit...

In recent years multigrid methods have been proven to be very e cient for solving large systems of linear equations resulting from the discretization of positive de nite di erential equations by either the nite di erence method or the h-version of the nite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which ar...

This paper deals with the orders of input/output equations satis ed by nonlinear systems. Such equations represent di erential (or di erence, in the discrete-time case) relations between highorder derivatives (or shifts, respectively) of input and output signals. It is shown that, under analyticity assumptions, there cannot exist equations of order less than the minimal dimension of any observa...

Several exact, cylindrically symmetric solutions to Einstein's vacuum equations are given. These solutions were found using the connection between Yang-Mills theory and general relativity. Taking known solutions of the YangMills equations (e.g. the topological BPS monopole solutions) it is possible to construct exact solutions to the general relativistic eld equations. Although the general rela...

The vebrane worldvolume theory in eleven dimensions is known to contain BPS threebrane solitons which can also be interpreted as a vebrane whose worldvolume is wrapped around a Riemann surface. By considering con gurations of intersecting vebranes and hence intersecting threebrane solitons, we determine the Bogomol'nyi equations for more general BPS con gurations. We obtain di erential equation...

We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial di erential equations. We introduce and prove a veri cation theorem which provides a su cient condition for optimality. Moreover we prove suband superoptimality principles of dynamic programming and present an explicit construction of -optimal ...

We describe herein the parallel implementation of the Bi-CGSTAB method with a block Red-Black Gauss-Seidel (RBGS) preconditioner applied to the systems of linear algebraic equations that arise from the Hermite collocation discretization of partial di erential equations in two spatial dimensions. The method is implemented on the Cray T3E, a parallel processing supercomputer. Speedup results are ...

The lattice gas automaton (LGA) for di usive-convective transport dynamics is constructed in terms of LGA building elements: propagation and mixing [1, 13]. The LGA transport dynamics is described by microdynamical equations and discrete Boltzmann equations, from which the corresponding macroscopic PDE's are derived [1, 13].