Adjoint recovery of superconvergent functionals from PDE approximations

Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasi-one-dimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multi-dimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations

A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many approximations of stochastic (ordinary) differential equations while it is recent research for stochastic partial differential equations. In this note it is shown how the availability of weak convergence results influences the number of samples in multilevel Monte Carlo schemes and therefore reduces the computational complexity of these schemes for a given accuracy of the approximations.Comment: 16 pages, 3 figures, updated to version published in the Proceedings of MCQMC1

Parastatistics of charged bosons partly localised by impurities

Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localised states (i.e. a small amount of disorder). The density of localised bosons and the specific heat show a peculiar non-uniform temperature dependence below the Bose-Einstein condensation temperature. The superfluid - Bose-glass phase diagram is discussed. A new phase is predicted which is a Bose-glass at T=0 but a superfluid at finite T.Comment: 6 pages, Revtex, 6 figures (available on request from the authors

Document Archiving, Replication and Migration Container for Mobile Web Users

With the increasing use of mobile workstations for a wide variety of tasks and associated information needs, and with many variations of available networks, access to data becomes a prime consideration. This paper discusses issues of workstation mobility and proposes a solution wherein the data structures are accessed in an encapsulated form - through the Portable File System (PFS) wrapper. The paper discusses an implementation of the Portable File System, highlighting the architecture and commenting upon performance of an experimental system. Although investigations have been focused upon mobile access of WWW documents, this technique could be applied to any mobile data access situation.Comment: 5 page

Analysis of Adjoint Error Correction for Superconvergent Functional Estimates

Earlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by using an adjoint PDE solution to reveal the sensitivity of the functional to the residual error in the original PDE solution. The present work provides a priori error analysis that correctly predicts the behaviour of the remaining leading order error term. Furthermore, the discussion is extended from the case of homogeneous boundary conditions and bulk functionals, to encompass the possibilities of inhomogeneous boundary conditions and boundary functionals. Numerical illustrations are provided for both linear and nonlinear problems.\ud \ud This research was supported by EPSRC under grant GR/K91149, and by NASA/Ames Cooperative Agreement No. NCC 2-5431

Colonel Utley\u27s Emancipation - Or, How Lincoln Offered to Buy a Slave

The reputation of Abraham Lincoln has see-sawed over the last half-century on the fulcrum of race, and the results have not been happy for that reputation. As Gerald Prokopowicz has written, the big question about Lincoln and slavery runs today like this: Was Lincoln really the Great Emancipator that we have traditionally been brought up to admire, or was he just a clever, lying, racist, white male politician who had no interest in the well-being of black America other than when it served his political interests? No longer is it necessary, as one historian has wryly remarked, for politicians to get right with Lincoln. Historians now yearn to get right with Frederick Douglass, and to judge by the recent freshet of literature on Lincoln and Douglass, it is now incumbent on Lincoln to be gotten right with Frederick Douglass, too. One of the most damaging accusations leveled against the possibility of justifying Lincoln on race appears in Lerone Bennett\u27s infamous screen, Forced into Glory: Abraham Lincoln\u27s White Dream, where, as the finale to a battery of accusations of racism, Bennett\u27s Lincoln personally ordered Union officers to return runaway slaves to slavemasters and turned a blind eye to Kentuckians, for example, who were selling and reenslaving African-Americans freed by the war and congressional acts. [excerpt

An introduction to the adjoint approach to design

Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets.\ud \ud This research was supported by funding from Rolls-Royce plc, BAe Systems plc and EPSRC grants GR/K91149 and GR/L95700