# Past Computational Mathematics and Applications Seminar

Dr Lawrence Daniels and Dr Iain Strachan
Abstract
In this talk we review experiences of using the Harwell Subroutine Library and other numerical software codes in implementing large scale solvers for commercial industrial process simulation packages. Such packages are required to solve problems in an efficient and robust manner. A core requirement is the solution of sparse systems of linear equations; various HSL routines have been used and are compared. Additionally, the requirement for fast small dense matrix solvers is examined.
• Computational Mathematics and Applications Seminar
10 May 2001
14:00
Prof Maciej Zworksi
Abstract
• Computational Mathematics and Applications Seminar
26 April 2001
14:00
Prof Heinz W Engl
Abstract
• Computational Mathematics and Applications Seminar
15 March 2001
14:00
Abstract
The sphere is an important setting for applied mathematics, yet the underlying approximation theory and numerical analysis needed for serious applications (such as, for example, global weather models) is much less developed than, for example, for the cube. \\ \\ This lecture will apply recent developments in approximation theory on the sphere to two different problems in scientific computing. \\ \\ First, in geodesy there is often the need to evaluate integrals using data selected from the vast amount collected by orbiting satellites. Sometimes the need is for quadrature rules that integrate exactly all spherical polynomials up to a specified degree $n$ (or equivalently, that integrate exactly all spherical harmonies $Y_{\ell ,k}(\theta ,\phi)$ with $\ell \le n).$ We shall demonstrate (using results of M. Reimer, I. Sloan and R. Womersley in collaboration with W. Freeden) that excellent quadrature rules of this kind can be obtained from recent results on polynomial interpolation on the sphere, if the interpolation points (and thus the quadrature points) are chosen to be points of a so-called extremal fundamental system. \\ \\ The second application is to the scattering of sound by smooth three-dimensional objects, and to the inverse problem of finding the shape of a scattering object by observing the pattern of the scattered sound waves. For these problems a methodology has been developed, in joint work with I.G. Graham, M. Ganesh and R. Womersley, by applying recent results on constructive polynomial approximation on the sphere. (The scattering object is treated as a deformed sphere.)
• Computational Mathematics and Applications Seminar
8 March 2001
14:00
Prof Wilhelm Heinrichs
Abstract
• Computational Mathematics and Applications Seminar
Abstract
Continuing advances in computing technology provide the power not only to solve increasingly large and complex process modeling and optimization problems, but also to address issues concerning the reliability with which such problems can be solved. For example, in solving process optimization problems, a persistent issue concerning reliability is whether or not a global, as opposed to local, optimum has been achieved. In modeling problems, especially with the use of complex nonlinear models, the issue of whether a solution is unique is of concern, and if no solution is found numerically, of whether there actually exists a solution to the posed problem. This presentation focuses on an approach, based on interval mathematics, that is capable of dealing with these issues, and which can provide mathematical and computational guarantees of reliability. That is, the technique is guaranteed to find all solutions to nonlinear equation solving problems and to find the global optimum in nonlinear optimization problems. The methodology is demonstrated using several examples, drawn primarily from the modeling of phase behavior, the estimation of parameters in models, and the modeling, using lattice density-functional theory, of phase transitions in nanoporous materials.
• Computational Mathematics and Applications Seminar
22 February 2001
14:00
Dr Oliver Ernst
Abstract
This talk reviews some recent joint work with Michael Eiermann and Olaf Schneider which introduced a framework for analyzing some popular techniques for accelerating restarted Krylov subspace methods for solving linear systems of equations. Such techniques attempt to compensate for the loss of information due to restarting methods like GMRES, the memory demands of which are usually too high for it to be applied to large problems in unmodified form. We summarize the basic strategies which have been proposed and present both theoretical and numerical comparisons.
• Computational Mathematics and Applications Seminar