## Numerical Analysis and Scientific Computing Seminars

## Forthcoming Seminars

29 Nov, 2019 |
Title : Reduced Precision Computing for Weather and Climate Models Dr. Jan AckmannPostdoctoral Research Associate, Department of Physics, University of Oxford. Abstract :Weather and Climate (W&C) prediction models are required to satisfy strict time-to-solution and energy-to-solution constraints and thus need to be as computationally efficient as possible on modern supercomputers. To explore possible gains in computational efficiency, we follow various approaches: Precision reduction for floating point operations, exploring alternative number formats, and replacing model components with machine-learned surrogates. Resulting computational savings could then be reinvested where they are needed more urgently.The justification for these approaches – that inevitably introduce additional model errors – is motivated by the presence of irreducible uncertainties in W&C model predictions. These uncertainties are due to the interplay of the W&C models’ two main components, the dynamical core, a discretization of the Navier-Stokes equations, and the so-called model physics – a collection of stochastic parametrizations for the unresolved subgrid-scale processes (turbulence, cloud physics, convection,…). In the presence of the resulting uncertainties, high precision is deemed unnecessary for many computational operations and model components.The first part of the talk will be about the group’s work on the use of low precision arithmetic for various model components (Spectral dynamical cores, Adjoint calculation, Data Assimilation, Legendre Transforms, and model physics), where often a level of half precision is found feasible. Also, alternative number formats such as Posits (emulated in software) and neural network approaches that replace parts of the model physics are discussed.The second part of the talk will be a more detailed account on reduced-precision preconditioned elliptic solvers in dynamical cores. Time : 2:00 PM to 3:00 PM.Venue : Frank Adams 1, Alan Turing Building. |

27 March, 2020 |
Title : TBA Prof. Heike FassbenderProfessor of Mathematics, Institut Computational Mathematics, AG Numerik Technische Universität Braunschweig Abstract : TBATime : 2:00 PM to 3:00 PM.Venue : Frank Adams 1, Alan Turing Building. |

## Past Seminars 2019-2020

22 Nov, 2019 |
Title : Compact Finite Differences and Cubic SplinesProf. RoberProfessor in School of Mathematics, and StatisticalComputational SciencesMathematics, University of Western Ontario.t M. CorlessIn this talk I uncover and explain—using contour integrals and residues—a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\’e scheme for generating fourth-order accurateAbstract :compact finite differences gives exactly the derivatives at the interior nodes needed to guarantee twice-continuous differentiability for cubic splines. I also introduce an apparently new spline-like interpolant that I call a compact cubic interpolant; this is similar to one introduced in 1972 by Swartz and Varga, but has higher order accuracy at the edges. I argue that for mildly nonuniform meshes the compact cubic approach offers some potential advantages, and even for uniform meshes offers a simple way to treat the edge conditions, relieving the user of the burden of deciding to use one of the three standard options: free (natural), complete (clamped), or “not-a-knot” conditions. Finally, I establish that the matrices defining the compact cubic splines (equivalently, the fourth-order compact finite difference formulas) are positive definite, and in fact totally nonnegative, if all mesh widths are the same sign. 2:00 PM to 3:00 PM.Time : Frank Adams 1, Alan Turing Building.Venue : |

8 Nov, 2019 |
Title : Rayleigh quotient optimizations and eigenvalue problemsProf. Zhaojun BaiProfessor of Computer Science and Mathematics, University of California, Davis. Abstract :Many computational science and data analysis techniques lead to optimizing Rayleigh quotient (RQ) and RQ type objective functions, such as computing excitation states (energies) of electronic structures, robust classification to handle uncertainty and constrained data clustering to incorporate a prior information. We will discuss origins of recently emerging RQ optimization problem, variational principles, and reformulations to algebraic linear and nonlinear eigenvalue problems. We will show how to exploit underlying properties of eigenvalue problems for designing eigensolvers, and illustrate the efficacy of these solvers in applications. Time : 2:00 PM to 3:00 PM.Venue : Frank Adams 1, Alan Turing Building. |

25 Oct, 2019 |
Title : Beyond Chebyshev TechnologyDr Marcus WebbLecturer in Department of Mathematics, The University of Manchester. Abstract : Chebfun is a MATLAB software package for computing numerically with functions, whose inner workings boil down essentially to approximating functions by Chebyshev polynomial expansions. In this talk we’ll discuss problems in which Chebyshev polynomials are not the best basis to use, necessitating the transformation to other bases such as Legendre and other Jacobi polynomials (and back again to Chebyshev). The main part of the talk will be on the state-of-the-art algorithm for transforming between different families of Jacobi polynomials, due to Townsend, myself, and Olver (https://doi.org/10.1090/mcom/3277), which involves Toeplitz matrices, Hankel matrices, low-rank matrix approximation, and the FFT. The analysis involves some rational approximation problems of Zolotarev (https://doi.org/10.1137/19M1244433). We conclude with interesting related miscellanea.Time : 2:00 PM to 3:00 PM.Venue : Frank Adams 1, Alan Turing Building. |