Talks

In Numerical Weather Prediction and Climate modelling, computational efficiency and numerical accuracy are paramount. This work aims to implement time-parallel Spectral Deferred Correction (SDC) methods in LFRic-Atmosphere, the Met Office’s next-generation atmospheric model, designed to exploit the new supercomputers with improved scalability; the use of a quasi-uniform cubed-sphere mesh is integral to this, as is the underlying lowest-order compatible finite element spatial discretisation. LFRic-Atmosphere has an iterative semi-implicit time stepping structure with a Method of Lines finite-transport scheme using an explicit Runge-Kutta time discretisation. Time parallel SDC offers increased temporal accuracy with small computation cost, this could be utilised over the whole time discretisation, or to target a specific time discretised component.
I will present two approaches in this talk. The first approach is using serial SDC as the time discretisation of LFRic-Atmosphere’s finite-volume transport scheme. The second approach is using a serial IMEX SDC time stepper to compare to the semi-implicit time stepping structure in LFRic-Atmosphere. My initial work has explored both using the shallow water equations, I will present results from the standard shallow water test-cases.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

The Maxey-Riley Equation (MRE) models the motion of a finite-sized, spherical particle moving in a fluid. Applications using the MRE are, for example, the study of the spread of Coronavirus particles in a room, the formation of clouds and the so-called marine snow. The MRE is a second-order, implicit integro-differential equation with a singular kernel at initial time. For over 35 years, researchers used approximations and numerical schemes with high storage requirements or ignored the integral term, although its impact can be relevant. A major break-through was reached in 2019, when Prasath et al. mapped the MRE to a time-dependent Robin-type boundary condition of the 1D Heat equation, thus removing the requirement to store the full history. They provided an implicit integral form of the solution by using the so-called Fokas method that could be later solved with a numerical scheme and a nonlinear solver. While Prasath et al.’s method can deliver numerical solutions accurately, the need to evaluate nested integrals makes it computationally costly and it becomes impractical for computing trajectories of a large number of particles. In this talk, we present a new fourth order finite differences scheme and compare its accuracy and performance with Prasath et al’s method as well as other existing schemes. We then apply our method for the calculation of Lagrangian Coherent Structures, a large scale fluid structure, and point out for which cases, the approximations on the MRE have a considerable influence on these structures and the use of the full MRE models is relevant.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

This presentation explores the intricacies of training large language models (LLM) on High-Performance Computing (HPC) systems, unveiling the key components, challenges, and optimizations involved in handling the computational demands of state-of-the-art language models. Delving into the nuances of model architecture, data preprocessing, and hyperparameter tuning, a comprehensive understanding of parallelization strategies, scalability challenges, and resource allocation will be given. Additionally, the talk touches on the implications for research, highlighting potential progress and future applications of LLMs.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

With exascale-capable supercomputers already on the horizon, reducing communication operations in orthogonalization kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods, first introduced in Swirydowicz et al. (Numer. Lin. Alg. Appl. 28(2):e2343, 2020), have been shown to improve the scalability of the Arnoldi method in high-performance, distributed computing. Block versions of low-synchronization Gram-Schmidt show further potential for speeding up algorithms, as column-batching allows for maximizing cache usage with matrix-matrix operations. We will examine how low-synchronization block Gram-Schmidt variants can be transformed into block Arnoldi variants for use in standard Krylov subspace methods like block generalized minimal residual methods (BGMRES). We also demonstrate how an adaptive restarting heuristic can handle instabilities that arise with the increasing condition number of the Krylov basis. The performance, accuracy, and stability of these methods are assessed via a flexible comparison tool written in MATLAB.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Zoomlink:
https://tuhh.zoom.us/j/81325639377?pwd=emRwaU9KOXhseStxUEU2M2NFS0Qwdz09