School on numerical analysis and algorithms towards exascale: CoS-1
The School on numerical analysis and algorithms towards exascale is the first out of four training workshops organised by HPC-LEAP for the students enrolled on the programme. Successful completion of any one of the programmes will be worth 5 ECTS accreditation units. The School will offer 15 extra positions for Students and Researchers that are not HPC-LEAP fellows. The assessment and topics covered by the four workshops is described below.
The organizing committee has secured special rates in hotel close to the venue of the event. For reservation, please contact Ms. Brigitte Schultz (This email address is being protected from spambots. You need JavaScript enabled to view it.).
Venue: Wuppertal
Dates: 23rd September - 13th October 2015
Credit: 5 ECTS
Scientists-in-charge: Andreas Frommer and Francesco Knechtli
Description:
The first School in the series is part of course CoS-1 and will present the mathematical foundations and algorithms needed for numerical simulation, with an emphasis on the concepts and issues needed to approach the exascale. The core techniques for the research interests of HPC-LEAP will be reviewed in four series of lectures, covering Monte Carlo methods, the underlying mathematical ideas behind efficient methods to find numerical solutions to molecular dynamics, iterative techniques to solve large, sparse linear systems and advanced topics such as numerical solutions to partial differential equations and the fast Fourier transform.
Topic | Lecture hours | Laboratory hours | |
Introduction to Markov Chain Monte Carlo | 6 | 3 | |
Numerical methods for molecular dynamics | 6 | 4 | |
Iterative solvers for linear systems | 6 | 4 | |
Advanced topics in numerical analysis | 8 | 4 | |
26 | 15 |
Components:
• Introduction to Markov Chain Monte Carlo: The mathematical framework for importance- sampling Monte Carlo estimations of the high-dimensional integration problems that arise in many physical simulations will be described. The focus will be on practical methods that enable students to start their own numerical investigations of simple examples such as the Ising or Potts in laboratory sessions. Topics covered will include the Metropolis algorithm and Gibbs sampler.
• Numerical methods for molecular dynamics: Modern, efficient Markov chain Monte Carlo methods rely on concepts borrowed from molecular dynamics. These ideas will be described in detail. The mathematical framework of symplectic integrators will be presented and students will be encouraged to develop simulation software to illustrate the ideas they learn. Examples covered will include numerical integration of the equations of motion for Newtonian gravity or the Lennard-Jones potential.
• Iterative solvers for linear systems: At the core of many computations is the need to solve large, sparse linear systems very efficiently. The techniques to solve these problems will be reviewed, introducing the students to Krylov subspace methods and preconditioning. Example problems will be presented and student will develop their understanding in computational laboratory sessions.
• Advanced topics in numerical analysis: To solve problems on massively parallel computers requires advanced algorithms. The School will conclude with a review of communication-avoiding algorithms and asynchronous iterations. The example will be to develop software to find a numerical solution to Poisson’s equation with different boundary conditions.
Analytical Schedule
Week 1
Lecture Room G.14.34 / Lab Room D.11.03
Date | 09:00 – 12:00 | 14:00 – 16:00 |
Wednesday, 23/09/2015 |
Opening (A. Frommer) Lecture Advanced Topics (AT) I a Partial Differential Equations M. Ehrhardt/M. Günther |
Lab AT I a |
Thursday, 24/09/2015 |
Lecture Advanced Topics (AT) I b |
Lab AT I a + b |
Friday, 25/09/2015 |
Lab AT I b |
Week 2
Lecture Room G.14.34 / Lab Room D.11.03
Date | 09:00 – 12:00 | 14:00 – 16:00 |
Monday, 28/09/2015 |
Lecture (2.5 h) Molecular Dynamics (MD) R. Hentschke |
Lab (1.5h)
MD |
Tuesday, 29/09/2015 |
Lecture Molecular Dynamics (MD) |
Questions & Answers MD |
Wednesday, 30/09/2015 |
Lab MD |
Excursion
to Museum für Frühindustrialisierung (Museum for early industrialization). Wuppertal |
Thursday, 01/10/2015 |
Lecture Iterative Solvers (ISo) A. Frommer/K. Kahl |
Lab ISo |
Friday, 02/10/2015 |
Lecture Iterative Solvers (ISo) |
Lab ISo |
Week 3
Lecture Room G.14.34 / Lab Room D.11.03
Date | 09:00 – 12:00 | 14:00 – 16:00 |
Monday, 05/10/2015 |
Questions & answers Iso |
Lab ISo |
Tuesday, 06/10/2015 |
Excursion
to Zeche Zollverein, Essen (Coal Mine Zollverein in Essen - UNESCO World Heritage Site) |
|
Wednesday, 07/10/2015 |
Lecture Advanced Topics (AT) II a: Communicaton-avoiding Algorithms |
Lecture Advanced Topics (AT) II b B. Lang/L. Grigori |
Thursday, 08/10/2015 |
Lecture Advanced Topics (AT) III a: Asynchronous Iterations |
Lecture Advanced Topics (AT) III b A. Frommer |
Friday, 09/10/2015 |
Lecture Monte-Carlo (MC) G. Moir |
Lab MC |
Week 4
Lecture Room G.14.34 / Lab Room D.11.03
Date | 09:00 – 12:00 | 14:00 – 16:00 |
Monday, 12/10/2015 |
Lecture Monte-Carlo (MC) |
Questions & Answers
MC |
Tuesday, 13/10/2015 |
Lab MC |
School wrap-up & Closing |
Download Schedule in pdf Format
Assessment:
Students will be assessed by a method common to all HPC-LEAP workshops. Over the course of each School, students will be required to develop software to solve a small number of substantial numerical problems. At the end of the three weeks, students will be required to submit their software, along with a report detailing the design, algorithm, testing methodology, results and performance of their projects. They will be expected then to give a 15 minute presentation to the examiners and their classmates, summarising their findings.
Additional Information: