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.).

Register here

 

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:

Hotel Area Map

Tranport from Airports to Wuppertal

Bus Lines

HPC-LEAP in a nutshell

Progress in computers and algorithms in the last years has made numerical simulation and modelling a key research methodology in both academia and industry, which in turn drives exascale computing in order to maintain excellence in research and innovation. A disruptive evolution in computer technologies is required for attaining exascale performances in the coming years bringing challenges that urgently need to be addressed across science and engineering fields. Therefore, new interdisciplinary strategies are required in order to educate the next generation of scientists to address such challenges enabling them to be at the forefront of their respective research fields. Instead of the traditional domain-specific training, integrated approaches are needed that can be best implemented by collaborative networks of universities, research institutes and industrial partners. HPC-LEAP is a highly interdisciplinary joint doctorate program realized by bringing together world-leading experts in applied mathematics, high performance computing technologies, particle and nuclear physics, fluid dynamics and life sciences to appropriately train researchers in Europe to exploit high performance computing, advance science and promote innovation. Students will be trained in mathematical and computational concepts underpinning current and future numerical simulations in turbulent flows, computational biology and lattice Quantum Chromodynamics. The research projects are designed to enhance collaborations and interactions across these disciplines, integrating non-academic partners, and to develop methodologies that efficiently use large-scale numerical simulations on future high performance computer systems. Students who complete this training program will be versatile to undertake highly interdisciplinary projects, well positioned to embark on a successful career in academia or the industrial sector.

Consortium Institutions

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