Cos-1 a: School on numerical analysis and algorithms towards exascale

The School on numerical analysis and algorithms towards exascale (CoS-1) is the first out of four training workshops organized by HPC-LEAP for the students enrolled on the programme.

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.

 

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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.

Prof. Henchel's introduction to molecular dynamics simulations.

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  Part 1 Part 2 Discussion session  

Part 1

Part 2

Discussion session

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.

To view the material please click on the link in the box below:

  Part 1 Part 2 Discussion session  

 

Part 1

Part 2

Discussion session

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.

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  Part 1 Part 2  

Part 1

Part 2

Advanced topics: Communicaton-avoiding Algorithms 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.

To view the material please click on the link in the box below:

  Part 1 Part 2  

Part 1

Part 2

Advanced topics: Asynchronous Iterations

 

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.

To view the material please click on the link in the box below: