School on HPC architectures and numerical methods: CoS-2
This is the second part of course CoS-2 and will develop the ideas presented in the first part of CoS-2 in more detail. The focus will be on three “case studies” of large-scale problems and existing code bases that will be review in some detail. These code bases will be chosen from the research areas of the project. 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.
Venue: Trinity College Dublin
Dates: 13th June - 1st July 2016
Credit: 5 ECTS
Scientists-in-charge: Mike Peardon
This is the second part of course CoS-2 and will develop the ideas presented in the first part of CoS-2 in more detail. The focus will be on three “case studies” of large-scale problems and existing code bases that will be review in some detail. These code bases will be chosen from the research areas of the project.
|Topic||Lecture hours||Laboratory hours|
|MPI Programming (II)||3||1|
|GPGPU Proramming (II)||2||2|
|Debugging, profiling and optimising parallel software (II)||3||2|
|Case Study I (solving large linear systems)||4||2|
|Case Study I (molecular dynamics)||4||2|
Symplectic Integrators – Prof. Anthony Kennedy (University of Edinburgh): I intend to begin with a discussion of Hamiltonian dynamics, explaining the role of the Hamiltonian, the fundamental 2-form, phase space (the cotangent bundle) energy conservation, and Liouville’s theorem. I will then introduce the leapfrog (Verlet) integrator and show that it is area-preserving, reversible, and good at conserving energy al- though it is not particularly good a following the true classical trajectory. I will explain how higher-order symmetric symplectic integrators may be constructed following Campostrini et al. I will then introduce Hamiltonian vector fields, and establish that commutators of Hamiltonian vector fields are themselves Hamiltonian vector fields ex- pressible in terms of Poisson brackets. I will then introduce the Baker-Campbell-Hausdorff formula show how it leads to an asymptotic expansion for the Shadow Hamiltonian, a quantity that is exactly conserved by a symplectic integrator. I will then show how examination of Poisson brackets may provide new symplectic integrator steps, such as the force-gradient. I will finally explain how (for extensive systems) measurement of the appropriate Poisson brackets may be used to optimize symplectic integrators.
Multigrid – Dr. Björn Leder (Humboldt Universität Berlin): Multigrid solvers are used in situations where basic iterative solvers are plagued by critical slowing down, i.e., the required number of iterations is diverging in the region of interest. Understanding the origin of this problem com- mon to all basic iterative solvers directly leads to the development of the ingredients of multigrid methods. While the main concepts will be introduced using a simple model problem (Poisson equation), also the application to more complex problems (QCD) will be sketched..
Optimisation – Dr. Michael Lysaght (ICHEC): The course will describe the architectural features of the Intel KNC/KNL architectures and describe how to use the AVX512 instruction set for software optimisation and the best strategies for memory management. The day-long course will conclude with some case studies.
MPI – Dermot Frost (TCHPC): This course will cover some advanced topics in MPI programming, beginning with topics in parallel IO using both native MPI calls and HDFS. Then, PMPI, the profiling interface to MPI will be discussed, with software examples presented.
Parallel Algorithms – Prof. Michael Peardon (TCD): A tour of a few classic numerical algorithms will be given, with a review of how they can be implemented effectively on parallel architectures. To begin, solving sparse linear systems such as those that arise from a finite-difference approximation to the Laplace equation and numerical integration of statistical systems will be reviewed before more advanced topics, such as the fast Fourier transform are described.
Data Analysis – Prof. John Bulava (TCD): Data analysis is a central part of obtaining and interpreting the results of Monte Carlo simulations. A brief review of probability and statistics will be given, before focusing on applications. There will be a particular focus on Markov Chain Monte Carlo.
- Visualisation – Jose Refojo (TCHPC): This course will describe basic scientific visualisation techniques. A general introduction will be given, focusing on different types of datasets and different techniques that can be used to visualize them.
Analytical Schedule *
* Ireland local time.
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.