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ExaSolvers - Extreme Scale Solvers for Coupled Systems

English title ExaSolvers - Extreme Scale Solvers for Coupled Systems
Applicant Krause Rolf
Number 145271
Funding scheme Project funding (Div. I-III)
Research institution Università della Svizzera Italiana
Institution of higher education Università della Svizzera italiana - USI
Main discipline Information Technology
Start/End 01.07.2013 - 30.06.2017
Approved amount 175'848.00
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Keywords (6)

exascale; parallelization in time; multi-grid; domain decomposition; energy effiency; H matrices

Lay Summary (Italian)

Lead
L'elevato parallelismo dei prossimi supercalcolatori introduce nuove e numerose problematiche nello sviluppo di appropriati algoritmi numerici. Nuovi metodi matematici devono essere sviluppati in modo da poter combinare gli elevati livelli di concorrenza di tali sistemi e la complessità ottimale in modo da essere pronti per l'era dell' "exaflop computing".
Lay summary
Gli attuali supercalcolatori contengono da centinaia a migliaia di processori. Per la fine del decennio ci si aspetta che i computer possano raggiungere capacità di calcolo dell'ordine dell'exaflop (10^18 operazioni floating point per secondo) e avere un numero di processori che va dai cento milioni al miliardo. Per utilizzare in maniera efficiente tali supercalcolatori, devono essere sviluppati nuovi metodi matematici che combinino una complessità ottimale con gli elevati livelli di concorrenza. Un'ulteriore problematica legata al calcolo su exascala è il consumo di energia elettrica, e quindi lo sviluppo di algoritmi efficienti si riflette anche in questi termini. Questo progetto tratta lo sviluppo di nuovi schemi numerici che possano affrontare i problemi descritti e quindi essere pronti per l'era dell'  "exascale computing". I metodi di risoluzione adatti a questo tipo di calcolo uniscono algoritmi allo stato dell'arte che provengono da diversi campi della matematica numerica in modo da creare un framework che possa utilizzare efficientemente le architetture dei prossimi supercalcolatori. L'SNF ha finanziato una parte del progetto. In particolare ha contribuito per lo sviluppo di nuovi metodi che permettono di parallelizzare l'avanzamento in tempo oltre che la parallelizzazione in spazio basata sulla decomposizione del problema su molteplici sottodomini. Il problema di benchmark di questo progetto è la simulazione numerica dei processi di permeazione della pelle umana. Questa applicazione e' di grande interesse per lo sviluppo di nuovi farmaci. Le capacità di calcolo su exascala sono necessarie in modo che le simulazioni numeriche siano in grande di risolvere tutte le scale che caratterizzano questo problema.
Direct link to Lay Summary Last update: 27.09.2016

Lay Summary (English)

Lead
The massive parallelism in future supercomputers leads to multiple and difficult challenges for numerical algorithms. New mathematical methods are required that combine extreme levels of concurrency with optimal complexity in order to be prepared for the era of exaflop computing.
Lay summary

Supercomputes today already have tens to hundreds of thousands of cores. It is expected that systems capable of achieving Exaflop performance (that is 1018 floating point operations each second) will emerge by the end of decade and that these computers will feature more than 100 million cores and probably up to 1 billion. To efficiently use such extreme numbers of cores in scientific computing requires new innovative mathematical methods that combine optimal complexity with a massive degree of concurrency. Also, power consumption will become a critical issue on exascale systems, mandating the development of algorithms that are not only fast but also efficient in terms of required electric energy. The project deals with the development of novel numerical schemes that can tackle these issues in order to prepare for the exascale era. Exasolvers combines state-of-the-art algorithms from different fields of numerical mathematics to develop a new software framework that can efficiently utilize upcoming high-performance computing architectures. The SNF-funded part of the project in particular deals with the development of a new method that provides parallelization in the time direction, in addition to parallelization in space by decomposing the problem into sub-problems. The benchmark problem of the project is the numerical simulation of permeation of human skin, an application that is of great interest for example for the development of pharmaceuticals. In order to be able to run numerical simulations that actually resolve all scales arising in this problem, exascale computing capabilities will be required.

Direct link to Lay Summary Last update: 27.09.2016

Responsible applicant and co-applicants

Employees

Publications

Publication
Time--parallel Gravitational Collapse Simulation
Kreienbuehl A., Benedusi P., Ruprecht D., Krause R. (2017), Time--parallel Gravitational Collapse Simulation, in Communications in Applied Mathematics and Computational Science, 12(1), 109-128.
A Parallel Multigrid Solver for Time--periodic Incompressible Navier--Stokes Equations in 3D
Benedusi P., Hupp D., Arbenz P., Krause R. (2016), A Parallel Multigrid Solver for Time--periodic Incompressible Navier--Stokes Equations in 3D, in Numerical Mathematics and Advanced Applications ENUMATH 2015, Ankara265-273, Springer International Publishing, Berlin265-273.
Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations
Grasedyck L., Löbbert C., Wittum G., Nägel A., Schulz V., Siebenborn M., Krause R., Benedusi P., Küster Uwe, Dick Björn (2016), Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations, in Neumann Philipp, Bungartz Hans-Joachim, Nagel Wolfgang E. (ed.), Springer, Cham, 507-523.

Collaboration

Group / person Country
Types of collaboration
RWTH Aachen Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
Universität Stuttgart Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
Universität Frankfurt Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
ETH Zürich Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Lawrence Livermore National Laboratory United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
LSSC '17 Talk given at a conference A Multilevel Iterative Approach Based on Discontinuous Galerkin Methods with Space--Time Coarsening 06.06.2017 Sozopol, Bulgaria Benedusi Pietro;
18th Copper Mountain Conference On Multigrid Methods Talk given at a conference An iterative approach for time-parallel time integration based on discontinuous Galerkin methods 26.03.2017 Copper Mountain, United States of America Benedusi Pietro;
International Conference on Domain Decomposition Methods Talk given at a conference Parallel space–time multigrid for the time--periodic Navier–Stokes equation 11.02.2017 Svalbard, Norway Benedusi Pietro; Krause Rolf; Wittum Gabriel;
THE MATHEMATICS OF FINITE ELEMENTS AND APPLICATIONS 2016 Talk given at a conference A Parallel Multigrid Solver for Time Periodic Incompressible N-S Equations 14.06.2016 London, Great Britain and Northern Ireland Benedusi Pietro;
SIAM Conference on Parallel Processing Talk given at a conference Time Parallel and Space Time Solution Methods From Heat Equation to Fluid Flow 14.03.2016 Paris, France Benedusi Pietro; Krause Rolf;
Workop on Adaptivity Talk given at a conference Parallel Multigrid Solution of the Incompressible Navier--Stokes Equations in 3D 10.12.2015 Simula, Oslo, Norway Krause Rolf;
ENUMATH conference Talk given at a conference A Parallel Multigrid Solver for Time--Periodic Incompressible Navier--Stokes Equations in 3D 15.09.2015 Ankara, Turkey Krause Rolf; Benedusi Pietro;


Self-organised

Title Date Place
Summer School: Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equation 18.07.2017 Lugano, Switzerland

Associated projects

Number Title Start Funding scheme
147597 Towards a space-time parallel Navier-Stokes solver 01.04.2013 International short research visits

Abstract

Today, exascale computers are characterized by billion-way parallelism. Computing on such extreme scale needs methods which scale perfectly and have optimal complexity. This project proposal brings together several crucial aspects of extreme scale solving. First, the solver itself must be of optimal numerical complexity - a requirement becoming more an more severe with increasing problem size - and at the same time scale efficiently on extreme scales of parallelism. Second, simulations on exascale systems will consume a lot of electric power, requiring algorithms and implementations with low power consumption. To that end, the present project combines domain decomposition, parallel multigrid and H-matrices. This technique has the potential to gain top efficiency on extreme scales while still maintaining optimal complexity. To further improve parallelism, this approach is combined with special methods for parallelization in time and solvers for optimization problems. Both cases have additional parallelization potential. Algorithms and implementations will be evaluated for energy efficiency in problem solving. Criteria and models for energy efficiency of numerical solvers will be developed in the project. The team has long standing experience in developing algorithms and software for large scale HPC cooperatively.
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