Project

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ExaSolvers - Extreme Scale Solvers for Coupled Systems

English title ExaSolvers - Extreme Scale Solvers for Coupled Systems
Applicant Krause Rolf
Number 162199
Funding scheme Project funding (Div. I-III)
Research institution Istituto di scienze computazionali (ICS) Facoltà di scienze economiche
Institution of higher education Università della Svizzera italiana - USI
Main discipline Information Technology
Start/End 01.07.2017 - 30.11.2020
Approved amount 181'008.00
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Keywords (5)

exascale; parallel-in-time integration; computational science; multigrid; high performance computing

Lay Summary (Italian)

Lead
Le scienze computazionali sono uno strumento moderno utilizzato per simulare sistemi complessi dell'ingegneria, delle scienze naturali, delle scienze sociali e di molti altri campi di ricerca. I problemi studiati necessitano di una straordinaria capacità di calcolo che è fornita tipicamente da supercomputer. Le necessità di calcolo crescono costantemente e così anche la potenza e l'architettura dei supercomputer deve adeguarsi. Per questo motivo è di fondamentale importanza lo sviluppo di nuovi metodi numerici che si adattino alle macchine del domani. In questo particolare progetto viene studiata un applicazione in campo medico.
Lay summary
I moderni supercomputer sono generalmente composti da una gran numero di nodi di calcolo, o "cores", collegati da reti ad alta velocità. I più potenti sistemi arrivano a contenere anche milioni di cores. Si stima che in futuro saranno costruiti supercomputer contenenti centinaia di milioni di cores, se non miliardi.  La futura architettura hardware richiede una ricerca in ambito computazionale e algoritmico: gli strumenti matematici utilizzati nelle scienze computazionali dovranno adattarsi ai nuovi sistemi di calcolo parallelo, mantenendo complessità e scalabilità ottimali. Anche i consumi energetici diverranno un punto critico nella progettazione di sistemi Exascale: saranno necessari algoritmi non solo veloci, ma anche efficienti dal punto di vista energetico.

L'obiettivo del progetto Exasolver è la realizzazione di nuovi schemi numerici che si adattino alle caratteristiche dei futuri supercomputer. In questo senso è necessaria la realizzazione di algoritmi estremamente paralleli ed efficienti da utilizzare per la soluzione di problemi complessi nel campo della matematica numerica. In particolare, l'SNF finanzia la realizzazione di un metodo per la soluzione di equazioni alle derivate parziali che sia parallelo anche nella dimensione temporale. Infatti la parallelizzazione avviene solitamente nel dominio spaziale, che viene suddiviso in sotto problemi che vengono risolti simulatamente. L'evoluzione temporale è generalmente un processo sequenziale, quindi più complesso da parallelizzare. Uno stato futuro può essere calcolato solo se si conoscono con precisione gli stati precedenti, e non simultaneamente ad essi.

Nella pratica il problema studiato è quello della diffusione di un liquido nella pelle umana, un applicazione di grande interesse nell'industria farmaceutica, per esempio. Per creare simulazioni abbastanza veloci e precise, che descrivano tutte le scale coinvolte in questo problema, saranno infatti necessari sistemi Exascale e adeguati Exasolvers.
Direct link to Lay Summary Last update: 27.09.2016

Lay Summary (English)

Lead
Computational Science helps us to understand complex processes in engineering, natural sciences, medicine, social sciences, climate, and many other areas., y means of numerical simulation. The supercomputers we use for carrying out these simulations get larger each year and are based on massive parallelism - we constantly get more and more computing cores. Developing numerical methods for these large machines is far from trivial and is carried out in this project for a medical application.
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
Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology
Ben Bader S., Benedusi P., Quaglino A., Zulian P., Krause R. (2021), Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology, in Journal of Computational Physics, 433, 110164-110164.
Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology
Ben Bader S., Benedusi P., Quaglino A., Zulian P., Krause R. (2021), Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology, in Journal of Computational Physics, 433, 110164-110164.
Space-Time FE-DG Discretization of the Anisotropic Diffusion Equation in Any Dimension: The Spectral Symbol
Benedusi Pietro, Garoni Carlo, Krause Rolf, Li Xiaozhou, Serra-Capizzano Stefano (2018), Space-Time FE-DG Discretization of the Anisotropic Diffusion Equation in Any Dimension: The Spectral Symbol, in SIAM Journal on Matrix Analysis and Applications, 39(3), 1383-1420.
An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
Benedusi Pietro, Minion Michael, Krause Rolf, An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem, in Computers and Mathematics with Applications.
Fast Parallel Solver for the Space-Time IgA-DG Discretization of the Anisotropic Diffusion Equation
benedusipietro, garonicarlo, ferraripaola, krauserolf, serra-capizzanostefano, Fast Parallel Solver for the Space-Time IgA-DG Discretization of the Anisotropic Diffusion Equation, in Journal of Scientific Computing.

Collaboration

Group / person Country
Types of collaboration
Lawrence Berkeley National Laboratory, Prof. Minion United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Exchange of personnel
Università dell'Insubria Italy (Europe)
- 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
SIAM Computer science and engineering 2021 Talk given at a conference A comparison of Space-Time Multigrid and PFASST with applications to Cardiac Electrophysiology 01.03.2021 virtual, United States of America Benedusi Pietro; Krause Rolf;
PinT 2020 - (Virtual) 9th Parallel in Time Workshop Talk given at a conference A comparison of Space-Time Multigrid and PFASST with applications to Cardiac Electrophysiology 15.06.2020 virtual, United States of America Krause Rolf; Benedusi Pietro;
Advanced parallel-in-time algorithms for computer simulations in physical sciences, social sciences and engineering Individual talk Multigrid Based Strategies for the Solution of Non--linear Space--time Problems 20.05.2019 Bielefeld, Germany Benedusi Pietro;
SIAM Conference on Computational Science and Engineering (CSE19) Talk given at a conference Multigrid Based Strategies for the Solution of Non--linear Space--time Problems 25.02.2019 Spokane , United States of America Benedusi Pietro;
25th International Domain Decomposition Conference (DD25) Talk given at a conference A Space--Time Multigrid Method for Electrophysiology 23.07.2018 St. John's, Newfoundland, Canada Benedusi Pietro;
Swiss Numerics Day Poster A Fully Parallel SpaceTime Multigrid Solver for Computational Electrophysiology 20.04.2018 ETH, Zürich, Switzerland Benedusi Pietro;


Self-organised

Title Date Place
Space-Time Approaches in Cardiac Electrophysiology 14.12.2020 Lugano, Switzerland
X-DMS 2019 03.07.2019 USI, Lugano, Switzerland
6th Parallel in time Workshop 23.10.2017 Ascona, , Switzerland

Awards

Title Year
SIAM Student Travel Award 2019

Associated projects

Number Title Start Funding scheme
186407 Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization 01.03.2020 Project funding (Div. I-III)

Abstract

This project is dealing with the development of parallel-in-time methods for massively parallel machines. We aim particularly at the design of adaptive multilevel methods in time, which then will be combined with the already existing spatial multilevel solvers. The newly developed methods are designed for the upcoming generation of massively parallel supercomputers with millions of computing units or cores. The project is part of the German Priority Programme 1648 "Software for Exascale Computing"
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