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Parallel multilevel solvers for coupled interface problems

Applicant Krause Rolf
Number 146167
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 Mathematics
Start/End 01.05.2014 - 30.04.2017
Approved amount 164'663.00
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All Disciplines (3)

Information Technology
Fluid Dynamics

Keywords (10)

distributed data management; non-standard coarse spaces; multilevel methods; parallel saddle point solvers; software for HPC; interface problems; contact problems; XFEM; droplet impact and spreading; crack problems

Lay Summary (German)

Numerical simulations is nowadays a standard tool in engineering and manufacturing. The development and testing of, e.g., new devices and machine parts, can be speeded up considerably using modern simulation methods on (super-)computers. A particular challenging problem class involves "moving interfaces", i.e. liquid-gas flows of droplets impacting on a wall or crack propagation. The detection and tracking of those moving interfaces is far from trivial and requires considerable methodological and computational effort. Moreover, the massively parallel architectures of modern computers requires new and specially tailored parallel solution algorithms.It is the goal of this project to develop and realize efficient parallel simulation tools, which will aloow for the numerical simulation of time-dependent interfaces and their application in computational fluid dynamics and in computational engineering.
Lay summary

Im Laufe der letzten Jahrzehnte hat sich die numerische Simulation als ein unentbehrliches Werkzeug in Forschung und Entwicklung etabliert. Mithilfe moderner Algorithmen auf Supercomputern können Probleme in den Ingenieurswissenschaften angegangen und gelöst werden, deren Behandlung früher nicht möglich gewesen wäre oder deutlich mehr Zeit in Anspruch genommen hätte ("Computational Engineering"). Die Behandlung von komplexen Problemen, die zeitabhängige und bewegliche Ränder (oder Grenzflächen) enthalten, ist allerdings nach wie vor eine algorithmische wie technische Herausforderung. Anwendungsbeispiele sind etwa Bruchmechanik (Bruchflächen) oder Grenzflächen in Flüssigkeiten.

Für die  massiv parallelen Architekturen der modernen Superrechner allerdings stehen zur Zeit keine effizienten und gut skalierberen Methoden zur Verfügung, die es gestatten würden, Problem mit zeitabhängigen Grenzflächen effizient zu behandeln. Es ist das Ziel dieses Projektes, auf der mathematischen Seite, d.h. auf der Seite der Algorithmen, wie auf der softwaretechnischen Seite, d.h. auf der Seite der Simulationswerkzeuge, diese Lücke durch die Entwicklung neuer Methoden un deren Implementierung zu schließen.

Direct link to Lay Summary Last update: 18.04.2014

Responsible applicant and co-applicants



A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems.
Krause Rolf, Steiner Johannes, Rigazzi Alessandro, A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems., in Computing and Visualization in Science.
A phase-field approach to pneumatic fracture
Bilgen Carola, Kopanicakova Alena, Krause Rolf, Weinberg Kerstin, A phase-field approach to pneumatic fracture, in Proceedings in Applied Mathematics and Mechanics.


Group / person Country
Types of collaboration
Ju¨lich Supercomputing Centre (JSC) Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Swiss Centre for Scientific Computing (CSCS) Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Research Infrastructure
RWTH Aachen Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Exchange of personnel

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
USNCCM 14 Talk given at a conference A Parallel Fictitious Domain Method for Fluid-Structure Interaction Based on Pseudo - L2 - Projections 17.07.2017 Montreal, Canada Krause Rolf;
X-DMS 2017 Talk given at a conference Invited talk in a minisimposium on Semi-geometric Mutigrid for Fracture Problems 19.06.2017 Umea, Sweden Reusken Arnold; Gross Sven; Kothari Hardik; Krause Rolf;
Invited Talk to University of Trento (Host: Davide Bigoni) Individual talk Multigrid Methods for Contact and Fracture 30.06.2016 Trento, Italy Krause Rolf;
ECCOMAS 2016 Talk given at a conference Fast solution methods for fracture problems 06.06.2016 Crete, Greece Krause Rolf;
CMSE 2016 Computational Mathematics in Science and Engineering Talk given at a conference Contact, Constraints, and Complexity or the Quest for Optimal Solu8on Methods 25.05.2016 Ostrava, Czech Republic Krause Rolf;
13th US National Congress on Computational Mechanics Talk given at a conference Massively Parallel Strategies for Contact Problems - Interface Detection, Transfer, and Solution 27.07.2015 San Diego, United States of America Krause Rolf; Kothari Hardik;


Title Date Place
PASC 17 Conference 26.06.2017 Lugano, Switzerland


Although during the last decades tremendous progress has been achieved in the area of parallel finite element simulations, the parallel solution of complex and constrained problems in, e. g., mechanics and fluid mechanics, still remains a challenging task. Usually, good scalability can be achieved relatively straightforwardly for homogeneous problems, i. e., problems with smooth data, and structured meshes. Parallel simulations involving unstructured and adaptive meshes have also been successfully carried out, using a wide variety of solution methods, ranging from Krylov subspace methods to domain decomposi- tion approaches or multilevel methods. The parallel treatment of constrained or strongly heterogeneous problems, i. e., problems with very rough data, however, is still far from trivial. This is caused by the more complex mathematical structure of the discrete systems to be solved and by the more advanced data structures employed for assembling, solving, and parallel data exchange.An additional and up to now only scarcely addressed difficulty arises if time-dependent interfaces have to be resolved, as is the case in, e.g., liquid-gas flows of droplets impacting on a wall or crack propagation. These interfaces do not only influence the discretization, but also the robustness of iterative solution methods. Moreover, the special treatment of the interface poses a challenge for the parallel distribution of geometric objects across large scale machines.Efficient solution methods for these problems and their scalable and flexible implementations put a high demand not only on underlying methodology but also on the software used. In this proposal, we therefore aim at the development and implementation of both, fast solution methods as well as efficient software tools. More precisely, we will develop and implement parallel multilevel solvers for saddle point problems which are able to deal with time-dependent interfaces in a robust manner. To this end, we will employ a new approach for the construction of multilevel hierarchies, which is based on non-standard transfer (i.e., restriction and interpolation) operators and solution-dependent coarse grid spaces. As a basis for this work, one central goal of this project is the development and implementation of a stand-alone high-level library for the parallel management of distributed geometric objects. In order to foster the broad applicability of this library, we will use it within two different software and application environments, namely DROPS at RWTH and ObsLib++ at USI. Despite the seemingly different application fields, RWTH with two-phase flow and USI with computational mechanics, contact and crack propagation, both applications lead to large saddle point problems, with the additional complication of time-dependent interfaces. As these interfaces are typically only resolved by the finest mesh of the multilevel hierarchy and not by its coarse meshes, the multilevel solvers and their parallelization have to be adapted carefully. This will be done by adapting the intergrid operators as well as the ansatz spaces on each level. This combined approach is expected not only to provide the necessary robustness of the solver but also to allow for clear and modular data structures, simplifying the parallel implementation without sacrificing scalability.For this project strong expertise in the handling of time-dependent interfacial constraints, multilevel methods and solvers for saddle point problems, non-standard transfer operators, and HPC software for efficient parallel data management is mandatory. The applicants at RWTH and USI together provide in a complementary manner this expertise, which motivated the formation of this research team and the Swiss-German cooperation.