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Framework For Massively Parallel Adaptive Finite Element Computational Fluid Dynamics On Tetrahedral Meshes
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0002-5020-1631
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0003-4256-0463
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0002-1695-8809
2012 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 1, C24-C42 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we describe a general adaptive finite element framework for unstructured tetrahedral meshes without hanging nodes suitable for large scale parallel computations. Our framework is designed to scale linearly to several thousands of processors, using fully distributed and efficient algorithms. The key components of our implementation, local mesh refinement and load balancing algorithms, are described in detail. Finally, we present a theoretical and experimental performance study of our framework, used in a large scale computational fluid dynamics computation, and we compare scaling and complexity of different algorithms on different massively parallel architectures.

Place, publisher, year, edition, pages
2012. Vol. 34, no 1, C24-C42 p.
Keyword [en]
adaptive methods, load balancing, unstructured local mesh refinement
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-30284DOI: 10.1137/100800683ISI: 000300937500028Scopus ID: 2-s2.0-84861384674OAI: oai:DiVA.org:kth-30284DiVA: diva2:399306
Funder
Swedish e‐Science Research Center
Note

QC 20120326

Available from: 2011-02-21 Created: 2011-02-21 Last updated: 2017-12-11Bibliographically approved
In thesis
1. High performance adaptive finite element methods for turbulent fluid flow
Open this publication in new window or tab >>High performance adaptive finite element methods for turbulent fluid flow
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Understanding the mechanics of turbulent fluid flow is of key importance for industry and society as for example in aerodynamics and aero-acoustics. The massive computational cost for resolving all turbulent scales in a realistic problem makes direct numerical simulation of the underlying Navier-Stokes equations impossible. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized where the mesh is adaptively resolved, based on a posteriori error control. These adaptive methods have been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task.

This work concerns the development of an adaptive finite element method for modern parallel computer architectures. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallellization of local mesh refinement methods such as recursive longest edge bisection.

We also address the load balance problem with the development of an a priori predictive dynamic load balancing method. Current results are encouraging with almost linear strong scaling to thousands of cores on several modern architectures.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xii, 29 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2011:02
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-30277 (URN)978-91-7415-878-6 (ISBN)
Presentation
2011-03-14, E3, KTH, Osquarsbacke 14, Stockholm, 10:15 (English)
Opponent
Supervisors
Note
QC 20110223Available from: 2011-02-23 Created: 2011-02-21 Last updated: 2011-02-23Bibliographically approved
2. High Performance Adaptive Finite Element Methods: With Applications in Aerodynamics
Open this publication in new window or tab >>High Performance Adaptive Finite Element Methods: With Applications in Aerodynamics
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The massive computational cost for resolving all scales in a turbulent flow makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized by adaptively resolution of the mesh, based on a posteriori error estimation. Such adaptive methods have previously been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations of turbulent flow for complex geometries with a posteriori error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph. We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than twelve thousands cores.

Abstract [sv]

Den höga beräkningskostnaden för att lösa upp alla turbulenta skalor för ett realistiskt problem gör en direkt numerisk simulering av Navier-Stokes ekvationer omöjlig. De senaste framstegen inom adaptiva finita element metoder ger ett nytt kraftfullt verktyg inom Computational Fluid Dynamics (CFD). Beräkningskostnaden för en simulering av turbulent flöde kan minimeras genom att beräkningsnätet adaptivt förfinas baserat på en a posteriori feluppskattning. Dessa adaptiva metoder har tidigare implementerats för seriella beräkningar, medan en effektiv parallellisering av metoden inte är trivial. I denna avhandling presenterar vi vår utveckling av en adaptiv finita element lösare, anpassad för att effektivt beräkna tidsupplösta approximationer i komplicerade geometrier med a posteriori felkontroll. Effektiva datastrukturer och metoder för ostrukturerade beräkningsnät av tetrahedrar presenteras. Avhandlingen behandlar även effektiv parallellisering av lokala nätförfiningsmetoder, exempelvis recursive longest edge bisection. Även lastbalanseringsproblematiken behandlas, där problemet lösts genom utvecklandet av en prediktiv dynamisk lastbalanseringsmetod, baserad på en viktad dualgraf av beräkningsnätet. Slutligen avhandlas även problematiken med att effektivt utnyttja nytillkomna superdatorarkitekturer, genom utvecklandet av en hybrid parallelliserings modell som kombinerar traditionell meddelande baserad parallellisering med envägskommunikation. Detta har resulterat i en generell samt effektiv implementation med god skalning upp till fler än tolv tusen processorkärnor.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xii, 50 p.
Series
TRITA-CSC-A, ISSN 1653-5723 ; 2013:07
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-125742 (URN)978-91-7501-814-0 (ISBN)
Public defence
2013-09-11, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20130816

Available from: 2013-08-16 Created: 2013-08-13 Last updated: 2016-02-02Bibliographically approved

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Jansson, NiclasHoffman, Johan

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