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Iterative and Adaptive PDE Solvers for Shared Memory Architectures
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys. (Software Aspects of High-Performance Computing)
2006 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)Alternativ tittel
Iterativa och adaptiva PDE-lösare för parallelldatorer med gemensam minnesorganisation (svensk)
Abstract [en]

Scientific computing is used frequently in an increasing number of disciplines to accelerate scientific discovery. Many such computing problems involve the numerical solution of partial differential equations (PDE). In this thesis we explore and develop methodology for high-performance implementations of PDE solvers for shared-memory multiprocessor architectures.

We consider three realistic PDE settings: solution of the Maxwell equations in 3D using an unstructured grid and the method of conjugate gradients, solution of the Poisson equation in 3D using a geometric multigrid method, and solution of an advection equation in 2D using structured adaptive mesh refinement. We apply software optimization techniques to increase both parallel efficiency and the degree of data locality.

In our evaluation we use several different shared-memory architectures ranging from symmetric multiprocessors and distributed shared-memory architectures to chip-multiprocessors. For distributed shared-memory systems we explore methods of data distribution to increase the amount of geographical locality. We evaluate automatic and transparent page migration based on runtime sampling, user-initiated page migration using a directive with an affinity-on-next-touch semantic, and algorithmic optimizations for page-placement policies.

Our results show that page migration increases the amount of geographical locality and that the parallel overhead related to page migration can be amortized over the iterations needed to reach convergence. This is especially true for the affinity-on-next-touch methodology whereby page migration can be initiated at an early stage in the algorithms.

We also develop and explore methodology for other forms of data locality and conclude that the effect on performance is significant and that this effect will increase for future shared-memory architectures. Our overall conclusion is that, if the involved locality issues are addressed, the shared-memory programming model provides an efficient and productive environment for solving many important PDE problems.

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis , 2006. , s. 49
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 218
Emneord [en]
partial differential equations, iterative methods, finite elements, conjugate gradients, adaptive mesh refinement, multigrid, cc-NUMA, distributed shared memory, OpenMP, page migration, TLB shoot-down, bandwidth minimization, reverse Cuthill-McKee, migrate-on-next-touch, affinity, temporal locality, chip multiprocessors, CMP
HSV kategori
Forskningsprogram
Beräkningsvetenskap
Identifikatorer
URN: urn:nbn:se:uu:diva-7136ISBN: 91-554-6648-6 (tryckt)OAI: oai:DiVA.org:uu-7136DiVA, id: diva2:168842
Disputas
2006-10-07, Auditorium Minus, Museum Gustavianum, Akademigatan 3, Uppsala, 13:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2006-09-15 Laget: 2006-09-15 Sist oppdatert: 2022-03-11bibliografisk kontrollert
Delarbeid
1. Improving Geographical Locality of Data for Shared Memory Implementations of PDE Solvers
Åpne denne publikasjonen i ny fane eller vindu >>Improving Geographical Locality of Data for Shared Memory Implementations of PDE Solvers
2004 (engelsk)Inngår i: Computational Science – ICCS 2004, Berlin: Springer-Verlag , 2004, s. 9-16Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
Berlin: Springer-Verlag, 2004
Serie
Lecture Notes in Computer Science ; 3037
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-71098 (URN)10.1007/b97988 (DOI)
Tilgjengelig fra: 2007-03-11 Laget: 2007-03-11 Sist oppdatert: 2018-01-10bibliografisk kontrollert
2. affinity-on-next-touch: Increasing the Performance of an Industrial PDE Solver on a cc-NUMA System
Åpne denne publikasjonen i ny fane eller vindu >>affinity-on-next-touch: Increasing the Performance of an Industrial PDE Solver on a cc-NUMA System
2005 (engelsk)Inngår i: Proc. 19th ACM International Conference on Supercomputing, New York: ACM Press , 2005, s. 387-392Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
New York: ACM Press, 2005
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-80041 (URN)10.1145/1088149.1088201 (DOI)1-59593-167-8 (ISBN)
Tilgjengelig fra: 2006-05-19 Laget: 2009-01-19 Sist oppdatert: 2018-01-13bibliografisk kontrollert
3. Algorithmic optimizations of a conjugate gradient solver on shared memory architectures
Åpne denne publikasjonen i ny fane eller vindu >>Algorithmic optimizations of a conjugate gradient solver on shared memory architectures
2006 (engelsk)Inngår i: International Journal of Parallel, Emergent and Distributed Systems, ISSN 1744-5760, E-ISSN 1744-5779, Vol. 21, s. 345-363Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-80937 (URN)10.1080/17445760600568139 (DOI)
Tilgjengelig fra: 2006-06-29 Laget: 2006-06-29 Sist oppdatert: 2018-01-13bibliografisk kontrollert
4. Multigrid and Gauss-Seidel smoothers revisited: Parallelization on chip multiprocessors
Åpne denne publikasjonen i ny fane eller vindu >>Multigrid and Gauss-Seidel smoothers revisited: Parallelization on chip multiprocessors
2006 (engelsk)Inngår i: Proc. 20th ACM International Conference on Supercomputing, New York: ACM Press , 2006, s. 145-155Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
New York: ACM Press, 2006
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-19810 (URN)10.1145/1183401.1183423 (DOI)1-59593-282-8 (ISBN)
Tilgjengelig fra: 2008-02-08 Laget: 2008-02-08 Sist oppdatert: 2018-01-12bibliografisk kontrollert
5. Geographical locality and dynamic data migration for OpenMP implementations of adaptive PDE solvers
Åpne denne publikasjonen i ny fane eller vindu >>Geographical locality and dynamic data migration for OpenMP implementations of adaptive PDE solvers
2008 (engelsk)Inngår i: OpenMP Shared Memory Parallel Programming, Berlin: Springer-Verlag , 2008, s. 382-393Konferansepaper, Publicerat paper (Fagfellevurdert)
sted, utgiver, år, opplag, sider
Berlin: Springer-Verlag, 2008
Serie
Lecture Notes in Computer Science ; 4315
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-17844 (URN)10.1007/978-3-540-68555-5_31 (DOI)000256573200031 ()978-3-540-68554-8 (ISBN)
Prosjekter
UPMARC
Tilgjengelig fra: 2008-09-05 Laget: 2008-09-05 Sist oppdatert: 2022-01-28bibliografisk kontrollert

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