Fast Multipole-Based Elliptic PDE Solver and Preconditioner

Handle URI:
http://hdl.handle.net/10754/621993
Title:
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Authors:
Ibeid, Huda ( 0000-0001-5208-5366 )
Abstract:
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.
Advisors:
Keyes, David E. ( 0000-0002-4052-7224 )
Committee Member:
Bagci, Hakan ( 0000-0003-3867-5786 ) ; Gao, Xin ( 0000-0002-7108-3574 ) ; Yokota, Rio ( 0000-0001-7573-7873 ) ; Gropp, William D.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Computer Science
Issue Date:
7-Dec-2016
Type:
Dissertation
Appears in Collections:
Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorKeyes, David E.en
dc.contributor.authorIbeid, Hudaen
dc.date.accessioned2016-12-11T06:27:53Z-
dc.date.available2016-12-11T06:27:53Z-
dc.date.issued2016-12-07-
dc.identifier.urihttp://hdl.handle.net/10754/621993-
dc.description.abstractExascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.en
dc.language.isoenen
dc.subjectFast Multiple Methoden
dc.subjectPerformance modelingen
dc.subjectBoundary element methoden
dc.subjectPreconditioningen
dc.titleFast Multipole-Based Elliptic PDE Solver and Preconditioneren
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberBagci, Hakanen
dc.contributor.committeememberGao, Xinen
dc.contributor.committeememberYokota, Rioen
dc.contributor.committeememberGropp, William D.en
thesis.degree.disciplineComputer Scienceen
thesis.degree.nameDoctor of Philosophyen
dc.person.id113051en
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