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Universite de Nice - Sophia-Antipolis December 13, 2013
PhD DefenseCedric Lachat
Design and validation of distributed-memory,parallel remeshing algorithms based on asequential remesher
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SUMMARY
Introduction
Data structures for parallel remeshing
Parallel remeshing
Experiments
Conclusion
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1Introduction
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Introduction
ContextI Numerical simulations are
needed in multiple domainsincluding:
I thermonuclear fusionI aeronauticsI meteorology, . . .
I Problems become bigger andmore and more complex:numerical simulations cannot berun on a single workstation→ Want of parallelizedcomputations→ Need to distribute dataacross the processors: domaindecomposition
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Introduction
Numerical simulation
I Space discretization:I mesh
I Finite number of points onwhich values of theproblem are computed,e.g.:
I temperatureI pressureI speed,. . .
I Solution precision dependson mesh quality:
I need for remeshing
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Introduction
Aim of this PhD thesis
I Achieve parallel remeshing based on a sequential remesherI Devise a scalable method→ distributed memory paradigm→ communication across subdomain boundaries
I Since distributed meshes are considered, need to devise acomplete framework for handling distributed meshes andrelated computations
I Parallel remeshing requires:I to iterate on mesh components to perform local computationsI to associate values with components
→ made available to users through an APII Improve locality of accesses in memory hierarchy:
I proper renumbering of entities on each subdomain
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Introduction
State of the art (1/2)
I Parallel partitioningI spectral [Pothen et al., 1990], combinatorial [Kernighan and
Lin, 1970, Fiduccia and Mattheyses, 1982],evolutionist [Dongarra et al., 1988]
I only multi-level [Chevalier, 2007, Chevalier and Safro, 2009]provides good efficiency and quality on big graph
I Parallel dynamic load balancingI many tools: DRAMA [Maerten et al., 1999], Zoltan [Devine
et al., 1999, 2002], PLUM [Oliker et al., 2000],ParFUM [Lawlor et al., 2006]. . .
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Introduction
State of the art (2/2)
I Parallel remeshingI parallelize remeshing techniques [Castanos and Savage, 1996,
Laemmer, 1997, Oliker et al., 2000, Chrisochoides and Nave,2003, Casagrande et al., 2005, Lawlor et al., 2006]
I re-use of sequential algorithms [Coupez et al., 2000, Cavalloet al., 2005, Dobrzynski and Remacle, 2007, Tremel et al.,2007, Digonnet et al., 2007, Ramadan et al., 2009]
I Renumbering [Lohner, 1993, Burgess and Giles, 1997, Lohner,1998, Amenta et al., 2003, Isenburg et al., 2006, Loseille andAlauzet, 2009]
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2Data structures
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Data structures for parallel remeshing
Definitions
I Mesh:
I NodeI EdgeI Element
I Mesh representation:
I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I Node
I EdgeI Element
I Mesh representation:
I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI Edge
I Element
I Mesh representation:
I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:
I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:
I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:I Vertex
I Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:I VertexI Entity
I main entityI RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:I VertexI Entity
I main entity
I RelationI Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:I VertexI Entity
I main entityI Relation
I Enriched graph
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Data structures for parallel remeshing
Definitions
I Mesh:I NodeI EdgeI Element
I Mesh representation:I VertexI Entity
I main entityI RelationI Enriched graph
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Data structures for parallel remeshing
Examples
I The same mesh can lead to different enriched graphsI Depending on the requirements of the numerical schemes
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Data structures for parallel remeshing
Distributed mesh
I On three processors
P0 P21P
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Data structures for parallel remeshing
Definitions
I Vertices, locally on P1:I LocalI HaloI Overlap
I Vertices, between P0and P1:
I FrontierI Vertices, globally:
I Internal
P0 P21P
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Data structures for parallel remeshing
Definitions
I Vertices, locally on P1:I LocalI HaloI Overlap
I Vertices, between P0and P1:
I FrontierI Vertices, globally:
I Internal
P0 P21P
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Data structures for parallel remeshing
Definitions
I Vertices, locally on P1:I LocalI HaloI Overlap
I Vertices, between P0and P1:
I FrontierI Vertices, globally:
I Internal
P0 P21P
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Data structures for parallel remeshing
Definitions
I Vertices, locally on P1:I LocalI HaloI Overlap
I Vertices, between P0and P1:
I FrontierI Vertices, globally:
I Internal
P0 P21P
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Data structures for parallel remeshing
Definitions
I Vertices, locally on P1:I LocalI HaloI Overlap
I Vertices, between P0and P1:
I FrontierI Vertices, globally:
I Internal
P0 P21P
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Data structures for parallel remeshing
Global numbering
I Necessary to describe the mesh in its entirety
P0 P21P
5
1
2 9
7
4
3 6 8
10
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Data structures for parallel remeshing
Local numbering
I Local indices are mandatory to address local data arrays
I For all local vertices onevery subdomain, verticesare indexed per entity
P0 P21P
1
1 1
12 2
1
1
1
2
I Local indices are extendedto index halo vertices aswell, e.g. with respect toprocessor P1:
P0 P21P
23
1
1
2 1 3
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3Parallel remeshing
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Parallel remeshing
State of the art (1/2)
I First class of parallel remeshing techniques:I Parallelization of existing sequential remeshing techniques
I introduced in 1996 [Castanos and Savage, 1996] for 2Dmeshes
I 3D remeshing in 2000 for homogeneous meshes [Oliker et al.,2000]
I Delaunay triangulation in 2003 [Chrisochoides and Nave, 2003]I 3D remeshing for mixed meshes [Lawlor et al., 2006]
I Problems:I Difficulties to parallelize each operator of the remesherI Remeshing some element requires neighborhood informationI Too much communication between subdomains is required to
achieve quality as high as in sequential processing→ This class of parallel remeshing methods cannot handlelarge-size meshes distributed across a large number ofprocessors
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Parallel remeshing
State of the art (2/2)
I Second class of parallel remeshing:I Re-use sequential remeshers in a parallel framework:
I introduced in 2000 [Coupez et al., 2000, Dobrzynski andRemacle, 2007]
I 3D remeshing for mixed meshes [Cavallo et al., 2005]I remeshing with hierarchical transport [Digonnet et al., 2007]I multi-grid remeshing [Ramadan et al., 2009]
→ Our approach is to generalize this class of parallelremeshing techniques so as to allow for plugging-in anysequential remesher
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Parallel remeshing
Requirements (1/2)
I How to remesh in parallel on distributed meshes?I Subdomain size could be greater than mesh size allowed by the
sequential remesher→ Need to identify in parallel non-overlapping zones ofprescribed size / workload
I Zone frontiers must be left unmodified so as to easereintegration of remeshed zones into the distributed mesh
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Parallel remeshing
Global scheme:Iterative process until all tagged elements are remeshed
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:Tag elements which need to be remeshed
1a Tagging
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:
Identify non overlapping zones in parallel
2 Identification
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:
Extract the zones which will be remeshed
3 Extraction
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:Remesh in sequential each zone
4 Remeshing
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:
Reintegrate the remeshed zones in the distributed mesh
5 Reintegration
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Global scheme:Tag again elements which need to be remeshed
1b Tagging
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Parallel remeshing
Global scheme:
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Requirements (2/2)
I How to determine which elements need to be remeshed?I Isotropic or anisotropic metric on verticesI Avoid elements of bad quality
I Which criteria on identified zones?I Measure zone skin size compared to zone volume:
I compute the isoperimetric quotient of the elementI value between 0 and 1I 0: worst quotient possibleI 1: optimal quotient, in the case of sphere and the
corresponding ball
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Parallel remeshing
Tagging (1/3)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Tagging (2/3)
I User-provided mesh:I Corresponding element
graph:
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Parallel remeshing
Tagging (3/3)I Tag elements which need to be remeshed:
P0
P2
P1
P3
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Parallel remeshing
Identification (1/9)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Identification (2/9)I Identify non-overlapping zones in parallel:
I each zone will be given to a sequential remesherI a weight is determined on each element according to the
dedicated work of the remesher→ Want of a good evaluation of the remesher work
P0
P2
P1
P3
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Parallel remeshing
Identification (3/9)
I How to compute efficiently non-overlapping zones in parallelon a distributed mesh?
I By using a graph multilevel scheme which provides very goodpartitions when combined to local optimization algorithms
Initialpartitioning
Coarsening Uncoarsening
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
I Pros:
I Number of zones does not depend on the number of processorsI Cons:
I Zones are not compact and have small isoperimetric quotient
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
I Pros:I Number of zones does not depend on the number of processors
I Cons:
I Zones are not compact and have small isoperimetric quotient
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
I Pros:I Number of zones does not depend on the number of processors
I Cons:
I Zones are not compact and have small isoperimetric quotient
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Parallel remeshing
Identification (3/9)
I Algorithm 1: parallel graph coarseningI without local refinement during uncoarsening so as to save
time
I Pros:I Number of zones does not depend on the number of processors
I Cons:I Zones are not compact and have small isoperimetric quotient
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Parallel remeshing
Identification (3/9)I Algorithm 1: parallel graph coarsening
I without local refinement during uncoarsening so as to savetime
I Pros:I Number of zones does not depend on the number of processors
I Cons:I Zones are not compact and have small isoperimetric quotient
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Parallel remeshing
Identification (5/9)
I Algorithm 2: parallel seed growing on a distributed enrichedgraph
I How to choose the seeds?I random positions can lead to zone conflictsI first try: pick one seed by subdomain
P0
P2
P1
P3
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Parallel remeshing
Identification (5/9)
I Algorithm 2: parallel seed growing on a distributed enrichedgraph
I How to choose the seeds?I random positions can lead to zone conflictsI first try: pick one seed by subdomain
P0
P2
P1
P3
I Pros:I Zone isoperimetric quotient becomes reasonably good enough
I Cons:
I Number of zones corresponds to the number of processors
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Parallel remeshing
Identification (5/9)
I Algorithm 2: parallel seed growing on a distributed enrichedgraph
I How to choose the seeds?I random positions can lead to zone conflictsI first try: pick one seed by subdomain
P0
P2
P1
P3
I Pros:I Zone isoperimetric quotient becomes reasonably good enough
I Cons:
I Number of zones corresponds to the number of processors
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Parallel remeshing
Identification (5/9)
I Algorithm 2: parallel seed growing on a distributed enrichedgraph
I How to choose the seeds?I random positions can lead to zone conflictsI first try: pick one seed by subdomain
P0
P2
P1
P3
I Pros:I Zone isoperimetric quotient becomes reasonably good enough
I Cons:I Number of zones corresponds to the number of processors
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:
I Yields satisfactory isoperimetric quotientsI Number of zones does not depend on the number of processors
I Cons:
I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:I Yields satisfactory isoperimetric quotients
I Number of zones does not depend on the number of processorsI Cons:
I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:I Yields satisfactory isoperimetric quotientsI Number of zones does not depend on the number of processors
I Cons:
I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:I Yields satisfactory isoperimetric quotientsI Number of zones does not depend on the number of processors
I Cons:
I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:I Yields satisfactory isoperimetric quotientsI Number of zones does not depend on the number of processors
I Cons:I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (6/9)
I Algorithm 3: parallel graph coarsening with parallel seedgrowing on a distributed enriched graph
I Constrain seed selection within prescribed areas
I Pros:I Yields satisfactory isoperimetric quotientsI Number of zones does not depend on the number of processors
I Cons:I Two algorithms are used on two different data structures:
I element graph and enriched graphI consumes more time than other algorithms
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Parallel remeshing
Identification (7/9)
I Algorithm 4: full-featured parallel partitioningI Local optimization is mandatory to obtain good isoperimetric
quotients
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Parallel remeshing
Identification (7/9)
I Algorithm 4: full-featured parallel partitioningI Local optimization is mandatory to obtain good isoperimetric
quotients
I Pros:
I Smooth skin which gives good enough isoperimetric quotientI Number of zones does not depend on number of processors
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Parallel remeshing
Identification (7/9)
I Algorithm 4: full-featured parallel partitioningI Local optimization is mandatory to obtain good isoperimetric
quotients
I Pros:I Smooth skin which gives good enough isoperimetric quotient
I Number of zones does not depend on number of processors
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Parallel remeshing
Identification (7/9)
I Algorithm 4: full-featured parallel partitioningI Local optimization is mandatory to obtain good isoperimetric
quotients
I Pros:I Smooth skin which gives good enough isoperimetric quotientI Number of zones does not depend on number of processors
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Parallel remeshing
Identification (8/9)
Algorithm Good IC #Zones Time spentGraph coarsening No Yes YesSeed growing Yes No YesGraph coarsening + seed growing Yes Yes NoGraph partitioning Yes Yes Yes
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Parallel remeshing
Identification (8/9)
Algorithm Good IC #Zones Time spentGraph coarsening No Yes YesSeed growing Yes No YesGraph coarsening + seed growing Yes Yes NoGraph partitioning Yes Yes Yes
→ Chosen algorithm is graph partitioning
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Parallel remeshing
Identification (9/9)I Propagate zone color on other vertices through cells:
P0
P2
P1
P3
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Parallel remeshing
Extraction (1/3)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Extraction (2/3)I Extract zones and distribute them throughout the processors:
I zone skins will not be remeshed, except zone skins whichcorrespond to mesh skin
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:
I load-balance according to the remesher workloadI minimize communication
P0
P1 P2
P3
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workload
I minimize communication
P0
P1 P2
P3 P2 P3P0 P1
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workload
I minimize communication
P0
P1 P2
P3
9 7 5 5 3 7 3
P2 P3P0 P1
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workload
I minimize communication
P0
P1 P2
P3
9 10 10 10
9 7 5 5 3 7 3
P2 P3P0 P1
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workload
I minimize communication
P0
P1 P2
P3
9 10 10 10
9 7 5 5 3 7 3
P2 P3P0 P1
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workloadI minimize communication
P0
P1 P2
P3
9 7 5 5 3 7 3
P2 P3P0 P1
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Parallel remeshing
Extraction (3/3)
I Two criteria must be considered:I load-balance according to the remesher workloadI minimize communication
P0
P1 P2
P3
9 10 10 10
9 7 5 5 3 7 3
P2 P3P0 P1
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Parallel remeshing
Remeshing (1/2)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Remeshing (2/2)
I Remesh sequentially each zone on separate processors:I Before remeshing: I After remeshing:
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Parallel remeshing
Reintegration (1/2)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Reintegration (2/2)I Fixed skin zone permit to reintegrate zones in distributed
mesh:
P0
P2
P1
P3
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Parallel remeshing
Tagging again (1/2)
1b Tagging
2 Identification
3 Extraction 4 Remeshing
5 Reintegration
1a Tagging
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Parallel remeshing
Tagging again (2/2)
I Remove tag on elements which are inside zonesI Yet a band from the skin is needed to remesh zone skin:I Before tagging:
P0
P2
P1
P3
I After tagging:
P0
P2
P1
P3
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4Experiments
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Experiments
Functional test case (1/3)
I Our work implemented in a library: PaMPAI PaMPA integrated in another library: Aerosol (continuous and
discontinuous finite elements library on hybrid meshes)I Comparison of Aerosol with the Aghora library (developed by
ONERA) in the Yee vortex test case:I implemented into Aerosol by Bacchus and Cagire teams
(not including me)I isentropic vortex in a 3D uniform and inviscid flowI 3D discretization with hexahedra on the unit square [0, 1]3
with periodic boundary conditionsI discontinuous Galerkin methodI explicit Runge-Kutta time stepping
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Experiments
Functional test case (2/3)I Comparison of the weak scalabilityI Varying the polynomial degree p:
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Experiments
Functional test case (3/3)
I Anisotropic propagation ofheat in a tokamak
I Unstationary anisotropicdiffusion
I Torus mesh composed ofprisms
I Discontinuous Galerkinmethod
I Implicit schemeI Linear system solved
with PETsCI Integrated by CAGIRE
team
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Experiments
Parallel remeshing (1/5)
Isotropic meshAnisotropic mesh
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Experiments
Parallel remeshing (2/5): isotropic meshMMG3D PaMPA-MMG3D
on 1 processor on 24 processors
Number of elements at the start 2 423 029Processor frequency (GHz) 2,40 3,06
Used memory (kb) 27 588 940 51 116 044Elapsed time 17h15m12s 00h21m14s
Elapsed time × number procs 17h15m12s 8h33m36sNumber of elements 108 126 515 115 802 876
Smallest edge length 0.1470 0.1395Largest edge length 6.3309 11.2415
Worst element quality 294.2669 294.2669Element quality between 1 and 2 99.65% 99.38%
Edge length between 0.71 and 1.41 97.25% 97.65%
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Experiments
Parallel remeshing (3/5): isotropic mesh
PaMPA-MMG3Don 120 processors
Number of elements at the start 4 509 655Elapsed time 00h34m54s
Elapsed time × number procs 69h48mNumber of elements 318 027 812
Smallest edge length 0.2862Largest edge length 6.2161
Worst element quality 235.6651Element quality between 1 and 2 99.58%
Edge length between 0.71 and 1.41 97.91%
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Experiments
Parallel remeshing (4/5): isotropic mesh
PaMPA-MMG3Don 240 on 480
processors processorsNumber of elements at the start 27 044 943
Used memory (kb) 651 185 792 542 832 960Elapsed time 00h34m59s 00h29m03s
Elapsed time × number procs 139h56m 232h24mNumber of elements 609 671 387 612 426 645
Smallest edge length 0.2911 0.1852Largest edge length 8.3451 7.3611
Worst element quality 335.7041 190.4122Element quality between 1 and 2 98.92% 98.97%
Edge length between 0.71 and 1.41 97.20% 97.39%
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Experiments
Parallel remeshing (4/5): isotropic mesh
1
10
96
385610
1 2 3 4 5 6 7
Num
ber
of
zones
Number of iteration
Comparison of number of zones at each iteration
240 processors480 processors
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Experiments
Parallel remeshing (5/5): anisotropic meshMMG3D PaMPA-MMG3D
on 1 processor on 5 processors
Number of elements at the start 254 501Elapsed time 00h08m25s 00h06m53s
Elapsed time × number procs 00h08m25s 00h34m25sNumber of elements 11 559 197 11 741 242
Smallest edge length 0.1154 0.1133Largest edge length 11.0161 10.1912
Worst element quality 37.7373 38.2374Element quality between 1 and 2 98.41% 98.10%
Edge length between 0.71 and 1.41 93.29% 93.04%
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Experiments
Parallel remeshing (5/5): anisotropic meshMMG3D PaMPA-MMG3D
on 1 processor on 5 processors
Number of elements at the start 254 501Elapsed time 00h08m25s 00h06m53s
Elapsed time × number procs 00h08m25s 00h34m25sNumber of elements 11 559 197 11 741 242
Smallest edge length 0.1154 0.1133Largest edge length 11.0161 10.1912
Worst element quality 37.7373 38.2374Element quality between 1 and 2 98.41% 98.10%
Edge length between 0.71 and 1.41 93.29% 93.04%
→ The mesh must be bigger in order to cover the overheadinduced by the iterative process
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5Conclusion
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Conclusion
Conclusion
I We have devised an efficient scheme for parallel remeshing ofvery large meshes, which can be coupled with any sequentialremesher
I We can achieve the same quality than sequential remeshersI Several algorithms as parallel zone identification have been
developed and implemented:I graph coarseningI seed / ”crystal” growingI graph partitioning
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Conclusion
Prospects
I Short-term prospects:I Remeshing large-size anisotropic meshesI Testing scalability on parallel remeshingI Renumbering entities in parallel remeshingI Remeshing mesh skin by plugging-in a sequential remesher
which remesh the skin: MMG3D5I Long-term prospects:
I parallel repartitioning during parallel remeshingI Adding more parallel zone identification algorithmsI parallel interpolation coupled with parallel remeshing (PhD
Thesis: Leo Nouveau)
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Thank you for your attention
PhD Defense
pampa.bordeaux.inria.fr
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Conclusion
About functional test caseI p degree means 5 ∗ (p + 1)3 ∗ 200 unknowns by sub-domain:
I p = 1: 8000 unknownsI p = 2: 27000 unknownsI p = 3: 64000 unknownsI p = 4: 125000 unknowns
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Conclusion
Nina Amenta, Sunghee Choi, and Gunter Rote. Incrementalconstructions con brio. In Proceedings of the nineteenth annualsymposium on Computational geometry, pages 211–219. ACM,2003.
D.A. Burgess and M.B. Giles. Renumbering unstructured grids toimprove the performance of codes on hierarchical memorymachines. Advances in Engineering Software, 28(3):189–201,1997.
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Conclusion
Cedric Chevalier. Conception et mise en oeuvre d’outils efficacespour le partitionnement et la distribution paralleles de problemenumeriques de tres grande taille. PhD thesis, Universite Scienceset Technologies-Bordeaux I, 2007.
Cedric Chevalier and Ilya Safro. Comparison of coarsening schemesfor multilevel graph partitioning. In Learning and IntelligentOptimization, pages 191–205. Springer, 2009.
Nikos Chrisochoides and Demian Nave. Parallel delaunay meshgeneration kernel. International Journal for Numerical Methodsin Engineering, 58(2):161–176, 2003.
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Karen Devine, Bruce Hendrickson, Erik Boman, Matthew St John,Courtenay Vaughan, and WF Mitchell. Zoltan: A dynamicload-balancing library for parallel applications; users guide.Sandia National Laboratories Tech. Rep, 1999.
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Conclusion
Karen Devine, Erik Boman, Robert Heaphy, Bruce Hendrickson,and Courtenay Vaughan. Zoltan data management services forparallel dynamic applications. Computing in Science &Engineering, 4(2):90–96, 2002.
Hugues Digonnet, Marc Bernacki, Luisa Silva, and Thierry Coupez.Adaptation de maillage en parallele, application a la simulationde la mise en forme des materiaux. In Congres Francais deMecanique Grenoble-CFM 2007, page 6 pages, Grenoble,France, 2007. URLhttp://hal-ensmp.archives-ouvertes.fr/hal-00521844.http://hdl.handle.net/2042/16046.
C Dobrzynski and JF Remacle. Parallel mesh adaptation.International Journal for Numerical Methods in Engineering,2007.
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Conclusion
J. J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson. Anextended set of FORTRAN Basic Linear Algebra Subprograms.ACM Transactions on Mathematical Software, 14(1):1–17,March 1988. ISSN 0098-3500. URLhttp://doi.acm.org/10.1145/42288.42291.
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Ing Lutz Laemmer. Parallel mesh generation. In Solving IrregularlyStructured Problems in Parallel, pages 1–12. Springer, 1997.
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Conclusion
Orion Lawlor, Sayantan Chakravorty, Terry Wilmarth, NileshChoudhury, Isaac Dooley, Gengbin Zheng, and Laxmikant Kale.Parfum: a parallel framework for unstructured meshes forscalable dynamic physics applications. Engineering withComputers, 22:215–235, 2006. ISSN 0177-0667. URLhttp://dx.doi.org/10.1007/s00366-006-0039-5.10.1007/s00366-006-0039-5.
Rainald Lohner. Some useful renumbering strategies forunstructured grids. International Journal for Numerical Methodsin Engineering, 36(19):3259–3270, 1993.
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Conclusion
Adrien Loseille and Frederic Alauzet. Shrimp User Guide. A FastMesh Renumbering and Domain Partionning Method. TechnicalReport RT-0362, INRIA, 2009. URLhttp://hal.inria.fr/inria-00362994.
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Conclusion
Alex Pothen, Horst D Simon, and Kang-Pu Liou. Partitioningsparse matrices with eigenvectors of graphs. SIAM Journal onMatrix Analysis and Applications, 11(3):430–452, 1990.
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U Tremel, KA Sørensen, S Hitzel, H Rieger, Oubay Hassan, andNigel P Weatherill. Parallel remeshing of unstructured volumegrids for cfd applications. International journal for numericalmethods in fluids, 53(8):1361–1379, 2007.