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1、Engineering with Computers manuscript No.(will be inserted by the editor)Efficient Distributed Mesh Data Structure for Parallel AutomatedAdaptive AnalysisE. Seegyoung Seol, Mark S. ShephardScientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.Received: date
2、/ Revised version: dateAbstract For the purposeofefficiently supportingpar-allel mesh-based simulations, we developed a partitionmodel and a distributed mesh data management systemthat is able to shape its mesh data structure dynamicallybased on the users representational needs to providethe needed
3、representation at a minimum cost (memoryand time), called Flexible distributed Mesh DataBase(FMDB). The purpose of the partition model is to rep-resent mesh partitioning and support mesh-level paralleloperations through inter-processor communication links.FMDB has been used to efficiently support pa
4、rallel au-tomated adaptive analysis processes in conjunction withexisting analysis engines.1 IntroductionAn automated adaptive analysis typically starts witha coarse mesh and a low-order numerical solution ofa problem and based on an estimate of the local dis-cretization error either refines the mes
5、h (h-refinement),increases the order of numerical solution (p-refinement),moves the mesh (r-refinement), or does combinations ofh-, p- and r-refinements to improve the quality of the so-lution 1,2. To run adaptive analysis in parallel, solversand adaptation steps should run on distributed meshespart
6、itioned over multiple processors 3.A distributed mesh data structure is an infrastruc-ture executing underneath providing all parallel mesh-based operations needed to support parallel adaptiveanalysis. An efficient and scalable distributed mesh datastructure is mandatory to achieve performance since
7、 itstrongly influences the overall performance of adaptivemesh-basedsimulations. In addition to the generalmesh-basedoperations4,suchas meshentitycreation/deletion,Correspondence to: seolescorec.rpi.eduadjacency and geometric classification, iterators, arbi-trary attachable data to mesh entities, et
8、c., the dis-tributed mesh data structure must support (i) efficientcommunication between entities duplicated over multi-ple processors, (ii) migration of mesh entities betweenprocessors, and (iii) dynamic load balancing.Papers have been published on the issues of paralleladaptive analysis including
9、parallel mesh generation 511, dynamic mesh load balancing techniques 1216,and data structure and algorithms for parallel struc-tured 1720 or unstructured mesh adaptation 11,2127.Parashar and Browne presented a distributed meshdata structure for parallel non-conforming h-refinementcalledDAGH (Distrib
10、uted AdaptiveGridHierarchy)20.DAGH represents a mesh with grid hierarchy. In case ofa distributed grid, inter-grid operations are performedlocally on each processor without involving any commu-nicationor synchronizationdueto the mesh refinementisnon-conforming. The mesh load balancing is performedby
11、 varying granularity of the DAGH blocks.LibMesh 23 is a distributed mesh data structuredeveloped at the university of Texas in order to sup-port parallel finite element simulations with refinement.It opted the classic element-node data structuresupport-ing only h- uniform refinement and serial mesh
12、partition-ing for initial distribution.Reference 28 presented a distributed mesh data str-cuture to support parallel adaptive numerical computa-tion based on refinement and coarsening 22. A meshdata consists of vertices, edges and regions with a linkedlist data structure and maintains the shared pro
13、cessorlists for entities on partition boundaries through themessage passing. Global identifiers are assigned to ev-ery entity, thus, all data structure are updated to con-tain consistent global information during adaptation. Itprovided the owning processor of shared entities which israndomly selecte
14、d and the dynamic mesh load balancingwith ParMETIS 29.2 E. Seegyoung Seol, Mark S. ShephardIn reference 26, Selwood and Berzins presented ageneral distributed mesh data structure that supportsparallelmeshrefinement and de-refinement.It representsa mesh with all d level mesh entities and adjacencies,
15、 andprovides dynamic load balancing with the Zoltan 30library. In order to be aware of the part of the meshdistributed on other processors, the pointers to the ad-jacent tetrahedron that are on other processors are keptfor each processor.Reference 14,21presenteda generaldistributed meshdata structur
16、e called PMDB (Parallel Mesh DataBase),which was capable of supporting parallel adaptive sim-ulations. In PMDB, the data related to mesh partition-ing were kept at the mesh entity level and the inter-processor links were managed by doubly-linked struc-tures. These structures provided query routines such asprocessor adjacency, lists of entities on partition bound-aries, and update operators such as insertion and dele-tion of these entities. The owning proc
