Mesh Algorithms for PDE with Sieve I: Mesh Distribution

Knepley, Matthew G.; Karpeev, Dmitry A.

doi:10.1155/2009/948613

Title: Mesh Algorithms for PDE with Sieve I: Mesh Distribution

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Abstract

We have developed a new programming framework, called Sieve, to support parallel numerical partial differential equation(s) (PDE) algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms acting on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode not only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated using the same fundamental mechanisms used to represent meshes. We present the complete description of an algorithm to encode a mesh partition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same algorithm. The use of a high level of abstraction withinmore »« less

Authors:

Knepley, Matthew G. ^[1]; Karpeev, Dmitry A. ^[1]

Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA

Publication Date:: Thu Jan 01 00:00:00 EST 2009

Sponsoring Org.:: USDOE

OSTI Identifier:: 1197977

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Published Article

Journal Name:: Scientific Programming

Additional Journal Information:: Journal Name: Scientific Programming Journal Volume: 17 Journal Issue: 3; Journal ID: ISSN 1058-9244

Publisher:: Hindawi Publishing Corporation

Country of Publication:: Egypt

Language:: English

Citation Formats


                    Knepley, Matthew G., and Karpeev, Dmitry A. Mesh Algorithms for PDE with Sieve I: Mesh Distribution.  Egypt: N. p., 2009. 
Web.  doi:10.1155/2009/948613.

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                    Knepley, Matthew G., & Karpeev, Dmitry A. Mesh Algorithms for PDE with Sieve I: Mesh Distribution.  Egypt.  https://doi.org/10.1155/2009/948613

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                    Knepley, Matthew G., and Karpeev, Dmitry A. Thu .  
"Mesh Algorithms for PDE with Sieve I: Mesh Distribution".  Egypt.  https://doi.org/10.1155/2009/948613.

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@article{osti_1197977,

  title        = {Mesh Algorithms for PDE with Sieve I: Mesh Distribution},

  author       = {Knepley, Matthew G. and Karpeev, Dmitry A.},

  abstractNote = {We have developed a new programming framework, called Sieve, to support parallel numerical partial differential equation(s) (PDE) algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms acting on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode not only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated using the same fundamental mechanisms used to represent meshes. We present the complete description of an algorithm to encode a mesh partition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same algorithm. The use of a high level of abstraction within the Sieve leads to several benefits in terms of code reuse, simplicity, and extensibility. We discuss these benefits and compare our approach to other existing mesh libraries.},

  doi          = {10.1155/2009/948613},

  journal      = {Scientific Programming},

  number       = 3,

  volume       = 17,

  place        = {Egypt},

  year         = {Thu Jan 01 00:00:00 EST 2009},

  month        = {Thu Jan 01 00:00:00 EST 2009}

}

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