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A flexible sparse matrix data format and parallel algorithms for the assembly of finite element matrices on shared memory systems.

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Title: A flexible sparse matrix data format and parallel algorithms for the assembly of finite element matrices on shared memory systems.
Authors: Sky, Adam1 (AUTHOR) adam.sky@tu-dortmund.de, Polindara, César2 (AUTHOR) cesar.polindara-lopez@uni-due.de, Muench, Ingo1 (AUTHOR) ingo.muench@tu-dortmund.de, Birk, Carolin2 (AUTHOR) statik-ftw@uni-due.de
Source: Parallel Computing. Sep2023, Vol. 117, pN.PAG-N.PAG. 1p.
Subjects: Sparse matrices, Matrices (Mathematics), Finite element method, Data structures, Degrees of freedom
Abstract: Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global stiffness matrix, which is commonly sparse. In this paper we focus on the assembly process of the global stiffness matrix and explore different algorithms and their efficiency on shared memory systems using C++. A key aspect of our investigation is the use of atomic synchronization primitives for the derivation of data-race free algorithms and data structures. Furthermore, we propose a new flexible storage format for sparse matrices and compare its performance with the compressed row storage format using abstract benchmarks based on common characteristics of finite element problems. • A new sparse matrix format, Compressed-Rows-Aligned-Columns (CRAC), ideal for hp-FEM. • Parallelization of the assembly procedure using atomic synchronization. • Local-to-global degrees of freedom maps for vectorization. • Integration of spin locks into CSR and CRAC without increase in storage requirements. • A comparative study of the novel methods. [ABSTRACT FROM AUTHOR]
Copyright of Parallel Computing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 171587171
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  Data: A flexible sparse matrix data format and parallel algorithms for the assembly of finite element matrices on shared memory systems.
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  Data: <searchLink fieldCode="JN" term="%22Parallel+Computing%22">Parallel Computing</searchLink>. Sep2023, Vol. 117, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Data+structures%22">Data structures</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink>
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  Data: Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global stiffness matrix, which is commonly sparse. In this paper we focus on the assembly process of the global stiffness matrix and explore different algorithms and their efficiency on shared memory systems using C++. A key aspect of our investigation is the use of atomic synchronization primitives for the derivation of data-race free algorithms and data structures. Furthermore, we propose a new flexible storage format for sparse matrices and compare its performance with the compressed row storage format using abstract benchmarks based on common characteristics of finite element problems. • A new sparse matrix format, Compressed-Rows-Aligned-Columns (CRAC), ideal for hp-FEM. • Parallelization of the assembly procedure using atomic synchronization. • Local-to-global degrees of freedom maps for vectorization. • Integration of spin locks into CSR and CRAC without increase in storage requirements. • A comparative study of the novel methods. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Parallel Computing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.parco.2023.103039
    Languages:
      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Sparse matrices
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Data structures
        Type: general
      – SubjectFull: Degrees of freedom
        Type: general
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      – TitleFull: A flexible sparse matrix data format and parallel algorithms for the assembly of finite element matrices on shared memory systems.
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            NameFull: Sky, Adam
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            NameFull: Polindara, César
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            NameFull: Muench, Ingo
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          Dates:
            – D: 01
              M: 09
              Text: Sep2023
              Type: published
              Y: 2023
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              Value: 117
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            – TitleFull: Parallel Computing
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