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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]
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Database: Engineering Source
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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]
ISSN:01678191
DOI:10.1016/j.parco.2023.103039