FastMat: A C++ library for multi-index array computations

Rodrigo R. Paz; Mario A. Storti; Lisandro D. Dalcin; Hugo G. Castro; Pablo A. Kler

doi:10.1016/j.advengsoft.2012.08.005

FastMat: A C++ library for multi-index array computations

Rodrigo R. Paz^*, Mario A. Storti, Lisandro D. Dalcin, Hugo G. Castro, Pablo A. Kler

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we introduce and describe an efficient thread-safe matrix library for computing element/cell residuals and Jacobians in Finite Elements and Finite Volume-like codes. The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations. The library implements an algorithm for choosing the optimal computation order when a product of several tensors is performed (i.e., the so-called 'multi-product' operation). Another key-point of the FastMat approach is that some computations (for instance the optimal order in the multi-product operation mentioned before) are computed in the first iteration of the loop body and stored in a cache object, so that in the second and subsequent executions these computations are retrieved from the cache, and then not recomputed. The library is open source and freely available within the multi-physics parallel FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can be exploited on distributed and shared memory architectures as well as in hybrid approaches. We studied the performance of the library in the context of typical FEM tensor contractions.

Original language	English (US)
Pages (from-to)	38-48
Number of pages	11
Journal	Advances in Engineering Software
Volume	54
DOIs	https://doi.org/10.1016/j.advengsoft.2012.08.005
State	Published - Dec 2012
Externally published	Yes

Bibliographical note

Funding Information:
This work has received financial support from European Research Council (ERC) (Spain, Advanced Grant, Real Time Computational Mechanics Techniques for Multi-Fluid Problems, Reference: ERC-2009-AdG, Dir: Dr. Sergio Idelsohn), Consejo Nacional de Investigaciones Cientı´ficas y Técnicas ( CONICET, Argentina , Grant PIP 5271/05 ), Universidad Nacional del Litoral (UNL, Argentina, Grants CAI+D 2009 65/334), Agencia Nacional de Promoción Cientı´fica y Tecnológica ( ANPCyT, Argentina , Grants PICT 01141/2007, PICT 2008–0270 “Jóvenes Investigadores”, PICT-1506/2006), Secretarı´a de Ciencia y Tecnologı´a de la Universidad Tecnológica Nacional, Facultad Regional Resistencia, Chaco ( UTN FRRe, Argentina , Grant PID 2012 25/L057 ) and Universidad Tecnológica Nacional, Facultad Regional San Nicolás (Buenos Aires).

Keywords

Finite element method
Finite volume method
Multi-index array library
Numerical analysis
Parallel computing
Thread-safe matrix library

ASJC Scopus subject areas

Software
General Engineering

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10.1016/j.advengsoft.2012.08.005

Cite this

@article{2fc45034cb8d43c4a5dc43f15f082b13,

title = "FastMat: A C++ library for multi-index array computations",

abstract = "In this paper we introduce and describe an efficient thread-safe matrix library for computing element/cell residuals and Jacobians in Finite Elements and Finite Volume-like codes. The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations. The library implements an algorithm for choosing the optimal computation order when a product of several tensors is performed (i.e., the so-called 'multi-product' operation). Another key-point of the FastMat approach is that some computations (for instance the optimal order in the multi-product operation mentioned before) are computed in the first iteration of the loop body and stored in a cache object, so that in the second and subsequent executions these computations are retrieved from the cache, and then not recomputed. The library is open source and freely available within the multi-physics parallel FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can be exploited on distributed and shared memory architectures as well as in hybrid approaches. We studied the performance of the library in the context of typical FEM tensor contractions.",

keywords = "Finite element method, Finite volume method, Multi-index array library, Numerical analysis, Parallel computing, Thread-safe matrix library",

author = "Paz, {Rodrigo R.} and Storti, {Mario A.} and Dalcin, {Lisandro D.} and Castro, {Hugo G.} and Kler, {Pablo A.}",

note = "Funding Information: This work has received financial support from European Research Council (ERC) (Spain, Advanced Grant, Real Time Computational Mechanics Techniques for Multi-Fluid Problems, Reference: ERC-2009-AdG, Dir: Dr. Sergio Idelsohn), Consejo Nacional de Investigaciones Cientı´ficas y T{\'e}cnicas ( CONICET, Argentina , Grant PIP 5271/05 ), Universidad Nacional del Litoral (UNL, Argentina, Grants CAI+D 2009 65/334), Agencia Nacional de Promoci{\'o}n Cientı´fica y Tecnol{\'o}gica ( ANPCyT, Argentina , Grants PICT 01141/2007, PICT 2008–0270 “J{\'o}venes Investigadores”, PICT-1506/2006), Secretarı´a de Ciencia y Tecnologı´a de la Universidad Tecnol{\'o}gica Nacional, Facultad Regional Resistencia, Chaco ( UTN FRRe, Argentina , Grant PID 2012 25/L057 ) and Universidad Tecnol{\'o}gica Nacional, Facultad Regional San Nicol{\'a}s (Buenos Aires). ",

year = "2012",

month = dec,

doi = "10.1016/j.advengsoft.2012.08.005",

language = "English (US)",

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AU - Paz, Rodrigo R.

AU - Storti, Mario A.

AU - Dalcin, Lisandro D.

AU - Castro, Hugo G.

AU - Kler, Pablo A.

N1 - Funding Information: This work has received financial support from European Research Council (ERC) (Spain, Advanced Grant, Real Time Computational Mechanics Techniques for Multi-Fluid Problems, Reference: ERC-2009-AdG, Dir: Dr. Sergio Idelsohn), Consejo Nacional de Investigaciones Cientı´ficas y Técnicas ( CONICET, Argentina , Grant PIP 5271/05 ), Universidad Nacional del Litoral (UNL, Argentina, Grants CAI+D 2009 65/334), Agencia Nacional de Promoción Cientı´fica y Tecnológica ( ANPCyT, Argentina , Grants PICT 01141/2007, PICT 2008–0270 “Jóvenes Investigadores”, PICT-1506/2006), Secretarı´a de Ciencia y Tecnologı´a de la Universidad Tecnológica Nacional, Facultad Regional Resistencia, Chaco ( UTN FRRe, Argentina , Grant PID 2012 25/L057 ) and Universidad Tecnológica Nacional, Facultad Regional San Nicolás (Buenos Aires).

PY - 2012/12

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N2 - In this paper we introduce and describe an efficient thread-safe matrix library for computing element/cell residuals and Jacobians in Finite Elements and Finite Volume-like codes. The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations. The library implements an algorithm for choosing the optimal computation order when a product of several tensors is performed (i.e., the so-called 'multi-product' operation). Another key-point of the FastMat approach is that some computations (for instance the optimal order in the multi-product operation mentioned before) are computed in the first iteration of the loop body and stored in a cache object, so that in the second and subsequent executions these computations are retrieved from the cache, and then not recomputed. The library is open source and freely available within the multi-physics parallel FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can be exploited on distributed and shared memory architectures as well as in hybrid approaches. We studied the performance of the library in the context of typical FEM tensor contractions.

AB - In this paper we introduce and describe an efficient thread-safe matrix library for computing element/cell residuals and Jacobians in Finite Elements and Finite Volume-like codes. The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations. The library implements an algorithm for choosing the optimal computation order when a product of several tensors is performed (i.e., the so-called 'multi-product' operation). Another key-point of the FastMat approach is that some computations (for instance the optimal order in the multi-product operation mentioned before) are computed in the first iteration of the loop body and stored in a cache object, so that in the second and subsequent executions these computations are retrieved from the cache, and then not recomputed. The library is open source and freely available within the multi-physics parallel FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can be exploited on distributed and shared memory architectures as well as in hybrid approaches. We studied the performance of the library in the context of typical FEM tensor contractions.

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KW - Finite volume method

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SN - 0965-9978

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JO - Advances in Engineering Software

JF - Advances in Engineering Software

ER -

FastMat: A C++ library for multi-index array computations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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