Tensors.jl — Tensor Computations in Julia
Journal article, 2019

Tensors.jl is a Julia package that provides efficient computations with symmetric and non-symmetric tensors. The focus is on the kind of tensors commonly used in e.g. continuum mechanics and fluid dynamics. Exploiting Julia’s ability to overload Unicode infix operators and using Unicode in identifiers, implemented tensor expressions commonly look very similar to their mathematical writing. This possibly reduces the number of bugs in implementations. Operations on tensors are often compiled into the minimum assembly instructions required, and, when beneficial, SIMD-instructions are used. Computations involving symmetric tensors take symmetry into account to reduce computational cost. Automatic differentiation is supported, which means that most functions written in pure Julia can be efficiently differentiated without having to implement the derivative by hand. The package is useful in applications where efficient tensor operations are required, e.g. in the Finite Element Method.

fluid dynamics

constitutive modeling


continuum mechanics

finite element method


Kristoffer Carlsson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Fredrik Ekre

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Journal of Open Research Software

20499647 (eISSN)

Vol. 7 1 7

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Subject Categories

Applied Mechanics

Computational Mathematics

Software Engineering



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