0640710 20260213094737.720251103235959.9 105019923693 001608319300003 10.1016/j.amc.2025.129778 19 s. P cav_un_epca*02561600096-3003513Elsevier Abstract linear algebra Code vectorization Finite element method Tensor structures Triangular meshes cav_un_auth*0459832 Moskovka Alexej UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0319984 Rahman T. NO cav_un_auth*0292941 Valdman Jan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0496135 Vatne J. E. NO https://library.utia.cas.cz/separaty/2025/MTR/valdman-0640710.pdf GA23-04766S GA ČR CZ cav_un_auth*0459138 When writing high-performance code for numerical computations in a scripting language such as MATLAB, it is crucial to vectorize operations within large for-loops. However, this vectorization process often obscures the original mathematical structure, making the code less readable. This issue is particularly pronounced in finite element method (FEM) implementations, despite the inherently structured nature of FEM. A practical remedy is to decouple the vectorization layer from the mathematical logic of the code. This can be effectively achieved by building on top of already-vectorized basic linear algebra subprograms. Over the past 15 years, this idea has been applied in a series of works, resulting in fast, structured, and maintainable code. In this paper, we present a vectorized basic linear algebra package and introduce a formalism based on multilinear algebra to define and explain its functions. We also incorporate MATLAB’s recently introduced page-wise functions to enhance expressiveness. We provide examples such as computing normal vectors, volumes, and finite element assembly to demonstrate the clarity and efficiency of the approach. The resulting codes closely follow mathematical abstraction, facilitate reuse and extension, and support rapid development and prototyping by scientists, engineers, and students. 2027 BA WOS 10000 10100 10101 RVO:67985556 https://hdl.handle.net/11104/0371072 S 129778 C MATHEMATICS.APPLIED 3.2 0.7 9 0.02526 0.838 33342 182 0.89 35.95 3.79 8064 Q1 3.200 534 Q1 96.9 2.08 Q1 96.9 2026 105019923693 SCOPUS PUBMED 001608319300003 WOS cav_un_epca*0256160 Applied Mathematics and Computation Roč. 513 č. 1 2026 0096-3003 1873-5649 Elsevier