Contents

This folder contains the source code of the Matlab functions required to use the Continuous Empirical Cubature Method, as well as the functions for the Sequential Randomized Singular Value Decomposition from this paper . It also contains the scripts for launching some of the examples shown in the paper.

Example 1

Univariate polynomials (section 6.1)

To determine the quadrature rule in the problem whose results are displayed in both Figure 4 and Figure 5(see below), launch script EXAMPLES_1D/CECM_1D.m

Example 2

Multivariate polynomials 2D (section 6.2)

To determine the quadrature rule in the problem whose results are displayed in both Figure 4 and Figure 5(see below), launch script EXAMPLES_2D/CECM_2D.m

Example 3

Multivariate polynomials 3D (section 6.2)

To determine the cubature rule in the problem whose results are displayed in Figure 6 (see below), launch script: EXAMPLES_3D/CECM_3D.m

Example 4

Sequential Randomized Singular Value Decompositions

Determine SVD of the snapshot matrix obtained by sampling the function shown in section 6.3: (see below)

To compare the performance of both the standard SVD and the proposed SRSVD, launch script: EXAMPLE_partSVD/TestSeqSVD.m

The size of the resulting snapshot matrix is determined by the variable:

SIZE_SNAPSHOT_MATRIX_IN_GBYTES = 2;

To enable the SRSVD, set

UsePartitionedRandomizedAlgorithm =1;

and specify the number of partitions by the following variable:

NUMBER_ROW_MATRICES_PARTITION =8 ;

If the entire matrix does not fit into memory, each block may be saved into hard memory. This is controlled by the variable:

LimitGbytesMatricesSnapshots = 2 ;

Citation

If this repo has been useful for you, please consider citing us as

@article{HERNANDEZ2024116552,
title = {CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {418},
pages = {116552},
year = {2024},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2023.116552},
url = {https://www.sciencedirect.com/science/article/pii/S004578252300676X},
author = {J.A. Hernández and J.R. Bravo and S. {Ares de Parga}},
keywords = {Empirical Cubature Method, Hyperreduction, Reduced-order modeling, Singular Value Decomposition, Quadrature}
}