Customization of finite elements for low dispersion error through grid dispersion analysis requires a symbolic expansion of a determinant of a representative dynamic stiffness matrix. Such an expansion turns out to be a bottleneck for many practical cases with the size of the representative matrix greater than eight or ten even if the modern computer algebra systems are applied. In this contribution, we propose an alternative approach for low-dispersion customization that avoids explicit determinant expansion. This approach reduces the customization problem to a series of quadratic programming problems and consist of two main steps. Firstly, the customization problem is reformulated as a rank minimization problem for the representative dynamic stiffness matrix evaluated at several discrete pairs of wavenumbers and frequencies. Secondly, the rank minimization problem is solved approximately via log-det heuristic. Examples for customization of reciprocal mass matrices illustrate capabilities of the proposed approach.
%0 Journal Article
%1 tkachuk2020customization
%A Tkachuk, Anton
%D 2020
%J International Journal for Numerical Methods in Engineering
%K DYN ibb from:maltevonscheven article Tetra
%P 690-711
%R 10.1002/nme.6240
%T Customization of reciprocal mass matrices via log-det heuristic
%V 121
%X Customization of finite elements for low dispersion error through grid dispersion analysis requires a symbolic expansion of a determinant of a representative dynamic stiffness matrix. Such an expansion turns out to be a bottleneck for many practical cases with the size of the representative matrix greater than eight or ten even if the modern computer algebra systems are applied. In this contribution, we propose an alternative approach for low-dispersion customization that avoids explicit determinant expansion. This approach reduces the customization problem to a series of quadratic programming problems and consist of two main steps. Firstly, the customization problem is reformulated as a rank minimization problem for the representative dynamic stiffness matrix evaluated at several discrete pairs of wavenumbers and frequencies. Secondly, the rank minimization problem is solved approximately via log-det heuristic. Examples for customization of reciprocal mass matrices illustrate capabilities of the proposed approach.
@article{tkachuk2020customization,
abstract = {Customization of finite elements for low dispersion error through grid dispersion analysis requires a symbolic expansion of a determinant of a representative dynamic stiffness matrix. Such an expansion turns out to be a bottleneck for many practical cases with the size of the representative matrix greater than eight or ten even if the modern computer algebra systems are applied. In this contribution, we propose an alternative approach for low-dispersion customization that avoids explicit determinant expansion. This approach reduces the customization problem to a series of quadratic programming problems and consist of two main steps. Firstly, the customization problem is reformulated as a rank minimization problem for the representative dynamic stiffness matrix evaluated at several discrete pairs of wavenumbers and frequencies. Secondly, the rank minimization problem is solved approximately via log-det heuristic. Examples for customization of reciprocal mass matrices illustrate capabilities of the proposed approach.},
added-at = {2021-03-09T13:41:01.000+0100},
author = {Tkachuk, Anton},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/22fcb72b3e9daeed177f3c87d82904c9c/ibb-publication},
doi = {10.1002/nme.6240},
interhash = {7c251a5c99133e62a7c9d6bf1e5eb558},
intrahash = {2fcb72b3e9daeed177f3c87d82904c9c},
journal = {International Journal for Numerical Methods in Engineering},
keywords = {DYN ibb from:maltevonscheven article Tetra},
pages = {690-711},
timestamp = {2021-03-09T12:41:01.000+0100},
title = {Customization of reciprocal mass matrices via log-det heuristic},
volume = { 121},
year = 2020
}
