Skip to main content

Correction to: Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods

  • The original article was published in Advanced Modeling and Simulation in Engineering Sciences 2020 7:21

Correction to: Adv. Model. and Simul. in Eng. Sci. (2020) 7:21 https://doi.org/10.1186/s40323-020-00157-2

Following publication of the original article [1], the authors reported the errors in the equation and in the text.

The corrected text and equation are given below:

First, we evaluate the quality and reliability of the results obtained when using the three methods investigated in this section. In Fig. 22, the errors in the energy norm

$$\begin{aligned} ||e||_{{\mathrm {E}}(\Omega _{\mathrm {e}})} = \sqrt{\left| \dfrac{{\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}}, \textit{\textbf{u}}_{\mathrm {ref}})-{\mathcal {B}}(\textit{\textbf{u}}, \textit{\textbf{u}})}{{\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}}, \textit{\textbf{u}}_{\mathrm {ref}})} \right| } \cdot 100 [\%], \end{aligned}$$
(20)

for various input parameters are presented, which should be minimized by the FCM solution on the energy space\(E(\Omega _{\mathrm {e}})\) over the domain \(\Omega _{\mathrm {e}}\) [3, 33]. In Eq. (20), \(\textit{\textbf{u}}\) is the displacement field obtained by the FCM solution and \(\textit{\textbf{u}}_{\mathrm {ref}}\) is the reference solution, obtained by p-FEM using blending functions [113] for an exact geometry mapping, resulting in a strain energy of \(1/2 \cdot {\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}},\textit{\textbf{u}}_{\mathrm {ref}}) = 0.7021812127\) [31]. Besides investigating the global quality of the results based on \(||e||_{{\mathrm {E}}(\Omega _{\mathrm {e}})}\), we also evaluate the solution based on point-wise values of the stress-fields \(\sigma _{\mathrm {vM}}\) and \(\sigma _{\mathrm {yy}}\) along the diagonal \(\overline{AB}\) in Fig. 21, where \(\sigma _{\mathrm {vM}}\) is the von Mises stress and \(\sigma _{\mathrm {yy}}\) the stress in the y-direction.

The original article [1] has been updated.

Reference

  1. 1.

    Márton P, Fabian D, Sascha E. Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods. Adv Model Simul Eng Sci. 2020;7:21.

    Article  Google Scholar 

Download references

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Márton Petö.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Petö, M., Duvigneau, F. & Eisenträger, S. Correction to: Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods. Adv. Model. and Simul. in Eng. Sci. 7, 34 (2020). https://doi.org/10.1186/s40323-020-00165-2

Download citation