---
_id: '4609'
author:
- first_name: R. H. W.
  full_name: Hoppe, R. H. W.
  last_name: Hoppe
- first_name: Svetozara
  full_name: Petrova, Svetozara
  id: '201871'
  last_name: Petrova
citation:
  alphadin: '<span style="font-variant:small-caps;">Hoppe, R. H. W.</span> ; <span
    style="font-variant:small-caps;">Petrova, Svetozara</span>: Multi-scale Method
    for the Crack Problem in Microstructural Materials. In: <i>Computational Methods
    in Applied Mathematics</i> Bd. 10, Walter de Gruyter GmbH (2010), Nr. 1, S. 69–86'
  ama: Hoppe RHW, Petrova S. Multi-scale Method for the Crack Problem in Microstructural
    Materials. <i>Computational Methods in Applied Mathematics</i>. 2010;10(1):69-86.
    doi:<a href="https://doi.org/10.2478/cmam-2010-0003">10.2478/cmam-2010-0003</a>
  apa: Hoppe, R. H. W., &#38; Petrova, S. (2010). Multi-scale Method for the Crack
    Problem in Microstructural Materials. <i>Computational Methods in Applied Mathematics</i>,
    <i>10</i>(1), 69–86. <a href="https://doi.org/10.2478/cmam-2010-0003">https://doi.org/10.2478/cmam-2010-0003</a>
  bibtex: '@article{Hoppe_Petrova_2010, title={Multi-scale Method for the Crack Problem
    in Microstructural Materials}, volume={10}, DOI={<a href="https://doi.org/10.2478/cmam-2010-0003">10.2478/cmam-2010-0003</a>},
    number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
    de Gruyter GmbH}, author={Hoppe, R. H. W. and Petrova, Svetozara}, year={2010},
    pages={69–86} }'
  chicago: 'Hoppe, R. H. W., and Svetozara Petrova. “Multi-Scale Method for the Crack
    Problem in Microstructural Materials.” <i>Computational Methods in Applied Mathematics</i>
    10, no. 1 (2010): 69–86. <a href="https://doi.org/10.2478/cmam-2010-0003">https://doi.org/10.2478/cmam-2010-0003</a>.'
  ieee: R. H. W. Hoppe and S. Petrova, “Multi-scale Method for the Crack Problem in
    Microstructural Materials,” <i>Computational Methods in Applied Mathematics</i>,
    vol. 10, no. 1, pp. 69–86, 2010.
  mla: Hoppe, R. H. W., and Svetozara Petrova. “Multi-Scale Method for the Crack Problem
    in Microstructural Materials.” <i>Computational Methods in Applied Mathematics</i>,
    vol. 10, no. 1, Walter de Gruyter GmbH, 2010, pp. 69–86, doi:<a href="https://doi.org/10.2478/cmam-2010-0003">10.2478/cmam-2010-0003</a>.
  short: R.H.W. Hoppe, S. Petrova, Computational Methods in Applied Mathematics 10
    (2010) 69–86.
date_created: 2024-05-29T08:58:54Z
date_updated: 2026-03-17T15:29:03Z
doi: 10.2478/cmam-2010-0003
intvolume: '        10'
issue: '1'
language:
- iso: eng
page: 69-86
project:
- _id: f432a2ee-bceb-11ed-a251-a83585c5074d
  name: Institute for Data Science Solutions
publication: Computational Methods in Applied Mathematics
publication_identifier:
  eissn:
  - 1609-9389
  issn:
  - 1609-4840
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Multi-scale Method for the Crack Problem in Microstructural Materials
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: '220548'
volume: 10
year: '2010'
...
---
_id: '4551'
author:
- first_name: Ronald H. W.
  full_name: Hoppe, Ronald H. W.
  last_name: Hoppe
- first_name: Svetozara
  full_name: Petrova, Svetozara
  id: '201871'
  last_name: Petrova
citation:
  alphadin: '<span style="font-variant:small-caps;">Hoppe, Ronald H. W.</span> ; <span
    style="font-variant:small-caps;">Petrova, Svetozara</span>: Applications of Primal-dual
    Interior Methods in Structural Optimization. In: <i>Computational Methods in Applied
    Mathematics</i> Bd. 3, Walter de Gruyter GmbH (2003), Nr. 1, S. 159–176'
  ama: Hoppe RHW, Petrova S. Applications of Primal-dual Interior Methods in Structural
    Optimization. <i>Computational Methods in Applied Mathematics</i>. 2003;3(1):159-176.
    doi:<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>
  apa: Hoppe, R. H. W., &#38; Petrova, S. (2003). Applications of Primal-dual Interior
    Methods in Structural Optimization. <i>Computational Methods in Applied Mathematics</i>,
    <i>3</i>(1), 159–176. <a href="https://doi.org/10.2478/cmam-2003-0011">https://doi.org/10.2478/cmam-2003-0011</a>
  bibtex: '@article{Hoppe_Petrova_2003, title={Applications of Primal-dual Interior
    Methods in Structural Optimization}, volume={3}, DOI={<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>},
    number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
    de Gruyter GmbH}, author={Hoppe, Ronald H. W. and Petrova, Svetozara}, year={2003},
    pages={159–176} }'
  chicago: 'Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual
    Interior Methods in Structural Optimization.” <i>Computational Methods in Applied
    Mathematics</i> 3, no. 1 (2003): 159–76. <a href="https://doi.org/10.2478/cmam-2003-0011">https://doi.org/10.2478/cmam-2003-0011</a>.'
  ieee: R. H. W. Hoppe and S. Petrova, “Applications of Primal-dual Interior Methods
    in Structural Optimization,” <i>Computational Methods in Applied Mathematics</i>,
    vol. 3, no. 1, pp. 159–176, 2003.
  mla: Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual Interior
    Methods in Structural Optimization.” <i>Computational Methods in Applied Mathematics</i>,
    vol. 3, no. 1, Walter de Gruyter GmbH, 2003, pp. 159–76, doi:<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>.
  short: R.H.W. Hoppe, S. Petrova, Computational Methods in Applied Mathematics 3
    (2003) 159–176.
date_created: 2024-04-25T13:14:17Z
date_updated: 2026-03-17T15:29:02Z
doi: 10.2478/cmam-2003-0011
intvolume: '         3'
issue: '1'
keyword:
- structural optimization
- nonlinear programming
- primal-dual interior-point methods
- eddy current equations
- elasticity equations
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 159-176
project:
- _id: f432a2ee-bceb-11ed-a251-a83585c5074d
  name: Institute for Data Science Solutions
publication: Computational Methods in Applied Mathematics
publication_identifier:
  eissn:
  - 1609-9389
  issn:
  - 1609-4840
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Applications of Primal-dual Interior Methods in Structural Optimization
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: '220548'
volume: 3
year: '2003'
...