Nonlocal integral equation continuum models: nonstandard symmetric interaction neighborhoods and finite element discretizations
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia
SIAM, Society for Industrial and Applied Mathematics
[2024]
|
| Schriftenreihe: | Computational science and engineering
31 |
| Links: | https://doi.org/10.1137/1.9781611978056 https://doi.org/10.1137/1.9781611978056 https://doi.org/10.1137/1.9781611978056 https://doi.org/10.1137/1.9781611978056 |
| Abstract: | The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. |
| Umfang: | 1 Online-Ressource (x, 176 Seiten) Illustrationen, Diagramme |
| ISBN: | 9781611978056 9781611978049 |
| DOI: | 10.1137/1.9781611978056 |
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| 245 | 1 | 0 | |a Nonlocal integral equation continuum models |b nonstandard symmetric interaction neighborhoods and finite element discretizations |c Marta D’Elia ; Max Gunzburger (Florida State University, Tallahassee, Florida, and University of Texas, Austin, Texas, USA), Christian Vollmann (Tesla Automation (previously at Trier University), Prüm, Germany) |
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| 520 | 3 | |a The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. | |
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| id | DE-604.BV049879157 |
| illustrated | Illustrated |
| indexdate | 2025-02-12T11:00:47Z |
| institution | BVB |
| isbn | 9781611978056 9781611978049 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035218557 |
| oclc_num | 1466913808 |
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| owner | DE-29 DE-91 DE-BY-TUM DE-20 DE-83 |
| owner_facet | DE-29 DE-91 DE-BY-TUM DE-20 DE-83 |
| physical | 1 Online-Ressource (x, 176 Seiten) Illustrationen, Diagramme |
| psigel | ZDB-72-SIA ZDB-72-SIA TUM_Paketkauf_2024 ZDB-72-SIA UBW_Paketkauf ZDB-72-SIA UER_Paketkauf_2024 |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | SIAM, Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Computational science and engineering |
| series2 | Computational science and engineering |
| spellingShingle | D'Elia, Marta Gunzburger, Max D. Vollmann, Christian Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations Computational science and engineering |
| title | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations |
| title_auth | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations |
| title_exact_search | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations |
| title_full | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations Marta D’Elia ; Max Gunzburger (Florida State University, Tallahassee, Florida, and University of Texas, Austin, Texas, USA), Christian Vollmann (Tesla Automation (previously at Trier University), Prüm, Germany) |
| title_fullStr | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations Marta D’Elia ; Max Gunzburger (Florida State University, Tallahassee, Florida, and University of Texas, Austin, Texas, USA), Christian Vollmann (Tesla Automation (previously at Trier University), Prüm, Germany) |
| title_full_unstemmed | Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations Marta D’Elia ; Max Gunzburger (Florida State University, Tallahassee, Florida, and University of Texas, Austin, Texas, USA), Christian Vollmann (Tesla Automation (previously at Trier University), Prüm, Germany) |
| title_short | Nonlocal integral equation continuum models |
| title_sort | nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations |
| title_sub | nonstandard symmetric interaction neighborhoods and finite element discretizations |
| url | https://doi.org/10.1137/1.9781611978056 |
| volume_link | (DE-604)BV040633113 |
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