Nonlocal integral equation continuum models: nonstandard symmetric interaction neighborhoods and finite element discretizations
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 lat...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, PA
SIAM, Society for Industrial and Applied Mathematics
[2024]
|
| Schriftenreihe: | Computational science and engineering
31 |
| Online-Zugang: | DE-91 DE-29 Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 Online-Ressource (x, 176 Seiten) Illustrationen, Diagramme |
| ISBN: | 9781611978056 |
| DOI: | 10.1137/1.9781611978056 |
Internformat
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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 (Pasteur Labs and Stanford University (previously at Sandia National Laboratories), Stanford, California, USA), 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. | |
| 700 | 1 | |a Gunzburger, Max D. |e Verfasser |0 (DE-588)1216653410 |4 aut | |
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| id | DE-604.BV049879157 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T13:12:13Z |
| institution | BVB |
| isbn | 9781611978056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035218557 |
| oclc_num | 1466913808 |
| open_access_boolean | |
| owner | DE-29 DE-91 DE-BY-TUM |
| owner_facet | DE-29 DE-91 DE-BY-TUM |
| physical | 1 Online-Ressource (x, 176 Seiten) Illustrationen, Diagramme |
| psigel | ZDB-72-SIA ZDB-72-SIA TUM_Paketkauf_2024 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 |
| spelling | D'Elia, Marta Verfasser (DE-588)1216653089 aut Nonlocal integral equation continuum models nonstandard symmetric interaction neighborhoods and finite element discretizations Marta D’Elia (Pasteur Labs and Stanford University (previously at Sandia National Laboratories), Stanford, California, USA), Max Gunzburger (Florida State University, Tallahassee, Florida, and University of Texas, Austin, Texas, USA), Christian Vollmann (Tesla Automation (previously at Trier University), Prüm, Germany) Philadelphia, PA SIAM, Society for Industrial and Applied Mathematics [2024] 1 Online-Ressource (x, 176 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Computational science and engineering 31 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. Gunzburger, Max D. Verfasser (DE-588)1216653410 aut Vollmann, Christian Verfasser (DE-588)119366148X aut Erscheint auch als Druck-Ausgabe 978-1-61197-804-9 Computational science and engineering 31 (DE-604)BV040633113 31 https://doi.org/10.1137/1.9781611978056 Verlag URL des Erstveröffentlichers Volltext |
| 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 (Pasteur Labs and Stanford University (previously at Sandia National Laboratories), Stanford, California, USA), 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 (Pasteur Labs and Stanford University (previously at Sandia National Laboratories), Stanford, California, USA), 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 (Pasteur Labs and Stanford University (previously at Sandia National Laboratories), Stanford, California, USA), 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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