Electromagnetic theory and computation: a topological approach
Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, al...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | Mathematical Sciences Research Institute publications
48 |
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| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book, first published in 2004, attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (ix, 278 pages) |
| ISBN: | 9780511756337 |
| DOI: | 10.1017/CBO9780511756337 |
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| 520 | |a Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book, first published in 2004, attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents | ||
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Datensatz im Suchindex
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| author | Gross, Paul W. 1967- |
| author_facet | Gross, Paul W. 1967- |
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| contents | 1. From vector calculus to algebraic topology -- 2. Quasistatic electromagnetic fields -- 3. Duality theorems for manifolds with boundary -- 4. The finite element method and data structures -- 5. Computing eddy currents on thin conductors with scalar potentials -- 6. An algorithm to make cuts for magnetic scalar potentials -- 7. A paradigm problem -- Mathematical appendix: Manifolds, differential forms, cohomology, Riemannian structures |
| ctrlnum | (ZDB-20-CBO)CR9780511756337 (OCoLC)699188825 (DE-599)BVBBV043942265 |
| dewey-full | 530.14/1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/1 |
| dewey-search | 530.14/1 |
| dewey-sort | 3530.14 11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1017/CBO9780511756337 |
| format | Electronic eBook |
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| spelling | Gross, Paul W. 1967- Verfasser aut Electromagnetic theory and computation a topological approach Paul W. Gross, P. Robert Kotiuga Electromagnetic Theory & Computation Cambridge Cambridge University Press 2004 1 online resource (ix, 278 pages) txt rdacontent c rdamedia cr rdacarrier Mathematical Sciences Research Institute publications 48 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. From vector calculus to algebraic topology -- 2. Quasistatic electromagnetic fields -- 3. Duality theorems for manifolds with boundary -- 4. The finite element method and data structures -- 5. Computing eddy currents on thin conductors with scalar potentials -- 6. An algorithm to make cuts for magnetic scalar potentials -- 7. A paradigm problem -- Mathematical appendix: Manifolds, differential forms, cohomology, Riemannian structures Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book, first published in 2004, attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents Electromagnetic theory Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Elektromagnetisches Feld (DE-588)4014305-3 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content Elektromagnetisches Feld (DE-588)4014305-3 s Randwertproblem (DE-588)4048395-2 s Algebraische Topologie (DE-588)4120861-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Kotiuga, P. Robert 1958- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-17523-4 Erscheint auch als Druckausgabe 978-0-521-80160-7 https://doi.org/10.1017/CBO9780511756337 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Gross, Paul W. 1967- Electromagnetic theory and computation a topological approach 1. From vector calculus to algebraic topology -- 2. Quasistatic electromagnetic fields -- 3. Duality theorems for manifolds with boundary -- 4. The finite element method and data structures -- 5. Computing eddy currents on thin conductors with scalar potentials -- 6. An algorithm to make cuts for magnetic scalar potentials -- 7. A paradigm problem -- Mathematical appendix: Manifolds, differential forms, cohomology, Riemannian structures Electromagnetic theory Numerisches Verfahren (DE-588)4128130-5 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd Randwertproblem (DE-588)4048395-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4014305-3 (DE-588)4048395-2 (DE-588)4120861-4 (DE-588)4006432-3 |
| title | Electromagnetic theory and computation a topological approach |
| title_alt | Electromagnetic Theory & Computation |
| title_auth | Electromagnetic theory and computation a topological approach |
| title_exact_search | Electromagnetic theory and computation a topological approach |
| title_full | Electromagnetic theory and computation a topological approach Paul W. Gross, P. Robert Kotiuga |
| title_fullStr | Electromagnetic theory and computation a topological approach Paul W. Gross, P. Robert Kotiuga |
| title_full_unstemmed | Electromagnetic theory and computation a topological approach Paul W. Gross, P. Robert Kotiuga |
| title_short | Electromagnetic theory and computation |
| title_sort | electromagnetic theory and computation a topological approach |
| title_sub | a topological approach |
| topic | Electromagnetic theory Numerisches Verfahren (DE-588)4128130-5 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd Randwertproblem (DE-588)4048395-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Electromagnetic theory Numerisches Verfahren Elektromagnetisches Feld Randwertproblem Algebraische Topologie Bibliografie |
| url | https://doi.org/10.1017/CBO9780511756337 |
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