Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

2013
journal article
article
30
cris.lastimport.wos2024-04-09T22:58:59Z
dc.abstract.enThe issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to competing ones, allowing to handle problems not addressable before. In particular, when generators are employed in the physical modeling of magneto-quasistatic problems, this algorithm solves one of the most long-lasting problems in low-frequency computational electromagnetics. In this case, the effectiveness of the algorithm and its ease of implementation may be even improved by introducing the novel concept of lazy cohomology generators.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowejpl
dc.contributor.authorDłotko, Paweł - 106866 pl
dc.contributor.authorSpecogna, Rubenpl
dc.date.accessioned2014-07-15T05:33:30Z
dc.date.available2014-07-15T05:33:30Z
dc.date.issued2013pl
dc.description.number10pl
dc.description.physical2257-2266pl
dc.description.volume184pl
dc.identifier.doi10.1016/j.cpc.2013.05.006pl
dc.identifier.issn0010-4655pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/29
dc.languageengpl
dc.language.containerengpl
dc.rights.licencebez licencji
dc.subject.enPhysics inspired algorithmspl
dc.subject.enAlgebraic topologypl
dc.subject.en(co)homologypl
dc.subject.enFirst De Rham cohomology group generatorspl
dc.subject.enDiscrete Hodge decompositionpl
dc.subject.enComputational physicspl
dc.subject.enMagneto-quasistaticspl
dc.subject.enEddy-currentspl
dc.subtypeArticlepl
dc.titlePhysics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundarypl
dc.title.journalComputer Physics Communicationspl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-09T22:58:59Z
dc.abstract.enpl
The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to competing ones, allowing to handle problems not addressable before. In particular, when generators are employed in the physical modeling of magneto-quasistatic problems, this algorithm solves one of the most long-lasting problems in low-frequency computational electromagnetics. In this case, the effectiveness of the algorithm and its ease of implementation may be even improved by introducing the novel concept of lazy cohomology generators.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.authorpl
Dłotko, Paweł - 106866
dc.contributor.authorpl
Specogna, Ruben
dc.date.accessioned
2014-07-15T05:33:30Z
dc.date.available
2014-07-15T05:33:30Z
dc.date.issuedpl
2013
dc.description.numberpl
10
dc.description.physicalpl
2257-2266
dc.description.volumepl
184
dc.identifier.doipl
10.1016/j.cpc.2013.05.006
dc.identifier.issnpl
0010-4655
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/29
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights.licence
bez licencji
dc.subject.enpl
Physics inspired algorithms
dc.subject.enpl
Algebraic topology
dc.subject.enpl
(co)homology
dc.subject.enpl
First De Rham cohomology group generators
dc.subject.enpl
Discrete Hodge decomposition
dc.subject.enpl
Computational physics
dc.subject.enpl
Magneto-quasistatics
dc.subject.enpl
Eddy-currents
dc.subtypepl
Article
dc.titlepl
Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary
dc.title.journalpl
Computer Physics Communications
dc.typepl
JournalArticle
dspace.entity.type
Publication

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