About: A direct solver for finite element matrices requiring O(N log N) memory places

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.math.cas.cz/am2013/proceedings/contributions/vejchodsky.pdf
Description	We present a method that in certain sense stores the inverse of the stiffness matrix in O(N log N) memory places, where N is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires O(N^(3/2)) arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with O(N log N) operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains, but it can be generalized to higher-order elements, variety of problems, and general domains. The method is based on a special hierarchical enumeration of vertices and on a hierarchical elimination of suitable degrees of freedom. Therefore, we call it hierarchical condensation of degrees of freedom. We present a method that in certain sense stores the inverse of the stiffness matrix in O(N log N) memory places, where N is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires O(N^(3/2)) arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with O(N log N) operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains, but it can be generalized to higher-order elements, variety of problems, and general domains. The method is based on a special hierarchical enumeration of vertices and on a hierarchical elimination of suitable degrees of freedom. Therefore, we call it hierarchical condensation of degrees of freedom. (en)
Title	A direct solver for finite element matrices requiring O(N log N) memory places A direct solver for finite element matrices requiring O(N log N) memory places (en)
skos:prefLabel	A direct solver for finite element matrices requiring O(N log N) memory places A direct solver for finite element matrices requiring O(N log N) memory places (en)
skos:notation	RIV/67985840:_____/13:00392419!RIV14-AV0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Vejchodský, Tomáš
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	58587
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00392419
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	stiffness matrix; efficient (en)
http://linked.open.../riv/klicoveSlovo	stiffness matrix efficient
http://linked.open...ontrolniKodProRIV	[BD5F9BFE6F2C]
http://linked.open...v/mistoKonaniAkce	Prague
http://linked.open...i/riv/mistoVydani	Praha
http://linked.open...i/riv/nazevZdroje	Applications of Mathematics 2013
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Vejchodský, Tomáš
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-05-15 (xsd:date)
number of pages	15 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Matematický ústav AV ČR, v.v.i
https://schema.org/isbn	978-80-85823-61-5

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