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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F13%3A00392419%21RIV14-AV0-67985840
rdf:type
n13:Vysledek skos:Concept
rdfs:seeAlso
http://www.math.cas.cz/am2013/proceedings/contributions/vejchodsky.pdf
dcterms: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.
dcterms: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
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
skos:notation
RIV/67985840:_____/13:00392419!RIV14-AV0-67985840
n13:predkladatel
n14:ico%3A67985840
n3:aktivita
n12:I
n3:aktivity
I
n3:dodaniDat
n9:2014
n3:domaciTvurceVysledku
n11:7004974
n3:druhVysledku
n20:D
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n8:predkladatel
n3:idSjednocenehoVysledku
58587
n3:idVysledku
RIV/67985840:_____/13:00392419
n3:jazykVysledku
n19:eng
n3:klicovaSlova
stiffness matrix; efficient
n3:klicoveSlovo
n5:efficient n5:stiffness%20matrix
n3:kontrolniKodProRIV
[BD5F9BFE6F2C]
n3:mistoKonaniAkce
Prague
n3:mistoVydani
Praha
n3:nazevZdroje
Applications of Mathematics 2013
n3:obor
n10:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:rokUplatneniVysledku
n9:2013
n3:tvurceVysledku
Vejchodský, Tomáš
n3:typAkce
n16:WRD
n3:zahajeniAkce
2013-05-15+02:00
s:numberOfPages
15
n21:hasPublisher
Matematický ústav AV ČR, v.v.i
n18:isbn
978-80-85823-61-5