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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00392419" target="_blank" >RIV/67985840:_____/13:00392419 - isvavai.cz</a>
Result on the web
<a href="http://www.math.cas.cz/am2013/proceedings/contributions/vejchodsky.pdf" target="_blank" >http://www.math.cas.cz/am2013/proceedings/contributions/vejchodsky.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A direct solver for finite element matrices requiring O(N log N) memory places
Original language 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 intriangular 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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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