0392419 - MÚ 2014 RIV CZ eng C - Conference Paper (international conference)
Vejchodský, Tomáš
A direct solver for finite element matrices requiring O(N log N) memory places.
Applications of Mathematics 2013. Praha: Matematický ústav AV ČR, v.v.i, 2013 - (Brandts, S.; Korotov, S.; Křížek, M.; Šístek, J.; Vejchodský, T.), s. 225-239. ISBN 978-80-85823-61-5.
[Applications of Mathematics 2013. Prague (CZ), 15.05.2013-18.05.2013]
Institutional support: RVO:67985840
Keywords : stiffness matrix * efficient
Subject RIV: BA - General Mathematics
http://www.math.cas.cz/~am2013/proceedings/contributions/vejchodsky.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0221294