Title:

A direct solver for finite element matrices requiring $O(N \log N)$ memory places (English) 
Author:

Vejchodský, Tomáš 
Language:

English 
Journal:

Applications of Mathematics 2013 
Volume:

Proceedings. Prague, May 1517, 2013 
Issue:

2013 
Year:


Pages:

225239 
. 
Category:

math 
. 
Summary:

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 higherorder 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. (English) 
Keyword:

sparse direct solver 
Keyword:

hierarchical condensation 
Keyword:

finite element method 
Keyword:

sparse matrices 
Keyword:

algorithm 
MSC:

65F05 
MSC:

65F50 
MSC:

65N30 
idZBL:

Zbl 1340.65038 
idMR:

MR3204447 
. 
Date available:

20170214T09:19:47Z 
Last updated:

20170320 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702950 
. 