# A direct solver for finite element matrices requiring $O(NlogN)$ memory places

- Applications of Mathematics 2013, Publisher: Institute of Mathematics AS CR(Prague), page 225-239

## Access Full Article

top## Abstract

top## How to cite

topVejchodský, Tomáš. "A direct solver for finite element matrices requiring $O(N \log N)$ memory places." Applications of Mathematics 2013. Prague: Institute of Mathematics AS CR, 2013. 225-239. <http://eudml.org/doc/287849>.

@inProceedings{Vejchodský2013,

abstract = {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.},

author = {Vejchodský, Tomáš},

booktitle = {Applications of Mathematics 2013},

keywords = {sparse direct solver; hierarchical condensation; finite element method; sparse matrices; algorithm},

location = {Prague},

pages = {225-239},

publisher = {Institute of Mathematics AS CR},

title = {A direct solver for finite element matrices requiring $O(N \log N)$ memory places},

url = {http://eudml.org/doc/287849},

year = {2013},

}

TY - CLSWK

AU - Vejchodský, Tomáš

TI - A direct solver for finite element matrices requiring $O(N \log N)$ memory places

T2 - Applications of Mathematics 2013

PY - 2013

CY - Prague

PB - Institute of Mathematics AS CR

SP - 225

EP - 239

AB - 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.

KW - sparse direct solver; hierarchical condensation; finite element method; sparse matrices; algorithm

UR - http://eudml.org/doc/287849

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.