| 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 15-17, 2013 |
| Issue:
|
2013 |
| Year:
|
|
| Pages:
|
225-239 |
| . |
| 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 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. (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:
|
2017-02-14T09:19:47Z |
| Last updated:
|
2017-03-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702950 |
| . |
