Original title: A direct solver for finite element matrices requiring O(N log N) memory places
Authors: Vejchodský, Tomáš
Document type: Papers
Conference/Event: Applications of Mathematics 2013, Prague (CZ), 2013-05-15 / 2013-05-18
Year: 2013
Language: eng
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.
Keywords: efficient; stiffness matrix
Host item entry: Applications of Mathematics 2013, ISBN 978-80-85823-61-5

Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://www.math.cas.cz/~am2013/proceedings/contributions/vejchodsky.pdf
Original record: http://hdl.handle.net/11104/0221294

Permalink: http://www.nusl.cz/ntk/nusl-154174


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