## Abstract

The structure of finite element matrices in congruent subdomains is studied. When a domain has a form of symmetries and/or periodicities, it is decomposed into a union of congruent subdomains, each of which is an image of a reference subdomain by an affine transformation with an orthogonal matrix whose components consist of -1, 0, and 1. Stiffness matrices in subdomains are expressed by one in the reference subdomain with renumbering indices and changing signs corresponding to the orthogonal matrices. The memory requirements for a finite element solver are reduced by the domain decomposition, which is useful in large-scale computations. Reducing rates of memory requirements to store matrices are reported with examples of domains. Both applicability and limitations of the algorithm are discussed with an application to the Earth's mantle convection problem.

Original language | English |
---|---|

Pages (from-to) | 1807-1831 |

Number of pages | 25 |

Journal | International Journal for Numerical Methods in Engineering |

Volume | 62 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2005 Apr 7 |

Externally published | Yes |

## Keywords

- Congruent subdomains
- Domain decomposition
- Finite element matrices
- Memory reduction
- Orthogonal transformation

## ASJC Scopus subject areas

- Engineering (miscellaneous)
- Applied Mathematics
- Computational Mechanics