### 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 |
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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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Applied Mathematics
- Computational Mechanics

### Cite this

*International Journal for Numerical Methods in Engineering*,

*62*(13), 1807-1831. https://doi.org/10.1002/nme.1248

**Finite element matrices in congruent subdomains and their effective use for large-scale computations.** / Suzuki, Atsushi; Tabata, Masahisa.

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Engineering*, vol. 62, no. 13, pp. 1807-1831. https://doi.org/10.1002/nme.1248

}

TY - JOUR

T1 - Finite element matrices in congruent subdomains and their effective use for large-scale computations

AU - Suzuki, Atsushi

AU - Tabata, Masahisa

PY - 2005/4/7

Y1 - 2005/4/7

N2 - 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.

AB - 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.

KW - Congruent subdomains

KW - Domain decomposition

KW - Finite element matrices

KW - Memory reduction

KW - Orthogonal transformation

UR - http://www.scopus.com/inward/record.url?scp=15844362640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15844362640&partnerID=8YFLogxK

U2 - 10.1002/nme.1248

DO - 10.1002/nme.1248

M3 - Article

AN - SCOPUS:15844362640

VL - 62

SP - 1807

EP - 1831

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 13

ER -