Abstract
In this paper, an O(n) algorithm for identification of isolated sub-domains is proposed. A brittle solid specimen is gradually broken into fragments when a dynamic propagation of cracks occurs in it. A sub-domain of the specimen is isolated from other part of it if the sub-domain is completely wrapped up in a set of fracture surfaces. Identification of domain isolation allows us an efficient numerical analysis such as hybridization of DEM (Distinct Element Method) and FEM for dynamic fracture problems. In the case of 2D problems, when a set of line segments forms a closed loop, the interior of the closed loop is isolated from other sub-domains. However, in the 3D case, closed loops can not identify an isolated sub-domain. If a computation and numerical errors are not considered, eigenvalue analysis is a way to identify domain isolation. However, it costs O(n2) computation and causes numerical errors by real number manipulation. So, an algorithm focused on the connectivity of nodal points is proposed. This algorithm has an O(n) computation and operates with only integer processing which does not cause numerical errors. Also it is independent of coordinates of nodal points and the dimension of the analysis domain. Some tests were carried out and it was confirmed that the computation is actually O(n).
| Original language | English |
|---|---|
| Title of host publication | ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers |
| Pages | 3567-3574 |
| Number of pages | 8 |
| Publication status | Published - 2012 |
| Event | 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria Duration: 2012 Sep 10 → 2012 Sep 14 |
Other
| Other | 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 |
|---|---|
| Country | Austria |
| City | Vienna |
| Period | 12/9/10 → 12/9/14 |
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Keywords
- Computational geometry
- Fracture analysis
- Graph theory
- Topological structure
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Applied Mathematics
Cite this
O(n) algorithm for identification of domain isolation by fracture surfaces. / Sumitomo, Hiroaki; Oguni, Kenji.
ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers. 2012. p. 3567-3574.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - O(n) algorithm for identification of domain isolation by fracture surfaces
AU - Sumitomo, Hiroaki
AU - Oguni, Kenji
PY - 2012
Y1 - 2012
N2 - In this paper, an O(n) algorithm for identification of isolated sub-domains is proposed. A brittle solid specimen is gradually broken into fragments when a dynamic propagation of cracks occurs in it. A sub-domain of the specimen is isolated from other part of it if the sub-domain is completely wrapped up in a set of fracture surfaces. Identification of domain isolation allows us an efficient numerical analysis such as hybridization of DEM (Distinct Element Method) and FEM for dynamic fracture problems. In the case of 2D problems, when a set of line segments forms a closed loop, the interior of the closed loop is isolated from other sub-domains. However, in the 3D case, closed loops can not identify an isolated sub-domain. If a computation and numerical errors are not considered, eigenvalue analysis is a way to identify domain isolation. However, it costs O(n2) computation and causes numerical errors by real number manipulation. So, an algorithm focused on the connectivity of nodal points is proposed. This algorithm has an O(n) computation and operates with only integer processing which does not cause numerical errors. Also it is independent of coordinates of nodal points and the dimension of the analysis domain. Some tests were carried out and it was confirmed that the computation is actually O(n).
AB - In this paper, an O(n) algorithm for identification of isolated sub-domains is proposed. A brittle solid specimen is gradually broken into fragments when a dynamic propagation of cracks occurs in it. A sub-domain of the specimen is isolated from other part of it if the sub-domain is completely wrapped up in a set of fracture surfaces. Identification of domain isolation allows us an efficient numerical analysis such as hybridization of DEM (Distinct Element Method) and FEM for dynamic fracture problems. In the case of 2D problems, when a set of line segments forms a closed loop, the interior of the closed loop is isolated from other sub-domains. However, in the 3D case, closed loops can not identify an isolated sub-domain. If a computation and numerical errors are not considered, eigenvalue analysis is a way to identify domain isolation. However, it costs O(n2) computation and causes numerical errors by real number manipulation. So, an algorithm focused on the connectivity of nodal points is proposed. This algorithm has an O(n) computation and operates with only integer processing which does not cause numerical errors. Also it is independent of coordinates of nodal points and the dimension of the analysis domain. Some tests were carried out and it was confirmed that the computation is actually O(n).
KW - Computational geometry
KW - Fracture analysis
KW - Graph theory
KW - Topological structure
UR - http://www.scopus.com/inward/record.url?scp=84871636424&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871636424&partnerID=8YFLogxK
M3 - Conference contribution
SN - 9783950353709
SP - 3567
EP - 3574
BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
ER -