Details
| Original language | English |
|---|---|
| Pages (from-to) | 345-361 |
| Number of pages | 17 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 203 |
| Issue number | 2 SPEC. ISS. |
| Publication status | Published - 15 Jun 2007 |
| Externally published | Yes |
Abstract
Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions-or as relaxation in a branch-and-bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse projections locally in time, based on the KKT systems' structural properties in space as induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a previously developed control space method and with the multifrontal solver MA27 are provided.
Keywords
- Gas network, Operative planning, PDE constrained optimization, Sparse direct KKT solver, Spatial projection algorithm
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 203, No. 2 SPEC. ISS., 15.06.2007, p. 345-361.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On PDE solution in transient optimization of gas networks
AU - Steinbach, Marc C.
N1 - Funding information: This work has been supported by the Federal Ministry of Education and Science (BMBF) under Grant 03STM5B4.
PY - 2007/6/15
Y1 - 2007/6/15
N2 - Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions-or as relaxation in a branch-and-bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse projections locally in time, based on the KKT systems' structural properties in space as induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a previously developed control space method and with the multifrontal solver MA27 are provided.
AB - Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions-or as relaxation in a branch-and-bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse projections locally in time, based on the KKT systems' structural properties in space as induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a previously developed control space method and with the multifrontal solver MA27 are provided.
KW - Gas network
KW - Operative planning
KW - PDE constrained optimization
KW - Sparse direct KKT solver
KW - Spatial projection algorithm
UR - http://www.scopus.com/inward/record.url?scp=33947691244&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2006.04.018
DO - 10.1016/j.cam.2006.04.018
M3 - Article
AN - SCOPUS:33947691244
VL - 203
SP - 345
EP - 361
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2 SPEC. ISS.
ER -