Optimal model switching for gas flow in pipe networks

Rüffler, Fabian; Mehrmann, Volker; Hante, Falk M.

doi:10.3934/nhm.2018029

Cited by 9 publications

(7 citation statements)

References 48 publications

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“…Conservation laws in the form of PDEs on hypergraphs have been used in the simulation and optimization of gas networks [37] and other networks of pipelines. They have been extended to networks of traffic (streets and data), (tele-)communication, and blood flow.…”

Section: Introductionmentioning

confidence: 99%

Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations

2022

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We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces—generalized by the term hypergraphs. To this end, we consider PDEs on hypergraphs as singular limits of PDEs in networks of thin domains (such as fault planes, pipes, etc.), and we observe that (mixed) hybrid formulations offer useful tools to formulate such PDEs. Thus, our numerical framework is based on hybrid finite element methods (in particular, the class of hybrid discontinuous Galerkin methods).

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Section: Introductionmentioning

confidence: 99%

Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations

2022

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“…We note that continuous reformulations of such problems with switching time and mode insertion optimization or combinatorial constraints can also be seen as an alternating direction method [8,29,32,33], but that the approach proposed here is different.…”

Section: Introductionmentioning

confidence: 99%

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

et al. 2021

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We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands.

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“…Conservation laws in the form of PDEs on hypergraphs have been used in the simulation and optimization of gas networks [RMH18] and other networks of pipelines. They have been extended to networks of traffic (streets and data), (tele-)communication, and blood flow.…”

Section: Introductionmentioning

confidence: 99%

Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations

Rupp,

Gahn,

Kanschat

2021

Preprint

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We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces-generalized by the term hypergraphs. To this end, we consider PDEs on hypergraphs as singular limits of PDEs in networks of thin domains (such as fault planes, pipes, etc.), and we observe that (mixed) hybrid formulations offer useful tools to formulate such PDEs. Thus, our numerical framework is based on hybrid finite element methods (in particular, the class of hybrid discontinuous Galerkin methods).

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Optimal model switching for gas flow in pipe networks

Cited by 9 publications

References 48 publications

Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations

Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations

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