Finding the conductors in circular networks from boundary measurements

Curtis, Edward B.; Mooers, Edith; Morrow, James

doi:10.1051/m2an/1994280707811

Cited by 43 publications

(93 citation statements)

References 3 publications

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“…This algorithm represents an extension of the one developed in [13,14], since we consider not only the Laplacian but Schrödinger operators. Although the guidelines are very similar to the ones in the above reference, we describe the algorithm entirely to show the relevance of the above results on overdetermined partial boundary value problems associated with positive semi-definite Schrödinger operators.…”

Section: Recovering the Conductances On Spider Networkmentioning

confidence: 99%

“…Also, it is important to remark that this recovery algorithm is equivalent to recovering q and the data used is different from the one in [13], since in this reference the Dirichlet-to-Robin matrix is assumed to be in Φ 0,1 . Notice, that the matrices in the last set are singular and weakly diagonally dominant.…”

Section: Recovering the Conductances On Spider Networkmentioning

confidence: 99%

“…For instance, Sylvester and Uhlmann treated in [9,18] the uniqueness of solution; Curtis, Ingerman and Morrow have worked on critical circular planar networks conductivity reconstruction [12,13,14,16]; Borcea, Druskin, Guevara and Mamonov have gone into EIT problems in depth and their last works on the subject treat numerical conductivity reconstruction [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, this type of problems were implicitly considered in some previous works, but only for specific networks and boundary data, see [13,14]. We analyze the uniqueness and existence of solution of overdetermined partial boundary value problems through the non-singularity of the partial Dirichlet-to-Neumann maps.…”

Section: Introductionmentioning

confidence: 99%

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Overdetermined partial boundary value problems on finite networks

Araúz

Carmona

Encinas

2015

Journal of Mathematical Analysis and Applications

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In this work we define a class of non self-adjoint boundary value problems on finite networks associated with Schrödinger operators. The novelty lies on the fact that on a part of the boundary no data is prescribed, whereas in another part of the boundary both the values of the function as of its normal derivative are given. We show that overdetermined partial boundary value problems are the key for solving inverse boundary value problems on finite networks, since they provide the theoretical foundations of the recovery algorithm. We analyze the uniqueness and existence of solution of overdetermined partial boundary value problems through the non-singularity of the partial Dirichlet-to-Neumann maps. These maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed. Afterwards, we execute a full conductance recovery for spider networks.

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Section: Recovering the Conductances On Spider Networkmentioning

confidence: 99%

Section: Recovering the Conductances On Spider Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Overdetermined partial boundary value problems on finite networks

Araúz

Carmona

Encinas

2015

Journal of Mathematical Analysis and Applications

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“…(Related literature). In electrical impedance tomography L red is also referred to as the Dirichlet-toNeumann map (Curtis et al, 1994(Curtis et al, , 1998. The Schur complement of a matrix and its corresponding graph is also referred to as Schur contraction (Ayazifar, 2002), it is known in the context of (block) Gaussian elimination (Saad, 2003), and serves as an application example in linear algebra (Fan, 2002;Stone and Griffing, 2009).…”

Section: Analysis Of the Kron Reduction Processmentioning

confidence: 99%

Synchronization of Power Networks: Network Reduction and Effective Resistance

Dörfler

Bullo

2010

IFAC Proceedings Volumes

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Abstract:In transient stability studies in power networks two types of mathematical models are commonly used -the differential-algebraic structure-preserving model and the reduced dynamic model of interconnected swing equations. This paper analyzes the reduction process relating the two power network models. The reduced admittance matrix is obtained by a Schur complement of the topological network admittance matrix with respect to its bus nodes. We provide a detailed spectral, algebraic, and graph-theoretic analysis of this network reduction process, termed Kron reduction, with particular focus on the effective resistance. As an application of this analysis, we are able to state concise conditions relating synchronization in the considered structurepreserving power network model directly to the state, parameters, and topology of the underlying network. In particular, we provide a spectral condition based on the algebraic connectivity of the network and a second condition based on the effective resistance among generators.

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Finding the conductors in circular networks from boundary measurements

Cited by 43 publications

References 3 publications

Overdetermined partial boundary value problems on finite networks

Overdetermined partial boundary value problems on finite networks

Synchronization of Power Networks: Network Reduction and Effective Resistance

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