Topological derivatives for networks of elastic strings

被引：3

作者：

Leugering, G. ^{[1
]}

Sokolowski, J. ^{[2
]}

机构：

[1] Univ Erlangen Nurnberg, Lehrstuhl Angew Math 2, Dept Math, D-91058 Erlangen, Germany

[2] Univ Nancy 1, Math Lab, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2011年 / 91卷 / 12期

关键词：

Differential equations on metric graphs; Steklov-Poincare operators on graphs; self-adjoint nodal conditions; topological sensitivities; INVERSE PROBLEM; QUANTUM; OPTIMIZATION; GRAPHS;

D O I：

10.1002/zamm.201000067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider linear second order differential equations on metric graphs under given boundary and nodal conditions. We are interested in the problem of changing the topology of the underlying graph in that we replace a multiple node by a subgraph or concentrate a subgraph to a single node. We wish to do so in an optimal fashion. More precisely, given a cost function we may look for its sensitivity with respect to these operations in order to find an optimal topology of the graph. Thus, in essence, we are looking for the topological gradient for linear second order problems on metric graphs. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：926 / 943

页数：18

共 28 条

[1] Avdonin S, 2008, INVERSE PROBL IMAG, V2, P1
[2] On an inverse problem for tree-like networks of elastic strings
Avdonin, Sergei
Leugering, Guenter
Mikhaylov, Victor
[J]. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2010, 90 (02): : 136 - 150
[3] Belishev M., 2006, J INVERSE ILL-POSE P, V14, P29, DOI 10.1515/156939406776237474
[4] Boundary spectral inverse problem on a class of graphs (trees) by the BC method
Belishev, MI
[J]. INVERSE PROBLEMS, 2004, 20 (03) : 647 - 672
[5] Bernot M., 2007, BRANCHED TRANSPORTAT
[6] BUTTAZZO G, 2005, SOME OPTIMIZATION PR
[7] Optimal dimensioning of pipe networks with application to gas transmission networks
DeWolf, D
Smeers, Y
[J]. OPERATIONS RESEARCH, 1996, 44 (04) : 596 - 608
[8] Architecture of optimal transport networks
Durand, M
[J]. PHYSICAL REVIEW E, 2006, 73 (01):
[9] EXNER P, 2007, ARXIV07060481
[10] Topology optimization of flow networks
Klarbring, A
Petersson, J
Torstenfelt, B
Karlsson, M
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (35-36) : 3909 - 3932

← 1 2 3 →