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Języki publikacji
Abstrakty
We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question: which graph is best suited to sustain the loads and the constraints. More precisely, given a cost function we may look at a multiple node of the graph with edge degree q and ask as to whether that node should be resolved into a number of nodes of edge degree less than q, in order to decrease the cost. With this question in mind, we are looking into the sensitivity analysis of a graph carrying a second order elliptic equation with respect to changing its topology by releasing nodes with high edge degree or including an edge. With the machinery at hand developed here, we are in the position to define the topological gradient of an elliptic problem on a graph.
Czasopismo
Rocznik
Tom
Strony
971--997
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
autor
- Lehrstuhl fur Angewandte Mathematik II, Friedrich-Alexander-University Erlangen-Nuremberg Martensstr. 3, D-91058 Erlangen, Germany, leugering@am.uni-erlangen.de
Bibliografia
- ALLAIRE, G., GOURNAY, F., JOUVE, F. and TOADER, A.M. (2004) Structural optimization using topological and shape sensitivities via a level set method. Ecole Poly technique, R.I. 555.
- AMSTUTZ, S. (2003) Aspects théoriques et numériques en optimisation de forme topologique. PhD Thesis, Toulouse.
- BERNOT, M., CASELLES, V. and MOREL, J.M. (2007/2008) Branched Transportation Networks. Springer-Verlag.
- BUTTAZZO, G. (2005) Optimization problems in the theory of mass transportation. Boll. Unione Mat. Hal. 9/1, 401-427.
- DE WOLF, D. and SMEERS, Y. (1996) Optimal dimensioning of pipe networks with application to gas transmission networks. Oper. Res. 44(4), 596-608.
- DURAND, M. (2006) Architecture of optimal transport networks, Physical Review E 73, 016116.
- HINTERMÜLLER, M.A. (2004) A combined shape-Newton topology optimization technique in real-time image segmentation. In: Real-Time PDE-Constrained Optimization, Comput. Sci. Eng., SIAM.org, 253-274.
- KOČVARA, M. and ZOWE, J. (1996) How mathematics can help in design of mechanical structures. In: Griffiths, D.F. et al., eds., Numerical Analysis 1995. Proceedings of the 16th Dundee conference on numerical analysis, University of Dundee, UK, June 27-30, 1995. Longman: Harlow. Pitman Res. Notes Math. Ser. 344, 76-93.
- LAGNESE, J.E., LEUGERING, G. and SCHMIDT, E.J.P.G. (1994) Modeling, Analysis and Control of Dynamic Elastic Multi-link Structures. Birkhäuser, Boston, Systems and Control: Foundations and Applications.
- LAGNESE, J.E. and LEUGERING, G. (2004) Domain Decomposition Methods in Optimal Control of Partial Differential Equations. ISNM. International Series of Numerical Mathematics 148. Birkhäuser, Basel.
- MASMOUDI, M., POMMIER, J. and SAMET, B. (2005) The topological asymptotic expansion for the Maxwell equation and some applications. Inverse Problems 21 (2), 547-564.
- MRÓZ, Z. and BOJCZUK, D. (2003) Finite topology variations in optimal design of structures. Struc. Multidisc. Optim. 25, 1-21.
- NOVOTNY, A., FEIJ’OO, R., TAROCO, E. and PADRA, C. (2007) Topological sensitivity analysis for three-dimensional linear elastic problem. Comp. Meth. Appl. Eng. 196, 41, 4354-4364.
- ROZVANY, G.I.N. (1998) Topology optimization of multi-purpose structures. Math. Methods Oper. Res. 47 (2), 265-287.
- SOKOLOWSKI, J. and ZOCHOWSKI, A. (1999) Topological derivatives for elliptic problems. Inverse Problems 15, 123-134.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0034-0009