Level set method with topologi al derivatives

Level set method with topologi al derivatives in shape optimization Piotr FULMANSKI†, Antoine LAURAIN‡, Jean-François SCHEID‡, Jan SOKO?OWSKI‡ † Universiti of ?ód?, Fa ulty of Mathemati s Bana ha 22, 90-232 ?ód?, Poland, fulmanpimul.math.uni.lodz.pl ‡ Institut Elie Cartan UMR 7502, Nan y-Université, CNRS, INRIA, B.P. 239, 54506 Vandoeuvre-lès-Nan y Cedex, Fran e, antoine.laurainie n.u-nan y.fr, jean-fran ois.s heidie n-u.nan y.fr, sokolows@ie n.u-nan y.fr Abstra t. A lass of shape optimization problems is solved numeri ally by the level set method ombined with the topologi al derivatives for topology optimization. A - tually, the topology variations are introdu ed on the basis of asymptoti analysis, by an evaluation of extremal points (lo al maxima for the spe i problem) of the so- alled topologi al derivatives introdu ed by Sokolowski and Zo howski [24? for ellipti boundary value problems. Topologi al derivatives are given for energy fun tionals of linear boundary value problems. We present results, in luding numeri al examples, whi h onrm that the appli ation of topologi al derivatives in the framework of the level set method really improves the e ien y of the method.

• topologi al


• fun tional


• solutions ? ?


• small parameter whi


• domain


• shape optimization


• fun tion


• ?n ?n


• sensitivity analysis