EVENTO
Numerical methods in shape optimization with the topological derivatives
Tipo de evento: Seminário LNCC
In the talk the topological derivatives for semilinear elliptic equation are determined by the compound asymptotic expansions. The expansion of solutions with respect to the small parameter which describes the size of the hole or cavity created in the domain of integration is established and justified. There are two problems considered in details. The first problem in three spatial dimensions with the Dirichlet boundary conditions on the hole. The complete proof of asymptotic expansion of the solution in the weighted Holder spaces is given. The order of the remainder is established by the Banach fixed point theorem in the weighted Holder spaces. The expansion of the solution is plug into the shape functional, and the first order term with respect to small parameter, is obtained. The second boundary value problem in two spatial dimensions enjoys the Neumann boundary conditions on the hole. The numerical results for the topological derivatives are given in two spatial dimensions by the finite element method combined with the Newton method for the nonlinear problems. The error estimates for the finite element method are also established.
Data Início: 22/11/2010 Hora: 14:00 Data Fim: Hora: 15:30
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Katarzyna Szulc - LNCC / MCT - -
