Inhalt des Dokuments
Preprint 06-2003
2nd Order Shape Optimization using Wavelet BEM
Author(s) :
Karsten Eppler
,
Helmut Harbrecht
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 06-2003
MSC 2000
- 49Q10 Optimization of shapes other than minimal surfaces
-
65N38 Boundary element methods
Abstract :
This present paper is concerned with second order methods for a
class of shape optimization problems. We employ a complete boundary
integral representation of the shape Hessian which involves
first and second order derivatives of the state and the adjoint
state function, as well as normal derivatives of its local
shape derivatives. We introduce a boundary integral formulation
to compute these quantities. The derived boundary integral
equations are solved efficiently by a wavelet Galerkin scheme.
A numerical example validates that, in spite of the higher effort
of the Newton method compared to first order algorithms,
we obtain more accurate solutions in less computational time.
Keywords :
shape optimization, boundary element method, multiscale methods, augmented Lagrangian approach, Newton method