Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization

In this paper, we present the details of a simple lightweight implementation of the so-called sparse forward mode automatic differentiation (AD) in the C++programming language. Our implementation and the well-known ADOL-C tool (which utilizes taping and compression techniques) are used to compute Jacobian matrices of two nonlinear systems of equations from the MINPACK-2 test problem collection. Timings of the computations are presented and discussed. Moreover, we perform the shape sensitivity analysis of a time-harmonic Maxwell equation solver using our implementation and the tapeless mode of ADOL-C, which implements the dense forward mode AD. It is shown that the use of the sparse forward …

Laskennallinen tiede - tieteen kolmas menetelmä : tilannekatsaus 2011

Shape optimization of systems governed by Bernoulli free boundary problems

On a topology optimization problem governed by two-dimensional Helmholtz equation

The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given. peerReviewed