On a topology optimization problem governed by two-dimensional Helmholtz equation
Haslinger, J., & Mäkinen, R. (2015). On a topology optimization problem governed by two-dimensional Helmholtz equation. Computational Optimization and Applications, 62 (2), 517-544. doi:10.1007/s10589-015-9746-4 Retrieved from http://www.researchgate.net/publication/274713225_On_topology_optimiza...
Published inComputational Optimization and Applications
© Springer Science+Business Media New York 2015. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
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.