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 t...

Full description

Saved in:
Bibliographic Details
Published in:Computational optimization and applications 2015-11, Vol.62 (2), p.517-544
Main Authors: Haslinger, Jaroslav, Mäkinen, Raino A. E.
Format: Article
Language:English
Subjects:
Approximation
Convex and Discrete Geometry
Discretization
Helmholtz equations
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Operations Research
Operations Research/Decision Theory
Optimization
Parametrization
Permeability
Propagation
Statistics
Studies
Topology
Topology optimization
Two dimensional
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-015-9746-4