On quasi-arithmetic mean based filters and their fast evaluation for large-scale topology optimization
2015 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 52, no 5, 879-888 p.Article in journal (Refereed) PublishedText
In material distribution topology optimization, restriction methods are routinely applied to obtain well-posed optimization problems and to achieve mesh-independence of the resulting designs. One of the most popular restriction methods is to use a filtering procedure. In this paper, we present a framework where the filtering process is viewed as a quasi-arithmetic mean (or generalized f-mean) over a neighborhood with the possible addition of an extra "projection step". This framework includes the vast majority of available filters for topology optimization. The covered filtering procedures comprise three steps: (i) element-wise application of a function, (ii) computation of local averages, and (iii) element-wise application of another function. We present fast algorithms that apply this type of filters over polytope-shaped neighborhoods on regular meshes in two and three spatial dimensions. These algorithms have a computational cost that grows linearly with the number of elements and can be bounded irrespective of the filter radius.
Place, publisher, year, edition, pages
Springer, 2015. Vol. 52, no 5, 879-888 p.
Topology optimization, Regularization, Filters, Fast algorithm, Large-scale problems
IdentifiersURN: urn:nbn:se:umu:diva-114034DOI: 10.1007/s00158-015-1273-5ISI: 000366590800003OAI: oai:DiVA.org:umu-114034DiVA: diva2:892676