Editing Topology optimization (section)

=== Solving with discrete/binary variables ===
Solving topology optimization problems in a discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the problem variables. In this case material density of one indicates the presence of material, while zero indicates an absence of material. Owing to the attainable topological complexity of the design being dependent on the number of elements, a large number is preferred. Large numbers of finite elements increases the attainable topological complexity, but come at a cost. Firstly, solving the FEM system becomes more expensive. Secondly, algorithms that can handle a large number (several thousands of elements is not uncommon) of discrete variables with multiple constraints are unavailable. Moreover, they are impractically sensitive to parameter variations.<ref>{{Cite journal |doi = 10.1007/s00158-013-0978-6|title = Topology optimization approaches |journal = Structural and Multidisciplinary Optimization|volume = 48|issue = 6|pages = 1031–1055|year = 2013 |author2-link=Kurt Maute|last1 = Sigmund|first1 = Ole|last2 = Maute|first2 = Kurt|s2cid = 124426387 }}</ref> In literature problems with up to 30000 variables have been reported.<ref>{{Cite journal |doi = 10.1007/BF01197709|title = Topology optimization using a dual method with discrete variables|journal = Structural Optimization|volume = 17|pages = 14–24|year = 1999|last1 = Beckers|first1 = M. |s2cid = 122845784|url=http://empslocal.ex.ac.uk/people/staff/reverson/uploads/MoodSwings/beckers.pdf}}</ref>