  This paper is concerned with topology optimization based on a level set
method using (doubly) nonlinear diffusion equations. Topology optimization
using the level set method is called level set-based topology optimization,
which is possible to determine optimal configurations that minimize objective
functionals by updating level set functions. In this paper, as an update
equation for level set functions, (doubly) nonlinear diffusion equations with
reaction terms are derived, and then the singularity and degeneracy of the
diffusion coefficient are applied to obtain fast convergence of configurations
and damping oscillation on boundary structures. In particular, the reaction
terms in the proposed method do not depend on the topological derivatives, and
therefore, sensitivity analysis to determine a descent direction for objective
functionals is relaxed. Furthermore, a numerical algorithm for the proposed
method is constructed and applied to typical minimization problems to show
numerical validity. This paper is a justification and generalization of the
method using reaction-diffusion equations developed by one of the authors in
Yamada et al. (2010).
