Step-size adaptive parametric level set method for structural topology optimization

In the structural topology optimization (STO), the step-size of the parametric level set method (PLSM) using the explicit scheme must satisfy the Courant-Friedrichs-Lewy (CFL) condition to ensure numerical stability. However, much larger step-sizes are arbitrarily used to speed up the convergence. For this reason, a narrowband in the velocity field is defined, and the step-size adaptive parametric level set method (SAPLSM) is proposed, which multiplies different step-sizes for the velocity of different nodes. The SAPLSM satisfies the CFL condition not only on the narrowband, but also on the entire design domain. Furthermore, a narrowband annealing (NA) scheme based on "annealing" is proposed to dynamically adjust the maximum step-size during the iterations. Numerical experimental results of several benchmark problems in two-dimensional minimum compliance show that: (1) The SAPLSM is more stable than PLSM under large step-sizes and complex problems. (2) The NA scheme not only accelerates the convergence of SAPLSM but also alleviates mesh dependence.