A discontinuous Galerkin level set method using distributed shape gradient and topological derivatives for multi-material structural topology optimization

A new level set method is developed for multi-material structural topology optimization. The method features in using the discontinuous Galerkin finite-element method for discretization of the level set transport equation and the distributed shape gradient. Moreover, the topological derivative is incorporated into the present algorithm as a possible way to escape from local minima through creating holes during optimization. Numerical examples are provided to verify effectiveness of the numerical algorithm.