Fictitious domain models for topology optimization of time-harmonic problems

A new fictitious domain model for topology optimization of time-harmonic problems based on a wave to diffusion equation transition is proposed. By employing negative values of appropriate material coefficients, a tuneable exponential decay of the field amplitude in the fictitious domains can be obtained, whereas for the conventional model a finite field amplitude is always present. To demonstrate the applicability of the model, we consider two topology optimization problems; a volume minimization problem for acoustic topology optimization for which intuitive meaningful designs are obtained with the proposed model unlike the case with a conventional contrast model. For a structural topology optimization example, the proposed model is shown to remove problematic issues with structural artifacts found for a certain dynamic compliance minimization problem.