The Phase-Field Method in Optimal Design

We describe the phase-field method, a new approach to optimal design originally introduced in Bourdin and Chambolle (2000, 2003). It is based on the penalization of the variation of the properties of the designs, and its variational approximation (in the sense of Г-convergence. It uses a smooth function, the phase-field, to represent all materials involved.We describe our approach, and detail its application to two problems.