Optimal Chip Layout on a Printed Circuit Board Using Design Sensitivity Analysis of Subdomain Configuration

A chip layout problem is formulated as a new class of shape optimal design called a subdomain optimization, where the chips correspond to subdomains whose configuration and location are to be decided. Shape design sensitivity analysis for a perturbed subdomain is made based on the concept of material derivative and adjoint system. Introducing a suitable category of design velocity fields, the change of the configuration is adequately describable. Sensitivities and optimal positions of chips on a printed circuit board are obtained and their accuracy discussed.