ePlace (Electrostatic Placement)

The idea

ePlace perfected the density half of nonlinear placement with a physics analogy carried to completion. Treat every cell (and every filler element occupying whitespace) as positive charge proportional to its area. The density constraint 'spread evenly' becomes the electrostatic statement 'this charge system should reach zero potential energy'. Solve Poisson's equation for the potential and field of the current charge distribution, efficiently and exactly on a grid by fast Fourier transform; each cell then feels a force, the field times its charge, pushing it from crowded regions toward empty ones, including away from macros (also modeled as charge). The total objective, smoothed wirelength plus a weighted electrostatic energy, is minimized by Nesterov's accelerated gradient method with a clever Lipschitz-constant-based step size, the penalty weight rising steadily so wirelength dominates early and legality dominates late.

Why it won

Every ingredient is principled: the energy is a globally smooth, well-behaved density measure (no bell-kernel locality artifacts), the FFT (Fast Fourier Transform) makes each gradient evaluation near-linear, and Nesterov acceleration converges in hundreds rather than thousands of iterations. Benchmarks of its era showed clear wirelength wins over the log-sum-exp-plus-bell-kernel generation, and the formulation remained effective across mixed-size, large-macro, and routability-driven variants.

Where you meet it today

Directly: RePlAce (next page) is its tuned open-source descendant inside OpenROAD, and DREAMPlace is this exact mathematics recast onto GPUs (Graphics Processing Units). When someone says 'modern analytical placement', they mean this.