An algebraic multigrid solver for analytical placement without layout based clustering

An efficient matrix solver is critical to the analytical placement. As the size of the matrix becomes huge, the multilevel methods turn out to be more efficient and more scalable. Algebraic Multigrid (AMG) is a multilevel technique to speedup the iterative matrix solver in K. Stuben (1999). We apply the algebraic multigrid method to solve the linear equations that arise from the analytical placement. A layout based clustering scheme is put forward to generate coarsening levels for the multigrid method. The experimental results show that the algebraic multigrid solver is promising for analytical placement.