Accelerated floating random walk algorithm for the electrostatic computation with 3-D rectilinear-shaped conductors

With the advancement of fabrication technology, the electrostatic coupling has increasing impact on the performance of very large-scale integrated (VLSI) circuits and micro-electromechanical systems (MEMS). For the structures in VLSI circuits which are mostly rectilinear geometries, the floating random walk (FRW) method using cubic transition domains has been successfully applied to calculate the electric capacitances among interconnect wires. In this work, the techniques of importance sampling and stratified sampling are presented to accelerate the FRW algorithm by improving the convergence rate of the Monte Carlo procedure. An efficient approach is then presented to parallelize the FRW algorithm with the graphic processing units (GPUs). GPU-friendly algorithmic flow and data structure are designed to reduce the divergence among random walks and the time of accessing the device memory. The presented techniques are also applicable to the calculation of electric field intensity, which is also an important problem for nowadays nanometer-technology circuits. Numerical results are presented with several simple structures and larger ones from real VLSI circuits or MEMS. The results validate the accuracy of the presented techniques and demonstrate up to 100× speedup due to the variance reduction and GPU-based parallel computing.